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Modeling the advantages and disadvantages of the coral-algal symbiosis

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Title:
Modeling the advantages and disadvantages of the coral-algal symbiosis
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English
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Gaydos, Dana Joy
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University of South Florida
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Tampa, Fla
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Subjects / Keywords:
Nutrient cycling
Translocation
Mixotrophy
Carbon
nitrogen
Dissertations, Academic -- Marine Science -- or Masters -- USF
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Coral reefs thrive in nutrient-deficient environments yet function among the most productive ecosystems on Earth as a consequence of the symbiosis between coral hosts and their symbiotic zooxanthellae. The symbiotic unit (holobiont) can utilize both inorganic and organic sources of nutrients for the accumulation of carbon and nitrogen required for metabolism, growth, and reproduction.An iterative model was created to describe the flux of carbon and nitrogen between a host and its algae. The model design is based on a previously published conceptual model of algal symbioses; functions and values of input parameters are based on published studies of the coral species Stylophora pistillata. The model is designed to simulate responses of the coral, zooxanthellae and the holobiont to different environmental variables, either one at a time or changing simultaneously. Simulations presented are for default values based on previously published data for S. pistillata adapted to^ high-light (shallow-euphotic) and low-light (deep-euphotic) environments, and for single-variable manipulations of rates of a) host feeding, b) photosynthesis, and c) dissolved inorganic nitrogen (DIN) uptake.Simulations examining feeding rates between 0% and 6.5% of host biomass indicate that biomass of both high-light and low-light adapted holobionts increase exponentially with increased feeding, with benefit to the high-light holobiont ~8 times greater than to the low-light holobiont. Increasing rates of photosynthesis illustrated that a low-light holobiont is carbon limited, is primarily dependent upon host feeding, and can benefit from a small increase in photosynthesis rate. Simulations examining rates of DIN input indicate that the high-light holobiont functions optimally when inorganic nitrogen input is very low. Increase in DIN up to 0.5% resulted in benefit to the holobiont, but more resulted in unrealistically excessive growth by the zooxanthellae until a function to mai ntain a fixed range for the host-zooxanthellae biomass ration function was included in the model. Simulations for the low-light holobiont did not indicate any benefit from DIN input.The model was originally designed using a spreadsheet-based program which frequently became overloaded when testing multiple variables. Modification of the model in software better designed for modeling is recommended for future work.
Thesis:
Thesis (M.A.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
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System requirements: World Wide Web browser and PDF reader.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Dana Joy Gaydos.
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Title from PDF of title page.
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Document formatted into pages; contains 196 pages.

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oclc - 138508224
usfldc doi - E14-SFE0001466
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ABSTRACT: Coral reefs thrive in nutrient-deficient environments yet function among the most productive ecosystems on Earth as a consequence of the symbiosis between coral hosts and their symbiotic zooxanthellae. The symbiotic unit (holobiont) can utilize both inorganic and organic sources of nutrients for the accumulation of carbon and nitrogen required for metabolism, growth, and reproduction.An iterative model was created to describe the flux of carbon and nitrogen between a host and its algae. The model design is based on a previously published conceptual model of algal symbioses; functions and values of input parameters are based on published studies of the coral species Stylophora pistillata. The model is designed to simulate responses of the coral, zooxanthellae and the holobiont to different environmental variables, either one at a time or changing simultaneously. Simulations presented are for default values based on previously published data for S. pistillata adapted to^ high-light (shallow-euphotic) and low-light (deep-euphotic) environments, and for single-variable manipulations of rates of a) host feeding, b) photosynthesis, and c) dissolved inorganic nitrogen (DIN) uptake.Simulations examining feeding rates between 0% and 6.5% of host biomass indicate that biomass of both high-light and low-light adapted holobionts increase exponentially with increased feeding, with benefit to the high-light holobiont ~8 times greater than to the low-light holobiont. Increasing rates of photosynthesis illustrated that a low-light holobiont is carbon limited, is primarily dependent upon host feeding, and can benefit from a small increase in photosynthesis rate. Simulations examining rates of DIN input indicate that the high-light holobiont functions optimally when inorganic nitrogen input is very low. Increase in DIN up to 0.5% resulted in benefit to the holobiont, but more resulted in unrealistically excessive growth by the zooxanthellae until a function to mai ntain a fixed range for the host-zooxanthellae biomass ration function was included in the model. Simulations for the low-light holobiont did not indicate any benefit from DIN input.The model was originally designed using a spreadsheet-based program which frequently became overloaded when testing multiple variables. Modification of the model in software better designed for modeling is recommended for future work.
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PAGE 1

Modeling the Advantages and Disadvantages of the Coral-Algal Symbiosis by Dana Joy Gaydos A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science College of Marine Science University of South Florida Major Professor: Pamela Hallock-Muller, Ph.D. Kendra Daly, Ph.D. Gary Huxel, Ph.D. Date of Approval: April 6, 2006 Keywords: nutrient cycling, transl ocation, mixotrophy, carbon, nitrogen Copyright 2006, Dana J. Gaydos

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ii Table of Contents List of Tables iv List of Figures v Abstract ix Introduction 1 Previous Models of Algal Symbiosis 4 Hallock (1981) Growth Model 4 Hallock (2001) NutrientLimiting Model 6 Jones and Yellowlees (1997) Space-limiting Model 9 Falkowski et al. (1984) Energy Budget 10 Stoecker (1998) Mixot rophic Nutrition Model 10 Thesis Objectives 12 Methods 13 Assumptions 13 Input and Output Parameters 16 Model Equations 18 Programming the Model 25 Results and Preliminary Comparisons 29 Trial 1: Basic Model 30 Shallow-Adapted Coral 30 Deep-Adapted Coral 39 Comparison of Results 41 Trial 2: Varying Rates of He terotrophic Feeding by Host 43 Shallow-Adapted Coral 43 Deep-Adapted Coral 47 Comparison of Results 51 Trial 3: Varying Rates of Photosynthesis in Algae 52 Shallow-Adapted Coral 53 Deep-Adapted Coral 60 Comparison of Results 63 Trial 4: Varying Rates of Nitrogen Uptake by the Algae 65

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iii Shallow-Adapted Coral 67 Deep-Adapted Coral 71 Comparison of Results 74 Discussion 78 Host/Algal Biomass Ratios 78 Heterotrophic Feeding 85 Light 88 Nutrients 92 References 102 Appendices 118 Appendix A: Programming Macros 119 Appendix B: Final values of the 100-it eration period with th e increase in host feeding rate (BIH) for the shallow-adapted coral. 133 Appendix C: Final values of the 100-it eration period with th e increase in host feeding rate (BIH) for the deep-adapted coral. 141 Appendix D: Final values of the 100-iter ation period with the increase in algal photosynthesis rate (CPA) for the shallow-adapted coral. 149 Appendix E: Final values of the 100-itera tion period with the in crease in algal photosynthesis rate (CPA) for the deep-adapted coral. 161 Appendix F: Final values of the 100-itera tion period with the in crease in nitrogen uptake rate (NIA) for the shallow-adapted coral. 173 Appendix G. Final values of the 100-iter ation period with the increase in nitrogen uptake rate (NIA) for the deep-adapted coral. 185

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iv List of Tables Table 1 Input parameters as defi ned by Falkowski et al. (1984). 17 Table 2 Parameters, definitions, and equations. 19 Table 3 Parameters and trial numbers for a shallow adapted corals. 27 Table 4 Parameters and corresponding tria l numbers for a deep adapted corals. 31 Table 5 Minimum and maximum results of a shallowand deep-adapted coral with an increase in host feeding rate (BIH) over 100 iterations. 44 Table 6 Minimum and maximum results of a shallowand deep-adapted coral with an increase in algal photosynthesis rate (CPA) over 100 iterations. 54 Table 7 Minimum and maximum results of a shallowand deep-adapted coral with an increase in algal nitrogen uptake rate (NIA) over 100 iterations. 66

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v List of Figures Figure 1 Hallock’s (1981) conceptual mode l of a host coral-algal symbiosis. 5 Figure 2 Hallock’s (2001) updated model of algal symbiosis based on subsequent studies that it is essentia l for the host to maintain control of the supply of fixed nitrogen (DIN) re aching the symbionts. 7 Figure 3 Hallock’s (2001) updated model of algal symbiosis indicating possible consequences of abundant dissolved inorganic nitrogen (DIN) in the environment. 8 Figure 4 Falkowski et al. ( 1984) energy budget diagram. 14 Figure 5 Carbon and nitrogen flow diagram. 32 Figure 6a Host (BH) and algal (BA) biomass for shallowand deep-adapted corals over 100 iterations using default parame ters from Falkowski et al. (1984) with host feeding rate (BIH) set at 1% for the shallow-adapted coral and 2.35% for the deep-adapted coral; algal nitrogen uptake rate (NIA) held constant at 0% in both cases. 33 Figure 6b Host (%BH) and algal (%BA) average percent change per iteration for shallowand deep-adapted corals ov er 100 iterations using parameters defined in Fig. 6a. 34 Figure 6c Carbon translocated (CTA) to the host for shallowand deep-adapted corals over 100 iterations using parame ters defined in Fig. 6a. 36 Figure 6d Required (NTH1) and available (NTH2) nitrogen translocated to the algal for shallowand deep-adapted corals ov er 100 iterations using parameters defined in Fig. 6a. 37 Figure 6e Excess carbon production (CEH) and nitrogen excretion (NEA) for shallowand deep-adapted corals over 100 iterat ions using parameters defined in Fig. 6a. 38 Figure 6f Host mucus (CMH), skeletal (CSH), and lipid (CLH) production for shallowand deep-adapted corals over 100 iterat ions using parameters defined in Fig. 6a. 40

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vi Figure 7a Final host (BH) and algal (BA) biomass with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapt ed corals over 100 iterations using default parameters from Falkowsk i et al. (1984) with algal nitrogen uptake rate (NIA) held constant at 0%. 45 Figure 7b Average host (%BH) and algal (%BA) percent change with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapted corals over 100 iterations using parameters as defined in Fig. 7a. 46 Figure 7c Average ca rbon translocated (CTA) to the host with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapted corals over 100 iterations using parameters as defined in Fig. 7a. 48 Figure 7d Average required (NTH1) and available (NTH2) nitrogen translocated to the algae with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapted corals over 100 iterations using parameters as defined in Fig. 7a. 49 Figure 7e Average exce ss carbon production (CEH) and nitrogen excretion (NEA) with an increase in heterotrophic feeding (% BIH) for shallowand deepadapted corals over 100 iterations usi ng parameters as defined in Fig. 7a. 50 Figure 8a Final host (BH) and algal biomass (BA) with an increase in algal photosynthesis rate (% CPA) for shallowand deep -adapted corals over 100 iterations using default parameters from Falkowski et al. (1984) with host feeding rate (BIH) set at 1% for the shallow-adapted coral and 2.35% for the deep-adapted coral; algal nitrogen uptake rate (NIA) held constant at 0% in both cases. 55 Figure 8b Average host (%BH) and algal (%BA) percent change with an increase in algal photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 iterations using paramete rs as defined in Fig. 8a. 57 Figure 8c Average carbon translocated (CTA) with an increase in algal photosynthesis rate (% CPA) for shallowand deep -adapted corals over 100 iterations using parameters as defined in Fig. 8a. 58 Figure 8d Average required (NTH1) and available (NTH2) nitrogen translocated with an increase in algal pho tosynthesis rate (% CPA) for shallowand deepadapted corals over 100 iterations using parameters as defined in Fig. 8a. 59

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vii Figure 8e Average exce ss carbon production (CEH) and nitrogen excretion (NEA) with an increase in alga l photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 iterations using parameters as defined in Fig. 8a. 61 Figure 9a Final host (BH) and algal (BA) biomass with an increase in algal nitrogen uptake rate (% NIA) for shallowand deep-adapted corals over 100 iterations using default parameters from Falkowski et al. (1984) with host feeding rate (BIH) set at 1% for the shallow-adapted coral and 2.35% for the deep-adapted coral. 68 Figure 9b Average host (%BH) and algal (%BA) percent change with an increase in algal nitrogen uptake rate (NIA) for shallowand deep-adapted corals over 100 iterations using parameters from Fal kowski et al. (1984) as defined in Fig. 9a. 69 Figure 9c Average in carbon translocated (CTA) with an increase in algal nitrogen uptake rate (NIA) for shallowand deep-adapt ed corals over 100 iterations using parameters from Falkowski et al. (1984) as defined in Fig. 9a. 70 Figure 9d Average required (NTH1) and available (NTH2) nitrogen translocated with an increase in algal nitrogen uptake rate (NIA) for shallowand deepadapted corals over 100 iterations usi ng parameters from Falkowski et al. (1984) as defined in Fig. 9a. 72 Figure 9e Average exce ss carbon production (CEH) and nitrogen excretion (NEA) with an increase in algal nitrogen uptake rate (NIA) for shallowand deepadapted corals over 100 iterations usi ng parameters from Falkowski et al. (1984) as defined in Fig. 9a. 73 Figure 10 Host (BH) and algal (BA) biomass for shallowand deep-adapted corals over 100 iterations without the assumption of ma intaining functional biomass ratios. 80 Figure 11 Host (BH) and algal (BA) biomass for shallowand deep-adapted corals over 100 iterations without the assumption of ma intaining functional biomass ratios. 81 Figure 12 Minimum and maximum biomass ratios examining the increase in host feeding rates (BIH) of the shallowand deep-adapted coral. 82 Figure 13 Minimum and maximum biomass ratios examining the increase in algal nitrogen uptake rates (NIA) of the shallowand deep-adapted coral. 83 Figure 14 Minimum and maximum biomass ratios examining the increase in algal photosynthesis rates (CPA) of the shallowand deep-adapted coral. 84

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viii Figure 15. Final host and algal bi omass with host feeding rate (BIH) set at 2.4% and 2.5% to show change from negative to positive growth. 97 Figure 16. Final host and algal biom ass with the photosynthesis rate (CPA) set at 2.4% and 2.5% to show change from negative to positive growth. 98 Figure 17. Trends associated with increasing host feeding (BIH) and algal photosynthesis (CPA) rates simultaneously in a shallow-adapted coral. 99 Figure 18. Trends associated with increasing algal photosynthesis (CPA) and nitrogen uptake (NIA) rates simultaneously in a shallow-adapted coral. 100

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ix Modeling the Advantages and Disadvantages of the Coral-Algal Symbiosis Dana Joy Gaydos Abstract Coral reefs thrive in nutrient-deficient environments yet function among the most productive ecosystems on Earth as a conseque nce of the symbiosis between coral hosts and their symbiotic zooxanthellae. The sy mbiotic unit (holobion t) can utilize both inorganic and organic sources of nutrients for the accumulation of carbon and nitrogen required for metabolism, growth, and reproduction. An iterative model was created to desc ribe the flux of carbon and nitrogen between a host and its algae. The model design is based on a previously published conceptual model of algal symbioses; function s and values of input parameters are based on published studies of the coral species Stylophora pistillata The model is designed to simulate responses of the coral, zooxa nthellae and the holobiont to different environmental variables, either one at a time or changing simultaneously. Simulations presented are for default values base d on previously published data for S. pistillata adapted to high-light (shallow-euphotic) and low-light (deep-euphotic) environments, and for single-variable manipulations of rates of a) host feeding, b) photosynthesis, and c) dissolved inorganic nitrogen (DIN) uptake.

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x Simulations examining feeding rates be tween 0% and 6.5% of host biomass indicate that biomass of both high-light and low-light adapted holobionts increase exponentially with increased f eeding, with benefit to the high-light holobiont ~8 times greater than to the low-light holobiont. Incr easing rates of photosynthesis illustrated that a low-light holobiont is carbon limited, is primarily dependent upon host feeding, and can benefit from a small increase in photosynthesis rate. Simula tions examining rates of DIN input indicate that the high-li ght holobiont functions optimal ly when inorganic nitrogen input is very low. Increase in DIN up to 0.5% resulted in benefit to the holobiont, but more resulted in unrealistically excessive gr owth by the zooxanthellae until a function to maintain a fixed range for the host-zooxanthe llae biomass ration function was included in the model. Simulations for the low-light hol obiont did not indicate any benefit from DIN input. The model was originally designed usi ng a spreadsheet-based program which frequently became overloaded when testing multiple variables. Modification of the model in software better designed for m odeling is recommended for future work.

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1 Introduction Coral reefs are among the most threaten ed (Goreau, 1992; Sebens, 1996; Bryant and Burke, 1998; Hoegh-Guldberg, 1999) as well as the most diverse and productive ecosystems in the world (Birkeland, 1997; Hall ock, 2001). Fisheries, tourism, and other aquatic resources, such as sport fishing a nd SCUBA diving industries, will decline if nothing is done to protect, restore, a nd maintain coral reefs (Koop et al., 2001). Coral reefs are able to exist in nutrien t-deficient environments yet remain highly productive ecosystems due to the prevalence of algal symbioses (Muscatine and Porter, 1977; Hallock, 1981, 2001; Falkowski et al., 1984). The holobiont cons ists of the coral host and its endosymbiotic zooxanthellae; th is trophic mode can be termed mixotrophic nutrition (Nybakken, 1997). The holobiont can util ize both inorganic and organic sources of nutrients for the accumulation of carbon and n itrogen that is required for metabolism, growth, and reproduction. The zooxanthell ae photosynthesize, pr oducing photosynthetic carbon or “photosynthate”, which is passed to the coral to be used for respiration, other aspects of metabolism, and for production of mucus, skeletal material, and lipids (Falkowski et al., 1984; Hallo ck, 2001), the latter being ar e critical for reproduction (Koop et al., 2001). Heterotrophic feeding is a source of organic carbon and nitrogen, which provides for fixed carbon (i.e., ener gy) needs not satisfied by the photosynthate and for essential nutrients required for growth of the holobiont. Hallock (2001) postulated that to keep the sy mbiosis in balance the coral ho st must control the amount of inorganic waste nutrients translocated to the zooxanthellae.

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2 Anthropogenic nutrient input to marine environments can harm coral reef ecosystems. Walsh (1984) repo rted a direct relationship be tween nutrient flux to coastal waters and human populations in the watershed. Factors such as deforestation, coastal clearing, agricultural pr actices, and other development, including the construction of roads, buildings, and protective barriers, pr omote soil erosion and runoff. Volume and composition of sediments in run-off dictate the rate and scale of coral loss of near shore barrier reefs and loss of fri nging reefs (Bryant et al., 1998) Agricultural processes, including the intensive use of fertilizers and the increased use of herbicides and pesticides, have significantly impacted the distribution of nut rients and harmful chemicals in the marine envi ronment (Hallock, 2001). Fiel d studies suppor t predictions of Hallock’s (1981) growth model, which indicated that the coral-zooxanthellae symbiosis is most advantageous in nutrientdeplete (oligotrophic) environments. With continued increase in anthropogenic nutrien t flux, corals have a lower chance of effectively competing with nutrient-loving or ganisms (Falkowski, 1977; Smith et al., 1981; Hallock, 2001). The symbiosis between the coral and zooxanthellae is a fragile relationship. The effects of nutrient enrichment on corals incl ude mortality, reduced gr owth rates (Hallock, 2001), reduced gamete production and larvae settlement (Harrison and Wallace, 1990), and reduced skeletal density (Hoegh-Guldbe rg and Smith, 1989; Muscatine et al., 1991; Stimson and Kinzie, 1991; Muller-Parker et al., 1994; Stambler et al., 1994; Koop et al., 2001). Numerous studies have found that increas es in nitrogen result in the increase of zooxanthellae densities and ch lorophyll concentrations (W iebe, 1975; D’Elia and Webb, 1977; Muscatine et al., 1991; Steven and Broa dbent, 1997). When nitrogen is available

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3 to the zooxanthellae, it is as similated into biomass; theref ore, decreasing the amount of photosynthate being transferred to the host. As a consequence, the host must consume more carbon from feeding to provide for resp iration and other metabolic needs, thereby limiting growth. This inefficacious symbiosis can cause stress to the coral, resulting in decreased skeletal and tissue growth (Tomas cik and Sander, 1985; Harrison and Wallace, 1990) and ultimately limiting re production (Koop et al., 2001).

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4 Previous Models of Algal Symbioses Several models have been developed to conceptualize the symbiotic relationships between zooxanthellae and invertebrate or pr otistan hosts (Muscatin e and Porter, 1977; Hallock, 1981; Falkowski et al., 1984; Jones and Yellowlees, 1997; Stoecker, 1998). Hallock (1981) Model of Algal Symbiosis Hallock (1981) examined the relative a dvantage of mixotrophi c nutrition to the host-symbiosis as compared to non-symbio tic autotrophs and he terotrophs using an iterative model (Fig. 1). Components with in her conceptual model describe the relationship and dynamics of growth between the host organism, such as a stony coral and its zooxanthellae. Several assumptions associated with Hallo ck’s (1981) model lim it its applicability (Hallock, 2001). One assumption is that light is not limiting, i.e., the model is not useful to interpret low-light environments. Anot her assumption is that photosynthesis is a function of nutrient supply and that any e ssential nutrient (i.e., nitrogen, phosphorus, or trace nutrients) can be growth limiting. Much more is now known about the physiolo gy of the host-symbiont relationship. For example, if the symbiotic algae have a higher photosynthetic rate as compared to the rate of nutrient uptake, alga l growth will diminish, and the excess carbon can be stored,

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5 Figure 1. Hallock’s (1981) conceptual mode l of a host-algal symbiosis. The algae photosynthesize and utilize the in organic input of nutrients from the environment to meet its metabolic and growth needs. The alga e photosynthesize, producin g photosynthate that is transferred to the host. The host can util ize this photosynthate to provide energy for its metabolic needs and growth, and can also util ize the organic input (i.e., captured food). The host’s nutrient wastes are passed to the algal symbiont.

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6 excreted, or directed to a secondary func tion (Dubinsky and Frank, 2001). Furthermore, studies have demonstrated that nitrogen is the most common limiting nutrient in the hostsymbiont relationship (Falkowski et al., 1984; Steven and Broadbent, 1997; Koop et al., 2001), thus allowing models to focus on nitrogen rather than the more general “nutrient” term used in Hallock’s (1981) model. Hallock (2001) Modified Algal-Symbiosis Model Hallock (2001) conceptually updated her original model based on research of coral and foraminiferal symbioses over the pr evious two decades (Fig. 2). Within the symbiosis, the host must maintain control of the nitrogen available to the algae (Falkowski et al., 1984; Steven and Broadbent, 1997). With ample sunlight in a nitrogendeficient environment, the symbionts photos ynthesize more organic carbon than they need for respiration and basic maintenance. This carbon-rich and nitrogen-deficient photosynthate is translocated to the host (Falkowski et al ., 1984; Steven and Broadbent, 1997; Hallock, 2001). The coral can utilize this photosynthate as an energy source for respiration, for synthesis of mucus and skelet al matrix, and for lipid production, which is essential for reproduction (Falkowski, 1977; Hallock, 1981, 2001; Koop et al, 2001). Hallock (2001) used her updated model to predict the effect s of nitrification (Fig. 3). When dissolved inorganic nitrogen (DIN) is available to the zooxanthellae for protein synthesis, the photosynt hate is retained for growt h. Corals must produce mucus to shed sediments and to fend off bacteria l attack (Rogers, 1990; Santavy and Peters, 1997). Hallock (2001) postulated that, when co rals are forced to c onsume organic carbon

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7 Figure 2. Updated model of algal symbiosis based on subsequent studies indicating that it is essential for the host to maintain c ontrol of the supply of fixed nitrogen (DIN) reaching the symbionts. When severely nutrient limited but in ample sunlight, the symbionts photosynthesize excess organic carbon (photosynthate), which is translocated to the host for use in respiration and for carbohydrate-rich compounds such as mucus or shell matrix macromolecules. Thus, protei n-rich food captured by the host can be used primarily for the host’s gr owth (from Hallock, 2001).

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8 Figure 3. Updated model indicating possibl e consequences of abundant dissolved inorganic nitrogen (DIN) in the environment. The symbiotic algae retain their photosynthate for growth, reduc ing the supply of photosyntha te to the host. The host must utilize its food for respir ation, releasing nitrogenous wastes to the algae, which also promotes algal growth. Ca rbohydrate-rich compounds, which the host need s to produce mucus and shell matrix, must also be derived from feeding (from Hallock, 2001).

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9 from captured food instead of using transl ocated carbon for metabolism, especially respiration, and for mucus production, carbon is diverted from growth and reproduction. She predicted that another consequence w ould be reduced mucus production, increasing the host’s susceptibility to disease. Hallo ck (2001) models suggest the advantages of mixotrophic nutrition to the host-algal symbiosi s in nutrient-deplete environments, while indicating that nitrifica tion is detrimental to the symbiotic relationship. Jones and Yellowlees (1997) Space-Limiting Model Jones and Yellowlees (1997) proposed a space-limiting model for zooxanthellae biomass, describing the stages of recovery of zooxanthellae dens ity after bleaching events. During the first stage when the zooxa nthellae density is th e lowest, the mitotic index (or division rate of the zooxanthellae) is highest. In this initial stage after the bleaching event, the low density of the z ooxanthellae limit the am ount of photosynthate to be translocated to the host, requiring the coral to metabolize heterotrophic sources, translocating waste nitrogen to the zooxant hellae. Both zooxa nthellae density and chlorophyll a concentrations increase until the co lony regain its normal coloration and chlorophyll a concentration. As the recovering population of zooxanthellae increase during the second stage, more photosynthate is translocated to the host, although the host remains reliant on its heterotrophic resources. The translocation of waste nitrogen to the zooxanthellae is reduced; therefore the mitotic index decreases to its original rate as the zooxanthellae return to their origin al population density. With stable light and zooxanthellae density, photosynthate translocation revert s to a steady state, where most is used for the host’s

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10 metabolic needs. The host then can use it s heterotrophic resour ces towards its own growth, thereby limiting the supply of nitrogen to the zooxanthellae. Falkowski et al. (1984) Energy Budget Falkowski et al. (1984) examined the energy budget for Stylophora pistillata developing equations to rela te measurable values for all parameters, which included photosynthesis, respiration, gr owth, and mucus and skeletal production, in both lightand shade-adapted colonies. Photosynthesis rate s, biomass of the z ooxanthellae separate from the coral animal, and respiration ra tes were measured to estimate carbon and nitrogen translocation, growth rates of the zooxanthellae and the coral animal, as well as the animal’s mucus and skeletal production. Falkowski et al. (1984) created energy budget diagrams for both lightand shade-adapted corals. Stoecker (1998) Mixot rophic Nutrition Models Stoecker (1998) conceptually mode led mixotrophic relationships, focusing primarily on mixotrophic protists. She exam ined three basic kinds of relationships, “ideal” mixotrophs that ar e equally dependent upon f eeding and photosynthesis, predominantly autotrophic protists that can supplement by uptake of dissolved inorganic carbon and photosynthesis, and predominan tly heterotrophic organisms that can supplement by the ingestion of particulate or ganic matter. Corals with zooxanthellae probably function as ideal mixotrophs or he terotrophs that supplement by photosynthesis, depending on environmental conditions. The other critical issue Stoecker (1998) noted was the additional energy requirements fo r mixotrophy; about 50% more energy is

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11 needed for a heterotrophic organism to suppor t the photosynthetic symbionts. Thus, the symbiont must be able to fi x at least 50% as much energy as the host can capture for holobiont to compete with asymbiotic heterotrophs.

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12 Thesis Objectives The goal of my thesis research was to develop functions that mathematically describe Hallock’s (2001) c onceptual nutrient-limiting model and to test the proposed hypotheses, which include that mixotrophic nutri tion is an advantage in nutrient deplete environments and that the coral host must c ontrol the supply of nitrogen to its symbiotic algae. Specific problems that are ad dressed within this thesis include: 1) to define parameters required to math ematically describe the conceptual models; 2) to find appropriate values in the published literature for each parameter; 3) to create a model that can be used to predict the response of the holobiont under specific individual and combinati ons of the following parameters: a. rates of host heterotrophic feeding, b. rates of algal photosynthesis, and c. rates of algae uptake of dissolved inorganic nitrogen.

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13 Methods An iterative model (Fig. 4) was created using assumpti ons from previous studies, which include the energy budget from Falkow ski et al. (1984), Jones and Yellowlees (1997) space-limiting model, and Hallock’s (2 001) nutrient-limiting model to portray the dynamics of growth in the host and symbiotic zooxanthellae. The model generates values for biomass accumulation, respiration rates for host and algae, and mucus, skeletal, and lipid production of the host, as well as valu es for the transloca tion and excretion of carbon and nitrogen between the organisms. The results will vary based on input parameters, which include rates of host feeding (BIH), algal photosynthesis (CPA), and nitrogen uptake (NIA). Assumptions One assumption within my model is th at inorganic carbon does not limit the holobiont due to the surplus of dissolved inorganic carbon (DIC) in seawater and availability of CO2 from respiration (Muscatine et al., 1989b; Weis, 1990; Lesser et al., 1994); therefore, photosynthesis will always oc cur if there is light available to the zooxanthellae (e.g., Dubinsky and Frank, 2001) The second assumption is that photosynthate is released to the host only afte r the metabolic needs of the zooxanthellae are satisfied, suggesting that the zooxanthell ae control the translocation of photosynthate independently of the host’s metabolic demands.

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14 Figure 4: Carbon and nitrogen flow diagram.

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15 Another assumption is that nitrogen is only translocated from the host to the zooxanthellae and not from the zooxanthellae to the host. This assumption is based upon the observations by Piniak et al. (2003), which found no evidence that nitrogen is translocated from the zooxanthellae. Ba sed on Jones and Yellowlees (1997) spacelimiting model, associated biomass ratios were included in my model to maintain a functional symbiosis between the coral host and its zooxanthellae. Therefore, the zooxanthellae must maintain a minimum and maximum percent biomass in relation to the coral host. Without these limitati ons within the model, there is the potential for either the host or the zooxanthellae to outgrow th e other under some simulated conditions. The last assumption of my model is that biomass is defined by the Redfield ratio (Redfield et al., 1963), which es timates the elemental ratios of carbon to nitrogen to phosphorus (C:N:P) as 106 carbon atoms to 16 nitrogen atoms to 1 phosphorus atom. C:N:P ratios of marine benthi c organisms can show spatial a nd temporal variations that may be altered by changes of concentrations in the water column or by relocation of the organism (Atkinson and Smith, 1983; Lapoint e, 1989; Muscatine et al., 1989; Wheeler and Bjornsater, 1992; Belda et al., 1993; F ong et al., 1993; Horrocks et al., 1995). My model only deals with C and one nutrient, N; moreover, changing the model to accommodate different C:N ratios (or changing to C:P or even C:Fe ratios) is mathematically trivial, so future studies could examine how changes in the C:N:P ratios might influence a symbiosis. A system of units was developed to tr ack carbon and nitroge n separately, using carbon and nitrogen units. One carbon unit is equal to one carbon atom, and one nitrogen units is equal to one nitrogen atom. Biom ass units (i.e., required C and N for living

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16 cells), refer to the combination of 6.6 carbon units to 1 nitrogen unit, hence the Redfield Ratio. Carbon and nitrogen atoms (units) can be absorbed, consumed, or translocated. My model is very sensitive to this fourth assumption and may be manipulated by the user for future studies. Input and Output Parameters The scleractinian coral species, Stylophora pistillata is very common in the Red Sea at depths of up to 100m (Gattuso et al., 1991) and has been ex tensively studied. All parameters included in my model (Fig. 5) have been studied by numerous researchers (Muscatine and D’Elia, 1978; Falkowski et al., 1984; McCloskey and Muscatine, 1984; Romaine et al., 1997; Ferrier-Pages et al., 1998; Gattuso, 1998). In particular, Falkowski et al. (1984) examined the bioenergetics of S. pistillata creating a nutrient flow and energy budget, and the reported values define the default values in my model due to similarities between parameters (Table 1). Each parameter created within my mode l is based upon the percentage of the appropriate biomass (i.e., host or algae), whic h is consistent with the Falkowski et al. (1984) energy budget; therefore, each parameter, such as rates of algal photosynthesis, nitrogen uptake, and algal respir ation are input or calculated as a percentage of the algal biomass, while rates of host feeding, host resp iration, and host mucus, skeletal, and lipid production are percentages of the host biomass. All other parameters, such as host and algal biomass, carbon produced by algal photo synthesis, carbon and nitrogen assimilated for host and algal growth, photosynthetic carbon translocated to the host, organic carbon and nitrogen input from host feeding, av erage excess carbon pr oduction, and algal

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17 Table 1: Input parameters as de fined by Falkowski et al. (1984). High Light (Shallow-adapted) Low Light (Deep-adapted) Description Value (g C/cm2) % Value (g C/cm2) % BH Host Biomass 1800 BH Host Biomass 1900 BA Algal Biomass 85 4.72% BA Algal Biomass 74 3.89% CRH Host Respiration 109 6.50% CRH Host Respiration 60 3.16% CRA Algal Respiration 5.4 0.30% CRA Algal Respiration 2 0.11% BIH Host Input BIH Host Input 44.7 2.35% CP Gross Photosynthesis 146 8.10% CP Gross Photosynthesis 30.7 1.62% CT Carbon Translocated 139 7.72% CT Carbon Translocated 28 1.47% CMH Host Mucus Production 8 0.44% CMH Host Mucus Production 14.4 0.76% CSH Host Skeletal Production 22.5 1.25% CSH Host Skeletal Production 1.1 0.06% CLH Host Lipid Production 0.75% CLH Host Lipid Production 0.75% BGH Host Growth 3.5 0.19% BGH Host Growth 0.2 0.01% BGA Algal Growth 1.1 0.06% BGA Algal Growth 0.7 0.04% Source: Falkowski et al., 1984. Light and the Bioenergetics of a Symbiotic Coral. BioScience 34: 705709.

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18 nitrogen excretion are calculated based on th e equations (Table 2) developed for the model and are considered the outputs parameters of the model. Default values used for all parameters are based on the Falkowski et al. (1984) energy budget. Model Equations A series of equations (Table 2) were de veloped to describe the relationship and dynamics of growth between coral and thei r symbiotic zooxanthell ae. For the first iteration (x = 1), the model begins with the user inputting the host biomass (BH1), BH1(x=1) = user input(x=1) (biomass units). (1) From this point forward, the model focuses on the symbiotic zooxanthellae. The algal biomass is calculated using a percentage of the host biomass, which can be set by the user; otherwise, it will be ca lculated using the default valu es (shallowor deep-adapted) from Falkowski et al. (1984) energy budget: BA1(x=1) = % (user input(x=1)) BH1(x=1) (biomass units). (2) For holobiont growth, functional algal/host biomass ratios must be maintained by setting limits on algal growth, which the user can alter. The default setting for the minimum biomass ratio, BAmin(x) = % (user input(x)) BH1(x) (biomass units), (3) is 4.72 algal to 100 host biomass units, or 4.72 % of the host biomass, in the shallowadapted coral and 3.89 algal to 100 host bioma ss units, or 3.89% of the host biomass, in the deep-adapted coral, whic h are the percentage s reported by Falkowski et al. (1984). The maximum biomass ratio was arbitrar ily selected to be double the minimum biomass,

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19 Table 2: Parameters, definitions, and equations. Parameter Units Time Equation x =User input BH1 protein x+1 = If BH(x) + BGH(x) > 0, use BH(x) + BGH(x). If not, use 0. x = % (User input) BH1(x) BA1 protein x+1 = BA1(x) + BGA(x) BAmax protein x = (% (User input) BH1(x)) 2 BA2 protein x = If BA1 > BAmax, use BAmax. If BAmin < BA1 > BAmax, use BA1. If BA1 < BAmin, use BAmin. NTH1 nitrogen x = If BA1(x) > BAmin(x), use 0. If not, use BAmin(x) BA1(x). BH2 protein x = If BA2(x) > BA1(x), use BH1(x) NTH1(x). If not, use, BH1(x). CPA carbon x = (% (User input) BA3(x)) 6.6 CRA carbon x = (% (User input) BA3(x)) 6.6 CFA carbon x = CPA(x) CRA(x) CGA carbon x = CFA(x) / 6.6 x = % (user input) BH2(x) NIA nitrogen x+1 = (% (user input) BH2(x+1)) + NTH2(x) NGA nitrogen x = NIA(x) BGA protein x = if CGA(x) > NGA(x), use NGA(x). If not, use CGA(x). CTA carbon x = If BGA(x) = 0, use CPA(x) CRA(x). If not, use CPA(x) CRA(x) (BGA(x)*6.6). NEA nitrogen x = NIA(x) BGA(x) BIH protein x = %(user input) BH2(x) CIH carbon x = BIH(x) 6.6 NIH nitrogen x = BIH(x) CRH carbon x = (%(user input) BH2(x)) 6.6 CMH carbon x = (%(user input) BH2(x)) 6.6 CSH carbon x = (%(user input) BH2(x)) 6.6 CLH carbon x = (%(user input) BH2(x)) 6.6 CUH carbon x = CRH(x) + CMH(x) + CLH(x) + CSH(x) BGH protein x = if CUH(x) < CTA(x), use BIH(x). If not, use (CTA(x) + CIH(x) CUH(x))/6.6 NTH2 nitrogen x = NIH(x) BGH(x) CEH carbon x = (CTA(x) + CIH(x)) (CUH(x) + (BGH(x) 6.6)) %BH % x = BH2(x)/BH2(x-1) -1 %BA % x = BA2(x)/BA2(x-1) -1

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20 BAmax(x) = (% (user input(x)) BH1(x)) 2 (biomass units); (4) therefore, the maximum biomass default value for algae is 9.44% of the host biomass in the shallow-adapted coral and 7.78% of the host biomass in the deep-adapted coral. If the biomass of the zooxanthell ae exceeds the maximum biomass ratio, if BA1(x) > BAmax(x), (5) the algal biomass (BA2) is reduced to the maximum biomass: BA2(x) = BAmax(x) (biomass units). (5a) If zooxanthellae biomass falls between th e minimum and maximum biomass ratios, if BAmin(x) < BA1(x) > BAmax(x), (5b) the original biomass (BA1) is maintained (BA2), BA2(x) = BA1(x) (biomass units). (5c) If the biomass of the zooxanthellae does not meet the minimum biomass ratio, if BA1(x) < BAmin(x), (5d) the minimum algal biomass (BA1) is sustained (BA2), BA2(x) = BAmin(x) (biomass units). (5e) To sustain the minimal algal biom ass in a nitrogen-limited system, if BA1(x) < BAmin(x), (6) nitrogen (required nitrogen, NTH1) must be translocated to the algae: NTH1(x) = BAmin(x) BA1(x) (N units), (6a) to maintain the associated minimum algal biomass to keep up with host growth and maintain a functional symbiosis. Otherwise, no required nitrogen is translocated to the algae, NTH1(x) = 0. (6b)

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21 and the initial biomass (BA1) is maintained (BA2). As previously stated, due to the nature of the Falkowski et al. (1984) energy budget, all parameters are calculated based a pe rcentage of the associated biomass. The zooxanthellae use light and carbon dioxide (CO2) to photosynthesize, producing organic carbon or photosynthate (CPA): CPA(x) = % (user input) BA1(x) 6.6 (C units). (7) The zooxanthellae respire, causing tissue turn over and consuming a portion of the photosynthate for their metabolic costs (CRA), CRA(x) = % (user input)* BA1(x) 6.6 (C units), (8) and the remaining fixed carbon (CFA), CFA(x) = CPA(x) CRA(x) (C unit), (9) is available for algal growth: CGA(x) = CFA(x) / 6.6. (10) Nitrogen is needed in the form of disso lved inorganic nitrogen (DIN) for algal growth. The amount of inorganic nitrogen available to be fixed by the algae (NIA) is a function of the rate of nitrogen uptake from the environment by the algae (default value or set by the user). In the first iteration, NIA(x) = % (user input) BA3(x) (N units). (11) Low rates of nitrogen uptake may restrict al gal growth in nutrientdeplete conditions, but in nutrient-replete conditions, carbon fr om photosynthesis limits algal growth. The amount of nitrogen available for algal growth (NGA) is determined by the amount of fixed nitrogen from the environmen t (DIN) and the rate of waste nitrogen

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22 translocated from the host. For the first ite ration, only nitrogen fr om the environment is available for algal growth: NGA(x) = NIA(x) (N units), (12) but for all other iterations, host wa ste nitrogen (available nitrogen, NTH2) from the previous iteration is translocated to the z ooxanthellae and therefore is available for algal growth, NGA(x) = NIA(x) + NTH2(x-1) (N units), (12a) The growth of the algae (BGA) is determined by whether carbon or nitrogen is limiting, i.e., if CGA(x) > NGA(x). (13) If carbon is the limiting element, the remaining carbon is exhausted for algal growth, BGA(x) = CGA(x) (biomass units). (13a) If nitrogen is the limiting element, all nitr ogen available (DIN or available nitrogen, NTH2) is assimilated for algal growth, BGA(x) = NGA(x) (biomass units), (13b) If necessary, algal biomass is consumed to satisfy its metabolic needs when carbon is limiting. Whether positive or negative, growth (BGA) is added to the or iginal biomass of the algae (BA1(x)) on the next iteration (x+1): BA1(x+1) = BA1(x) + BGA(x) (biomass units). (14) As a consequence of Equation 11, generally there will either be carbon or nitrogen limiting the holobiont. If the symbiosis is nitrogen-limited (i.e., there is no nitrogen available for algal growth), if BGA(x) = 0, (15)

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23 the remaining photosynthate (CTA) is translocated to the coral host: CTA(x) = CPA(x) CRA(x) (C unit). (15a) If there is nitrogen available for algal growth, it is exhausted for biomass assimilation, and the unused portion of photos ynthate is translocated (CTA): CTA(x) = CPA(x) CRA(x= – (BGA(x) 6.6) (C unit), (15b) On the other hand, if the holobiont is carbon-limited, the remaining photosynthetic carbon is consumed by algal gr owth, and the excess nitrogen (NEA) is excreted from the holobiont: NEA(x) = NIA(x) – BGA(x) (N units). (16) Once all parameters for the zooxanthellae have been calculated, the model calculates the parameters associated with the host. The host inputs organic matter by heterotrophic feeding on phytoplankton, zoopl ankton, and detritus in the water column (BIH), which can be varied by the user, BIH(x) = % (user input) BH2(x) (biomass units). (17) The organic matter ingested can be separated into carbon: CIH(x) = BH2(x) 6.6 (C units), (18) and nitrogen: NIH(x) = BH2(x) 1 (N units). (19) The input parameters associated with the host metabolic costs can be set by the user. All processes must occur, which allow for negati ve growth within the host. There is no priority at which these processes occur. Host metabolism incl udes host respiration (CRH), CRH(x) = (% (user input) BH2(x)) 6.6 (C units). (20) the production of carbon-rich mucus (CMH),

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24 CMH(x) = (% (user input) BH2(x)) 6.6 (C units), (21) skeletal carbohydrate matrices (CSH), CSH(x) = (% (user input) BH2(x)) 6.6 (C units), (22) and lipids for reproducti on and energy storage (CLH): CLH(x) = (% (user input) BH2(x)) 6.6 (C units). (23) For simplicity, the host metabolic costs (CUH) are summed: CUH(x) = CRH(x) + CMH(x) + CSH(x) + CLH(x) (C units). (24) The translocated photosynthate from th e zooxanthellae provides a carbon (i.e., energy) source for the host. The assumption th at no nitrogen is translocated from the zooxanthellae to the host defines maximum host growth (BGH) to be equal to the input of organic matter from heterotrophic f eeding. If the carbon translocated (CTA) satisfies all the host’s metabolic costs, if CUH(x=1) < CTA(x=1) (C units), (25) the host can exploit all organic i nput from heterotrophic feeding (BIH) towards its growth (BGH): BGH(x) = BIH(x) (biomass units). (25a) If the photosynthate does not satisfy the hos t’s metabolic demands, then the host must consume organic carbon from heterotrophic feeding: BGH(x) = ((CTA(x) + CIH(x)) – CUH(x))/6.6 (C units). (25b) Whether positive or negative, growth is added to the biomass of the host (BH2) on the next iteration (x+1): BH1(x+1) = BH2(x) + BGH(x) (biomass units). (26)

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25 If host growth is positive and the host metabolic demands are not satisfied by the translocated photosynthate, the host must cons ume organic carbon from feeding to satisfy its metabolism. Therefore, waste nitrogen (available nitrogen, NTH2) from the host is available to be translocated to the symbiont: NTH2(x) = NGH(x) – BGH(x) (N units). (27) If host growth is nitrogen-limited or limited by feeding, the remaining carbon (CEH) is excess, CEH(x) = (CTA(x) + CIH(x)) – (CUH(x) + (BGH(x) 6.6)). (28) and can be excreted from the holobiont as mu cus, synthesized into skeletal matrix, or manufactured into lipids for reproduction or energy storage. For comparison to other studies, the change in the algal (% BA) biomass per iteration: % BA(x) = (BA2(x)/BA2(x-1)) – 1, (29) and the host (% BH) biomass per iteration: % BH(x) = (BH2(x)/BH2(x-1)) – 1, (30) is also calculated. Programming the Model The model was created by writing macros (Appendix A) in Microsoft Excel, Version 2003. One option in the tools menu a llows for macros to be created and run within the file. Upon opening the program, a series of boxes defines each parameter, which can be modified by the user with ea ch run of the model. Once the user has determined the parameters to be varied by c licking in the appropriate boxes, a series of

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26 questions follow, and there are se veral options at that point. The first option is to change the parameter from its default setting (Table 1) to a constant value of the user’s choice. The second option is to have the parameter va ry randomly over a range specified by the user. Upon completing the series of questions for each parameter, the user must click on the: “Finish Input Parameters” box, then the program automatically calculates the equations and plots the biomass of the host a nd algae on the spreadsheet labeled “Model Chart”. The user can plot other parameters by selecting the assigned boxes on the second spreadsheet labeled “Create Dynamic Chart”. Once the parameters have been selected, the chosen parameters are plotted on a second graph labeled “Dynamic Chart”. While there is an infinite variety of possi ble scenarios to use this model, three sets of simulations, which include mani pulating rates of host feeding (BIH), algal photosynthesis (CPA), and nitrogen uptake (NIA), were examined for this thesis. Initially, my model was run with the default values fr om the Falkowski et al. (1984) energy budget for shallow-adapted (or light-adapted) and deep-adapted (or shade-adapted) corals. Secondly, the model was run varying each pa rameter independently (single parameter trials) for a period of 100 iterations at each interval for both lightand shade-adapted corals. Table 3 shows the associated trials (Trial 2 through Trial 4) for each parameter varied. The rate of each parameter is a per centage of the biomass, whether associated with the host or the algal symbiont. Lastly, my model was run varying a combination of two parameters simultaneously (two-parameter trials) for the shallow-adapted coral. Trial 5 varied host feeding rate (BIH) with algal photosynthesis rate (CPA), and Trial 6 varied algal

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27 Table 3: Parameters with corresponding trial numbers for shallowand deepadapted corals. Trial 1 represents the results using Falkowski et al. (1984) energy budget. Parameters Host Feeding Rates (BIH) Photosynthesis Rates (CPA) Nitrogen Uptake Rate (NIA) Host Feeding Rates (BIH) Trial 2 Photosynthesis Rates (CPA) Trial 5 Trial 3 Parameters Nitrogen Uptake Rate (NIA) Trial 6 Trial 4

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28 photosynthesis rate (CPA) with nitrogen uptake rate (NIA) over 100 iterations simultaneously. For the two-parameter trials, specific rate s for each parameter were selected and run in the program for the shallow-adapted co ral. For host feeding, rates relating to different environmental constraints and feed ing regimes were used. These corresponding feeding regimes were no feeding, which was 0% BIH; minimal feeding, which was ranged between 0.001% and 0.1% BIH; optimal feeding, which was 1% BIH; extreme feeding, which was 2% BIH; and excessive feeding, which was 3% BIH. For photosynthesis, these corresponding rates were no phot osynthesis, which was 0% CPA; minimal photosynthesis, which ranged between 2% and 4% CPA; optimal photosynthesis, which ranged between 6% and 8% CPA; high photosynthesis, which ranged between 10% and 12% CPA; and excessive photosynthesis, which ranged between 14% and 16% CPA. For nitrogen uptake by the symbiont, these corresponding rates were no nitrogen uptake (NIA = 0%), which was 0% NIA; minimal nitrogen uptake, whic h ranged between 0.001% and 0.1% NIA; optimal nitrogen uptake, which ranged between 1% and 2% NIA; high nitrogen uptake, which ranged between 3% to 5%; and excessi ve nitrogen uptake, which ranged between 6% and 10% NIA.

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29 Results and Preliminary Comparisons For consistency among the numerous graphs and charts, the color blue represents the host or products being tran slocated by the host, and th e color green re presents the zooxanthellae or products being translocated by the zooxanthe llae. The shallow-adapted coral is illustrated with the lighter or thinne r line, whether hostor algalassociated, and the deep-adapted coral is illustrated with the da rker or thicker line. Host mucus, skeletal, and lipid production are depicted by red, or ange, and yellow, respectively. Figures containing changes in host or algal respiration are not included because the trend is the same as with changes in host biomass. All trials were run for a maximum of 100 iterations with the initial host biomass set at 10 biomass units. Appendix B contains all results for each trial. Translocation of nitrogen to the zooxanthe llae occurs in two stages, required and available translocation. The primary st age, required nitrogen translocation (NTH1), occurs when nitrogen is essential for algal growth to maintain the minimum biomass ratio and is automatically translocated befo re the host can use it for bi omass assimilation. Required nitrogen is represented by the turquoise colo r. Available nitrogen translocation occurs when waste nitrogen becomes available when organic carbon from heterotrophic feeding must be consumed to satisfy the host’s metabolic needs; available N is represented by the blue color used to represent the host. Excess photosynthetic car bon not required for maintenance or growth may be excreted as host mucus, synthesi zed into skeleton matrices, or stored as lipids This excess carbon is summed into one parameter, average

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30 excess carbon production (CEH) and is represented by the colo r blue as it is removed from the holobiont through associated host functions. Any excess nitrogen (NEA) is excreted from the holobiont and is re presented by the color green as it cannot be utilized by the zooxanthellae. Trial 1: Basic Model The basic model was initially tested usi ng values from the Falkowski et al. (1984) energy budget (Table 1, Fig. 5) for both the sh allowand deep-adapted corals. Input for host feeding (BIH) of the shallow-adapted coral was set arbitrarily at 1% to have a minimal input of organic nitrogen given that Falkowski et al. (1984) did not report any feeding. Dissolved inorganic nitrogen (DIN) is considered below uptake minimum in the environment, thereby restricting the avai lable nitrogen for algal growth to host translocation. Table 4 shows the results of the basic trial using th e default values as defined by the Falkowski et al. (1984) en ergy budget for both the shallowand deepadapted corals. Shallow-Adapted Coral In the shallow-adapted coral, the host biomass (BH) increased from 10 to 25 biomass units, 2.5 times its original biomass, and the algal biomass (BA) increased from 0.47 to 1.28 biomass units (Fig. 6a), almost thre e times it original biomass, at the end of 100 iterations. The host average percent change per iteration (%BH) initially dropped to minimum of 0.56% within the first few iteratio ns (Fig. 6b) then remained steady around Table 4. Minimum and maximum results of shallowand deep-adapted corals holding Falkowski et al. (1984) energy budg et constant over 100 iterations. Host

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31 feeding rate (BIH) was held constant at 1% and 2.4% for the shallowand deepadapted coral, respectively. Shallow-Adapted Coral Deep-Adapted Coral Parameter Minimum Value Time Maximum Value Time Minimum Value Time Maximum Value Time Host Biomass (biomass units) BH 10 1 25.47 100 0.14 100 10 1 Algal Biomass (biomass units) BA3 0.47 1 1.28 100 0.39 1-2 0.75 4 Host APC %BH 0.56% 2-3 1% -1.54% 3 -0.07% 7-100 Algal APC %BA 0% 9.14% 4 -0.7% 7-100 41.38% 3 Average Carbon Translocated (C units) CTA 5.34 1 14.51 0.9 2 1.81 7 Average Available Nitrogen Translocated (N units) NTH1 0 0.39 97 0 2 0.38 3 Average Required Nitrogen Translocated (N units) NTH2 0 0.39 96 0.22 100 0.38 2 Average Excess Carbon Production (C units) CEH 0 1 0.36 100 0 * Average Algal Nitrogen Excretion (N units) NEA 0 * 0 0.21 2 refers to instances that continually o ccur throughout the 100-iteration period.

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32 Figure 5: Falkowski et al. (1984) energy budget diagram. Scal ed flow path of carbon in S. pistillata : a. high light-adapted; b. shade-adap ted. Fluxes are in units of g C cm-2 d-1; biomass values are in units of g C cm-2. Symbols BZ,A Biomass of zooxanthellae and animal, respectively Ia Absorbed photosynthetically active radiation PG Gross photosynthesis of whole coral (PG = PN + RC) C Standing crop of zooxanthellae carbon Io Incident photosynthetically active radiation PN Net photosynthesis of whole coral A Daily increment of growth of animal tissue c Specific growth rate of zooxanthellae carbon ( = net daily carbon fixed by zooxanthellae normalized to standing crop of zooxanthellae carbon) PDOC Particulate and/or dissolved organic carbon excreted or secreted by the coral S Daily increment of growth of skeleton z Specific growth rate of zooxanthellae cells RC,A,Z Respiration of whole coral, animal, or zooxanthellae Z Daily increment of growth of zooxanthellae N Number of zooxanthellae cells TC Carbon translocated from zooxanthellae to animal

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33 0 5 10 15 20 25 30 110192837465564738291100Iterations (time x)Host Biomass (biomass units)0 0.2 0.4 0.6 0.8 1 1.2 1.4Algal Biomass (biomass units) Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted)Figure 6a. Host (BH) and algal (BA) biomass for shallowand deep-adapted corals over 100 iterations using defau lt parameters from Falkowski et al. (1984) with host feeding rate (BIH) set at 1% for the shallow-adapted coral and 2.35% for th e deep-adapted coral; alga l nitrogen uptake rate (NIA) held constant at 0% in both cases.

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34 -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 110192837465564738291100Iterations (time x)Percent Change per Iteration Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted) Figure 6b. Host (%BH) and algal (%BA) average percent change per iteration for shallo wand deep-adapted corals over 100 iterations using parameters defined in Fig. 6a.

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35 1% with occasional lower oscillations when organic carbon from feeding is consumed to satisfy hosts energy needs, allowing available nitrogen to be translocated and assimilated for algal growth. The slight os cillations in host growth co incide with the peaks in the algal growth. The algal average percent change per iteration (%BA) has a maximum peak of 9.14% within the first few iteration, whic h is due to the integration of nitrogen translocation, followed by periods of no gr owth (0%) at times when nitrogen was limiting, then has intermittent peaks at ~3.5% when the host shunted waste (available, NTH2) nitrogen to the algae. Both the host and algae sustained positive growth over time. Photosynthate translocated (CTA) to the host nearly tripled from 5.34 C units to a maximum of 14.5 C (Fig. 6c) with step-like os cillations, which are associated with the increase in algal biomass (Fig. 6a). Availa ble nitrogen was translocated to the algae over the 100 iterations in a series of peaks spanning between 2 to 4 iterations. The available nitrogen (NTH2) translocated fluctuated from no n itrogen translocated (0 N units) to a maximum of 0.384 N units and is shown in Figure 6d. The amount of excess carbon produced (CEH) peaked in association with algal growth, fluctuating from no carbon excretion (0 C units) to a maximum of 1.05 C units when the holobiont is nitrogen limited and photos ynthate is in excess of the host’s energy needs (Fig. 6e). The peaks of excess carbon production are correlated with the step-like increases of photosynthate translocation, and the maximum of each peak coincides with the stabilization of al gal growth. No nitrogen was excreted (NEA) from the holobiont in the shallow-adapted coral because carbon was available in excess and the holobiont was nitrogen limited.

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36 0 2 4 6 8 10 12 14 16 110192837465564738291100Iterations (time x)Carbon Translocated to the Host (C units) Carbon (Shallow-Adapted) Carbon (Deep-Adapted) Figure 6c. Carbon translocated (CTA) to the host for shallowand deep-adapted corals over 100 iterations using parameters defined in Fig. 6a.

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37 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 110192837465564738291100Iterations (time x)Required Nitrogen Translocated to the Algae (N units)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Available Nitrogen Translocated to the Algae (N units) Required N (Deep-Adapted) Available N (Deep-Adapted) Required N (Shallow-Adapted) Available N (Shallow-Adapted) Figure 6d. Required (NTH1) and available (NTH2) nitrogen translocated to the algal for sh allowand deep-adapted corals over 100 iterations using parameters defined in Fig. 6a.

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38 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 110192837465564738291100Iterations (time x)Excess Carbon Production (C units)0 0.05 0.1 0.15 0.2 0.25Nitrogen Excretion (N units) Carbon (Shallow-Adapted) Carbon (Deep-Adapted) Nitrogen (Shallow-Adapted) Nitrogen (Deep-Adapted) Figure 6e. Excess carbon production (CEH) and nitrogen excretion (NEA) for shallowand deep-adapted corals over 100 iterations using parameters defined in Fig. 6a.

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39 Host mucus production ranged from a mini mum of 0.29 (time, x = 1) to 0.74 C units at the end of 100 iterati ons (Fig. 6f). Host skel etal production ranged from 0.83 (time, x = 1) to 2.1 C units (time, x = 100), and host lipid production ranged from 0.5 (time, x = 1) to 1.3 C units (time, x = 100). These host requirements are correlated with and increase in paralle l with host growth. Deep-Adapted Coral The host biomass of the deep-adapted cora l progressively decreased overall by 10% decreasing to 9.1 biomass units at the end of 100 iter ations due to the lack of available carbon for growth (Fig. 6a). Therefore, th e default value for host feeding, based on the Falkowski et al. (1984) energy budg et was insufficient to main tain host bioma ss. Within the first few iterations, the algal biomass initially peaked at 0.75 biomass units, which became restricted by the maximum biomass ratio when nitrogen was translocated. At the end of the 100 iterations, the algal biomass was reduced to 0.7 biomass units, which is almost double the original biomass but overa ll, did not produce e nough photosynthate to satisfy the host’s metabolism. The deep-adapted coral sustained slight negative growth, resulting in an overall decrease in bioma ss. The host percent change per iteration dropped to a minimum of -1.5% wi thin the first few iterations due to th e incorporation of nitrogen translocation, then st abilized at -0.07% as the maxi mum biomass ratio restricted its growth (Fig. 6b). The algal biomass initiall y spiked to 41% in the first few iterations, then also stabilized at 0.07%; this was an artifact of the functional biomass ratio limitation built into the model.

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40 0 0.5 1 1.5 2 2.5 110192837465564738291100Iterations (time x)Host Mucus, Skeletal, and Lipid Production (C units) Mucus Production (Shallow-Adapted) Skeletal Production (Shallow-Adapted) Lipid Production (Shallow-Adapted) Mucus Production (Deep-Adapted) Skeletal Production (Deep-Adapted) Lipid Production (Deep-Adapted) Figure 6f. Host mucus (CMH), skeletal (CSH), and lipid (CLH) production for shallowand deep-adapted corals over 100 iterations using parameters defined in Fig. 6a.

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41 Within the first few iterations of the basic trial for the deep-adapted coral, the amount of photosynthate translocated to hos t reached a minimum of 0.9 C units as the zooxanthellae retained carbon for growth as nitrogen became available, then reached a maximum of 1.8 C units (Fig. 6c) shortly after, which is associ ated with the spike in algal biomass, gradually decreasing to 1.7 C units. Nitrogen translocation to the algae initially peaked within the first three iterations, then declined to a sustainable point, slightly decreasing over the remainder of the iterati ons as host biomass declined, reducing the maximum biomass ratio (Fig. 6d). No required nitrogen (NTH1) translocated to the algae due to lack of host grow th. Available nitrogen (NTH2) was continuously translocated, peaking at 0.38 N units (time x=2), declined to 0.23 N units at itera tion time x=4, then slightly decreased to 0.22 N units over th e remainder of the iterations (Fig. 6d). For the deep-adapted coral, there was no excess production of carbon (CEH) due to overall carbon limitation (Fig. 6e). Excess nitrogen was initially excreted from the holobiont (NEA) (time, x=2), then continuously decreased from 0.25 N units to 0.21 N units at the end of 100 iterati ons. Host mucus, skeletal, and lipid production declined with host biomass. Host mucus production decreased from a maximum of 0.5 (time, x = 0) to 0.45 C units at the end of 100 iterations. Host skelet al production decreased from a maximum of 0.4 C units at time, x = 0 to 0.36 C units (time, x = 100), and host lipid production decreased from 0.5 (time, x = 0) to 0.45 C units (time, x = 100). Comparison of Results Overall, the shallow-adap ted coral was carbon rich due to higher photosynthesis rates and nitrogen limitation. The deep-adapted coral was carbon limited and not able to

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42 sustain itself using input values based on Fa lkowski et al. (1984) energy budget. The shallow-adapted holobiont increased its bi omass by 1.5 times the starting value, which resulted from the alternation of the hos t occasionally being carbon limited and the zooxanthellae being nitrogen limited. The deep-adapted holobiont had insufficient carbon supplies from host feeding or algal photosynthesis to su stain its biomass, therefore progressively decreasing in biomass by 10% due to overall carbon-limitation (Fig. 6a). Carbon was translocated when nitrogen limited algal growth in the shallowadapted coral. For the deep-adapted coral, carbon was translocated but not enough to satisfy the host’s metabolic requirements (Fig. 6c). The periodic translocation of available nitrogen in the shallow-adapted coral is a result of the occasional reliance of the host on its heterotrophic res ources; whereas, there was a st eady decrease of available nitrogen translocation as th e host biomass decreased in the deep-adapted coral due to insufficient energy supplies from host feedin g and algal photosynthe sis (Fig. 6d). Thus, there was no excess carbon production in the d eep-adapted coral due to overall carbon limitation. In contrast, ther e was periodic excess carbon production in the shallowadapted coral due to nitrogen limitation (Fig 6e). Due to nitr ogen limitation in the shallow-adapted coral, there was no excre tion of nitrogen from the holobiont; whereas, there was continual excreti on of nitrogen in the deep-adapted coral (Fig. 6e). It is important to recall that the default values for shallow-adapted coral were augmented by providing host with food input, wh ich was lacking in the Falkowski et al. (1984) budget. Future simulations should co mparably augment the carbon input to the deep-adapted coral so that minimal growth could occur.

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43 Trial 2: Varying Rates of He terotrophic Feeding by Host (BIH) In this trial, host heterotrophi c feeding (BIH) rates ranged from 0% to 6.5% of the host biomass and were examined for 100 iterations. Inputs for all other parameters were held constant at the default values from the energy budget by Falkowski et al. (1984). DIN is considered below uptake minimum in the environment, restricting nitrogen for algal growth to host transloc ation. Table 5 shows the results from the shallow-adapted coral and deep-adapted coral. Both increase in biomass with an increase in host feeding rate. The figures for this section exte nd only to the host feeding rate of 6.5% BIH due to scaling issues at th e end of 100 iterations. Shallow-Adapted Coral With no host feeding, the shallow-adapted host biomass decreased sli ghtly from initial 10 biomass units to 9.9 biomass units at the end of 100 iterations (Fig. 7a ). For higher rates of host feeding, the host biomass increased exponentially to 3866 biomass units at a feeding rate of 6.5%. The biomass of the zooxanthellae increased in parallel as host feeding increased. The minimum algal biom ass was 0.6 biomass units at the end of 100 iterations with no feeding, and the maximum algal biomass was 183 with a feeding rate of 6.5%. Average percent change per itera tion for the host was -0.1% with no feeding (BIH = 0%) and increased to 6.2% when host feeding was set at 6.5% BIH (Fig. 7b). The average percent change per iteration for the zooxanthellae was 0.25% with no feeding (BIH = 0%) and increased to 6.3% when host feeding was set at 6.5% BIH (Fig. 7b).

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44 Table 5. Minimum and maximum results of a shallowand deep -adapted coral with an increase in host feeding rate (BIH) over 100 iterations. All other parameters were held consta nt using Falkowski et al (1984) energy budget. Shallow-Adapted Coral Deep-Adapted Coral Parameter Minimum Value % BIH Maximum Value % BIH Minimum Value % BIH Maximum Value % BIH Host Biomass (biomass units) BH 9.9 0% 3866 6.5% 0.85 0% 513 6.5% Algal Biomass (biomass units) BA3 0.6 0% 183 6.5% 0.066 0% 40 6.5% Host APC %BH -0.1% 0% 6.2% 6.5% -2.5% 0% 4% 6.5% Algal APC %BA 0.25% 0% 6.3% 6.5% -1.7% 0% 5% 6.5% Carbon Translocated to the Host (C units) CTA 6.9 0% 383 6.5% 0.66 0% 24 6.5% Required Nitrogen Translocated to the Algae (N units) NTH1 0 0% 0.17 6.5% 0 0% 0.00011 6.5% Available Nitrogen Translocated to the Algae (N units) NTH2 0.00066 0% 2 6.5% 0.089 0% 3.1 6.5% Excess Host Carbon Production (C units) CEH 0.15 0.9% 5.2 6.5% 0 0-3.7% 0.00074 6.5% Algal Nitrogen Excretion (N units) NEA 0 * 0.023 0% 2.5 6.5% refers to instances that continually occu r throughout the 100 -iteration period.

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45 0 500 1000 1500 2000 2500 3000 3500 4000 45000% 0.5% 1. 0% 1. 5% 2.0 % 2.5% 3 .0% 3. 5% 4.0 % 4.5% 5.0% 5 .5% 6. 0% 6.5 %BIHHost Biomass (biomass units)0 20 40 60 80 100 120 140 160 180 200Algal Biomass (biomass units) Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted) Figure 7a. Final host (BH) and algal (BA) biomass with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapted corals over 100 iterations usin g default parameters from Falkowski et al. (1984) with algal ni trogen uptake rate (NIA) held constant at 0%.

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46 -3% -2% -1% 0% 1% 2% 3% 4% 5% 6% 7%0% 0 .5 % 1 .0 % 1 5% 2.0% 2.5% 3 .0 % 3 5% 4 0% 4 5% 5.0% 5 .5 % 6 0% 6 5%BIHAverage Percent Change per Iteration Host (Shallow-Adapted) Algal (Shallow-Adapted) Host (Deep-Adapted) Algal (Deep-Adapted) Figure 7b. Average host (%BH) and algal (%BA) percent change with an increa se in heterotrop hic feeding (% BIH) for shallowand deep-adapted corals over 100 iterations using parameters as defined in Fig. 7a.

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47 The average amount of carbon translocated to the host was 6.9 C units with no host feeding (BIH = 0%) and increased to 383 C units at feeding rates of 6.5% per iteration (Fig. 7c). Both the amount of required nitrogen (NTH1) and the amount of available nitrogen (NTH2) translocated increased exponent ially (Fig. 7d). The amount of required nitrogen translocated was 0 N units w ith a feeding rate of 0% and increased to 0.17 N units with a feeding rate of 6.5% (Fig 7e). The amount of available nitrogen translocated was 0.00066 N units no feeding (BIH = 0%) and increased to 2 N units with a feeding rate of 6.5%. For the shallow-adapted coral, average excess carbon production fluctuated slightly but overall increased with an increas e in host feeding rate (Fig. 7e). The amount of excess carbon production was 0.15 C units at low feeding rate (BIH = 0.9%) and increased to 5.2 C units with the highest feed ing rate of 6.5%. Nitrogen was not excreted from the shallow-adapted coral due to overall nitrogen limitation. Deep-Adapted Coral With no host feeding, the bioma ss of the deep-adapted coral decreased significantly when compared to the shallow-adapted coral, fr om 10 biomass units initially to 0.85 biomass units at the end of 100 iterations. With hos t feeding, the host biom ass increased to 513 biomass units at the feeding rate of 6.5%. Th ere was also a parallel exponential increase in algal biomass with increased host feed ing rates (Fig. 7a) with a minimum of 0.066 biomass units with no feeding (BIH = 0%) and a maximum of 40 biomass units with the highest feeding rate (BIH = 6.5%). The host average percent

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48 0 50 100 150 200 250 300 350 400 4500% 0. 5 % 1. 0 % 1. 5 % 2 .0 % 2.5% 3. 0 % 3. 5 % 4. 0 % 4 .5 % 5.0% 5. 5 % 6. 0 % 6 .5 %BIHAverage Carbon Translocated to the Host (C units) Shallow-Adapted Deep-Adapted Figure 7c. Average carbon translocated (CTA) to the host with an increase in heterotrophic feeding (% BIH) for shallowand deepadapted corals over 100 iterations usi ng parameters as defined in Fig. 7a.

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49 0 0.5 1 1.5 2 2.5 3 3.50% 0 5% 1 .0 % 1 5% 2 .0 % 2.5% 3 0% 3 .5 % 4 0% 4 .5 % 5.0% 5 5% 6.0% 6 5%BIHAverage Nitrogen Translocated to the Algae (N units) Required N (Shallow-Adapted) Required N (Deep-Adapted) Available N (Shallow-Adapted) Available N (Deep-Adapted) Figure 7d. Average required (NTH1) and available (NTH2) nitrogen translocated to the algae with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapted corals over 100 it erations using parameters as defined in Fig. 7a.

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50 0 1 2 3 4 5 60 % 0.5% 1. 0 % 1 .5 % 2.0% 2. 5 % 3. 0 % 3.5% 4.0% 4. 5 % 5 .0 % 5.5% 6. 0 % 6 .5 %BIHAverage Excess Carbon Production (C units)0 0.5 1 1.5 2 2.5 3Average Nitrogen Excretion (N units) Carbon (Shallow-Adapted) Carbon (Deep-Adapted) Nitrogen (Shallow-Adapted) Nitrogen (Deep-Adapted) Figure 7e. Average excess carbon production (CEH) and nitrogen excretion (NEA) with an increase in heterotrophic feeding (% BIH) for shallowand deep-adapted corals over 100 iterat ions using parameters as defined in Fig. 7a.

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51 change per iteration ranged fr om -2.5% with no feeding (BIH = 0%) to 4% when host feeding was set at 6.5% BIH. The average algal percent ch ange per iteration was -1.7% with no feeding (BIH = 0%) and increased to 5% with the highest feedi ng rate of 6.5% (Fig. 7b). The amount of carbon translocated to the host in the deep-ada pted coral was 0.66 C units with no host feeding (BIH = 0%) and increased to 24 C un its with a feeding rate of 6.5% (Fig. 7c). Both the amount of required nitrogen (NTH1) and the amount of available nitrogen (NTH2) translocated also increased exponentia lly (Fig. 7d) with an increase in host feeding rate. No required nitrogen (NTH1) was translocated with no feeding (BIH = 0%), but increased to an av erage of 0.00011 N units with a feeding rate of 6.5%. The average amount of available nitrogen (NTH2) translocated was 0.089 N units with no feeding (BIH = 0%) and increased to 3.1 N units with a feeding rate of 6.5%. Initially, there was no excess carbon produ ced within the holobiont due to carbon limitation, but as the feeding rate increased, carbon assimilation increased proportionally. With feeding rates of 3.8% and higher, excess carbon was minimally produced with the maximum being 0.00074 C units at a feeding rate of 6.5%. The amount of nitrogen excreted from the holobiont was 0.023 N units with no feeding (BIH = 0%) and increased to 2.5 N units at the feeding rate of 6.5% (Fig. 7e). Comparison of Results Host and algal biomass both increased exponentially as host feeding rates increased for both the shallowand deep-ada pted corals. However, the difference in magnitudes of increase demonstrates clearly the tremendous potential for shallow-water

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52 corals (Fig. 7a). With no heterotrophic input, the holobi ont biomass in the shallowadapted coral decreased by 10% over 100 iterations but increas ed by 11% with the initial input of heterotrophic feeding (BIH = 0.1%). The metabolic needs of the shallow-adapted coral were satisfie d with photosynthetic carbon alone and the holobiont biomass increased with minimal feeding rates (0.1% a nd higher). For the deep -adapted coral, the holobiont mainly is dependent on its heterotr ophic energy source and doesn’t maintain its initial biomass (10 biomass units) until a feeding rate of 2.5%. This can be seen in Figure 7b when the percent change per iterati on crosses from negative growth to positive growth. There was a linear increa se in average percent change with the linear increase in host feeding for both the shallowand deep-adapted coral (Fig. 7b). There was a similar trend for carbon (Fig. 7c) and nitrogen (Fi g. 7d) translocated due to the increase in the holobiont growth with the same magn itude of difference between the shallowand deep-adapted corals There were some mi nor fluctuations in the shallow-adapted simulations due to the ho lobiont being strictly nitrogen limited. For the shallow-adapted coral, average excess car bon production increased with an increase in host feeding rates, while the deep-adapted coral ha d no excess carbon production due to carbon limitation (Fig 7e). Since the shallo w-coral is strictly nitrogen limited, they did not excrete any nitrogen, but nitrogen excret ion in the deep-adapted coral steadily increased due to overall carbon limitation (Fig. 7e). Trial 3: Varying Rates of Photosynthesis in Algae (CPA) In this trial, algal photosynthesis rates (CPA) are examined at intervals ranging from no photosynthesis (CPA = 0%) to excessive photosynthesis (CPA = 8.5%) and were

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53 run for 100 iterations. The orig inal photosynthesis rates fr om Falkowski et al. (1984) were 8.1% for the shallow-adapted coral and 1.6 % for the deep-adapted coral. Inputs for all other parameters are held constant at the default values from the energy budget by Falkowski et al. (1984), w ith the exception that the input for host feeding (BIH) was set at 1% for the shallow-adapted coral. DIN is considered below uptake minimum in the environment, restricting the available nitrogen for algal growth to host translocation. Table 6 shows the results found for a shallowa nd deep-adapted coral w ith an increase in algal photosynthesis rates. The figures for th is section extend to the algal photosynthesis rate of 8.5% CPA at which steady states for both corals are reached. Shallow-Adapted Coral The final host biomass of the shallowadapted coral increased exponentially from 0.0028 biomass units with no photosynthesi s to 22 biomass units at 4.4% CPA, then slightly increased to 25 biomass units until st eady state. The final algal biomass of the shallow-adapted coral ranged from 0.00026 biom ass units with no photosynthesis to a maximum of 2.1 biomass units at photosynthetic saturation of 4.4% with the steady state of 1.2 biomass units reached at a photo synthesis rate of 8.5% (Fig. 8a). The average percent change per iteration of the shallow-adapted host ranged from -7.9% with no photosynthesis to a maximu m of 0.95%, with a steady state of 0.95%, which was reached at 8.5% CPA. The x-intercept for the shallow-adapted coral, which indicates the photosynthesis rate at which the average percent change becomes positive is 4.1% CPA. The average percent change per iteration of the shallow-adapted algae ranged

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54 Table 6. Minimum and maximum results of a shallowand deep-ada pted coral with an increase in algal photosynthesis rate (CPA) over 100 iterations. Host feeding rate (BIH) was held constant at 1% and 2.4% for the shallowand deep-adapted coral, respectively, and nitrogen not available in the environment. A ll other parameters were held constant using Falkowski et al. (1984) energy budget. Shallow-Adapted Deep-Adapted Parameter Minimum Value % CPA Maximum Value % CPA Stead y State (CPA = 8.5%) Minimum Value % CPA Maximum Value % CPA Stead y State (CPA = 5.3%) Host Biomass (biomass units) BH 0.0028 0% 25 8.5% 25 0.53 0% 99 5.3-8.5% 99 Algal Biomass (biomass units) BA3 0.00026 0% 1.7 4.3% 1.2 0.041 0% 6 2.6% 3.9 Host APC %BH -7.9% 0% 0.95% 8.1-8.5% 0.95% -2.9% 0% 2.4% 5.3-8.5% 2.5% Algal APC %BA -7.3% 0% 1.7% 4.4-4.5% 0.99% -2.2% 0% 3% 2.6% 2.4% Average Carbon Translocated (C units) CTA 0 0% 10 6.7% 9.8 0 0% 31 8.5% 31 Average Required N itrogen Translocated (N units) NTH1 0 0-7.7% 0.000031 8.5% 0.000031 0 0-2.8% 0.035 5.3-8.5% 0.035 Average Available N itrogen Translocated (N units) NTH2 0.0077 8.2% 0.12 3.3% 0.0081 0 5.3-8.5%2.3 1.8% 0 Average Excess Carbon Production (C units) CEH 0 0-4.4% 0.71 6.7% 0.089 0 0-2.6% 18 8.5% 18 Algal Nitrogen Excretion (N units) NEA 0 6.7-8.5% 1.3 3.1% 0 0 3.5-8.5%2.2 1.70% 0 refers to instances that continually occu r throughout the 100 -iteration period.

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55 0 20 40 60 80 100 1200 % 0. 5% 1% 1.5% 2% 2. 5% 3% 3.5% 4 % 4. 5% 5% 5.5% 6 % 6. 5% 7% 7.5% 8 % 8. 5%CPAHost Biomass (biomass units)0 1 2 3 4 5 6 7Algal Biomass (biomass units) Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted)2.6% CPA 5.3% CPA4.3% CPA8.5% CPA Figure 8a. Final host (BH) and algal biomass (BA) with an increase in alga l photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 iterations using default parameters fr om Falkowski et al. (1984) with host feeding rate (BIH) set at 1% for the shallowadapted coral and 2.35% for the deep-adapt ed coral; algal nitr ogen uptake rate (NIA) held constant at 0 in both cases.

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56 from -6.8% with no photosynthesis to a maxi mum of 1.8% with a steady state of 0.98%, which was reached at 8.5% CPA. The x-intercept for the average percent change of algal biomass was reached at a photosynthesis rate of 3.7% (Fig. 8b). The maximum host average percent change was reach ed and maintained at 7.7% CPA and higher; while the algal average percent change per iteration in the shallow-adapted coral peaked at 4.2% CPA and slightly declined until steady state was reached at the photosynthesis rate of 8.5%. No carbon was translocated to the host in the absence of light. At photosynthesis rates (CPA) above 6.7%, the average maximum amount of carbon translo cated to the host was 10 C units, which was more than needed by the host for its metabolism, so excess carbon was produced. Before steady state was reached at 8.5% CPA, the average amount of carbon translocated to the host increased expone ntially until the z ooxanthellae became photosynthetically saturated at th e photosynthesis rate of 4.2%, then it slightly increased and decreased before steady state was reached (Fig. 8c). The average amount of carbon translocated at 8.5% CPA, was 9.8 C units. No required nitrogen (NTH1) was translocated to the algae as photosynthesis rates increased. An initial linear in crease in available nitrogen (NTH2) translocation was followed by an exponential decrease, which at photosynthetic saturation continued to decrease linearly (Fig. 8d). The linear increas e in average available nitrogen translocated peaked at a maximum of 0.12 N units at a pho tosynthesis rate of 3.3%. The exponential decrease in available nitrogen declined to 0.067 N units before photosynthetic saturation (CPA = 4.2%), then decreased linearly to 0.0081 N units until steady state was reached at 8.5% CPA.

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57 -10% -8% -6% -4% -2% 0% 2% 4%0% 0. 5 % 1% 1.5% 2% 2 .5 % 3 % 3. 5 % 4% 4. 5 % 5% 5.5% 6% 6 .5 % 7% 7. 5 % 8%CPAAverage Percent Change Host (Shallow-Adapted) Algal (Shallow-Adapted) Host (Deep-Adapted) Algal (Deep-Adapted) 2.6% CPA4.2% CPA Figure 8b. Average host (%BH) and algal (%BA) percent change with an increase in algal photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 iterations using parameters as defined in Fig. 8a.

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58 0 2 4 6 8 10 12 140 % 0 .5% 1% 1.5% 2% 2. 5 % 3% 3. 5% 4% 4.5% 5% 5. 5 % 6% 6. 5% 7% 7.5% 8%CPAAverage Carbon Translocated to the Host (C units ) Shallow-Adapted Deep-Adapted2.6% CPA4.3% CPA Figure 8c. Average carbon translocated (CTA) with an increase in algal photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 iterations using para meters as defined in Fig. 8a.

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59 0 0.05 0.1 0.15 0.2 0.250% 0.5% 1% 1.5% 2 % 2 .5 % 3 % 3 .5 % 4 % 4 .5 % 5 % 5 .5 % 6 % 6 5% 7 % 7 5% 8 %CPAAverage Nitrogen Translocated to the Algae (N units) Required N (Shallow-Adapted) Required N (Deep-Adapted) Available N (Shallow-Adapted) Available N (Deep-Adapted)2.6% CPA4.3% CPA5.3% CPA Figure 8d. Average required (NTH1) and available (NTH2) nitrogen translocated with an increa se in algal photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 iter ations using parameters as defined in Fig. 8a.

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60 No excess carbon was produced in the shallow-adapted coral as all carbon was consumed, by host and algal growth until phot osynthetic saturation occurred. The peak in excess carbon produced occurred at 0.71 C un its at a photosynthesi s rate of 6.7% and decreased to 0.089 C units at steady state (Fi g. 8e). Nitrogen was excreted from the holobiont due to initial carbon limitation at low rates of photosynthesis, eventually decreasing to 0 with an incr ease in photosynthesis as the symbiosis switched to nitrogen limitation (Fig. 8e). The initial linear incr ease in nitrogen excretion peaked at a maximum of 1.3 N units at a photosynthesis rate of 3.1%, exponent ially decreased to 0.0063 N units at a photosynthetic rate of 4.5%, then linearly decreased to 0 as steady state (CPA = 8.5%) was reached. Deep-Adapted Coral The final host biomass of the deep-adapted coral ranged from 0.53 biomass units with no photosynthesis to a maximum of 99 biomass un its at the steady state. The final algal biomass of the deep-adapted coral ranged from 0.041 biomass units with no photosynthesis to a maximum of 6 bioma ss units at photosynthetic saturation (CPA = 2.6%) with steady state at 5.3% CPA producing 3.9 biomass units (Fig. 8a). The average percent change per iteration for the host ranged from -2.9% with no photosynthesis to a maximum of 2.4% with photosynthesis rates of 5.3% and higher (Fig. 8b). The average percent change per it eration for the algae ranged from -2.2% with no photosynthesis to a maximum of 3% (Fig. 8b), which wa s reached at photosynthetic saturation (CPA = 2.6%). The x-intercept for the algal average percent change was reached at a photosynthesis rate of 1.2% (Fig. 8b). The algal average percent change per

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61 0 2 4 6 8 10 12 14 160% 0.5% 1 % 1.5% 2 % 2. 5 % 3 % 3. 5 % 4 % 4. 5 % 5% 5. 5 % 6% 6. 5 % 7% 7. 5 % 8%CPAAverage Excess Carbon Production (C units)0 0.05 0.1 0.15 0.2 0.25Average Nitrogen Excretion (N units) Carbon (Shallow-Adapted) Carbon (Deep-Adapted) Nitrogen (Deep-Adapted) Nitrogen (Shallow-Adapted)2.6% CPA4.3% CPA5.3% CPA Figure 8e. Average ex cess carbon production (CEH) and nitrogen excretion (NEA) with an increase in al gal photosynthesis rate (% CPA) for shallowand deep-adapted corals over 100 ite rations using parameters as defined in Fig. 8a.

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62 iteration in the deep-adapted coral peaked at 2.6% CPA and slightly declined until steady state (CPA = 5.3%). No carbon was translocated to the host in the absence of light. With the initial input of light, the amount of carbon transloc ated to the host increased exponentially (Fig. 8c), with an increase in photos ynthesis until photos ynthetic saturation (CPA = 2.6%). The maximum amount of carbon tr anslocated to the host was 13 C units at steady state, which was reached at 5.3% CPA. No required nitrogen (NTH2) was translocated to the algae prior to steady state, which was reached at 5.3%, but the average amount of required nitrogen translocated was maintained at 0.035 N units for photosynthetic ra tes higher than steady state. There was an overall decrease in the averag e amount of available nitrogen (NTH2) translocated to the zooxanthellae (Fig. 8d). Initia lly, the average amount of ava ilable nitrogen peaked at a maximum of 0.23 N units at a photosynthesis rate of 1.8%, then rapidl y decreased to 0.06 N units at photosynthetic saturation (CPA = 2.6%), then was further reduced to 0 N units at steady state, which was reached at 5.3% CPA. No excess carbon was produced in the deep-adapted coral as it was exhausted for host and algal growth, until photosynthetic saturation occurred at a photosynthesis rate of 2.6% (Fig. 8e). When photosynthesis rates increased beyond steady state (CPA = 5.3%), the average amount of excess carbon producti on increased linearly as it could not be utilized for growth due to nitrogen limitation. Nitrogen was excreted from the symbiosis due to initial carbon limitation at low rates of photosynthesis, eventually decreasing to 0 C units with the increase in photosynthesis (CPA = 2.6%) as the symbiosis switched to nitrogen limitation (Fig. 8e).

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63 Comparison of Results In both shallow and deep-adapted corals the host and algal biomass increased exponentially with increasing photosynthesi s rates until photosynthetic saturation occurred (Fig. 8a). Photosynthetic saturation occurred at lower rates in the deep-adapted coral (CPA = 2.6%), compared to the shallow-adapted coral (CPA = 4.2%). Moreover, there was an extreme difference in biomass accumulation between the shallowand deepadapted coral. At steady state, the holobi ont biomass of the d eep-adapted coral (99 biomass units) is almost fourfold the holobiont biomass of the shallow-adapted coral (25 biomass units). The shallow-adapted coral wa s consistently nitroge n limited; whereas, the deep-adapted coral was carbon limited at low photosynthe sis rates, so increasing carbon from photosynthesis could be translated to holobiont growth. Also, the steady state of the deep-adapted coral was reached at lower photosynthesis rates (CPA = 5.3%) when compared to the shallow-adapted coral (CPA = 8.5%). The host biomass gradually increased until steady state was reached at 8.5% CPA in the shallow-adapted coral and 5.3% CPA in the deep-adapted coral. These resu lts are due to the higher default feeding rate assigned to with the deep-adapted coral. The deep-adapted coral reached steady state (CPA = 5.3%) at a lower photosynthesis rate than th e shallow-adapted coral (CPA = 8.5%). A similar trend is seen when comparing rate when positive biomass was accumulated. Positive growth in the deep-adapted coral began at photosynthesis rate of 1.3% and 1.7% for the zooxanthellae and host, respectively, and 3.7% and 4.1% for the zooxanthella e and host, respectively, for the shallow-adapted coral (Fig. 8b).

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64 With no light, there is no photosynthesis; therefore, no carbon is translocated (CTA) to the host. With an increase in phot osynthesis, the amount of carbon translocated increased exponentially until photosynthetic saturation (CPA = 4.3% for shallow-adapted, CPA = 2.6% for deep shallow-adapted, CPA= 8.5% for shallow-adapted). Nitrogen availability caused a reduction in carbon tran slocation as carbon was consumed for algal growth after photosynthetic saturation (Fig. 8c). At low photosynthesis rates, available ni trogen was translocated to maintain biomass ratios (Fig. 8d), which was comparab le between the shallowand deep-adapted coral. The amount of nitrogen translocated de creased with the increase in photosynthesis. Once the zooxanthellae became nitrogen limited at higher photosynthesis rates, the host translocated enough required nitrogen (NTH2) to maintain functional biomass ratios. At steady state, the deep-adapted coral translo cated more than thr ee times the amount of required nitrogen than the shallow-adapted coral, which was due to higher feeding rates assigned by the default values for the deep-adapted coral. With no light or low photosynthetic rate s, no photosynthate was translocated to the host; therefore, all organi c carbon was exhausted by the host’s metabolic needs, and there is no excess carbon production for either shallowand deep-adapted corals (Fig. 8e). As photosynthesis increased and photosynthetic saturation occurred, the zooxanthellae produced extra carbon that neith er the host nor algae could utilize, so a small but variable amount of excess carbon was produced. With excessive photosynthesis, the amount of excess carbon produced increased. The difference in magnitude of excess carbon production betwee n the shallowand deep-adapted was a

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65 consequence of the default values. At steady state, the deep-adapted coral produced three times more excess carbon than the shallow-adapted coral. Due to carbon limitation associated w ith low photosynthesis rates and carbon production, the nitrogen not ut ilized towards biomass growth was excreted from the holobiont until the symbiosis became nitrogen limited; then no further nitrogen was excreted (Fig. 8e). The amount of nitrogen excreted initially was 1.5 times more in the deep-adapted coral than the shallow-adapted, which is due to the higher input of organic carbon from host feeding. The d eep-adapted coral became n itrogen limited at lower rates of photosynthesis (CPA = 2.6%) than the shallow-adapted coral (CPA = 4.2%), which is also due to higher host feeding ra tes assigned by the default values. Trial 4: Varying Rates of Algal Nitrogen Uptake (NIA) In this trial, uptake of dissolved inorganic nitrogen (NIA) from the environment was examined at intervals ranging from no DIN (NIA = 0%) to excessive nitrogen uptake (NIA = 8.5%), for 100 iterations. The host feeding rate (BIH) for the shallow-adapted coral was held constant at 1% as in previous trials, and all other parameters were constant using the default values from Falkowski et al. (1984). The DIN uptak e rate is based on host biomass (BH), as it is comparable to the am ount of nitrogen input by host feeding (BIH). Each DIN uptake rate was increase d by 0.1% until steady state was reached. Table 7 shows the results for a shallow-and de ep-adapted coral. The figures for this section end at 8.5% NIA because steady states for the symbioses were reached.

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66 Table 7. Minimum and maximum results of a shallowand deep-ada pted coral with an increase in algal nitrogen uptake rate (NIA) over 100 iterations. Host feeding rate (BIH) was held constant at 1% and 2.35% fo r the shallowand deep-adapted coral, respectively, and all other parameters were held cons tant using Falkowski et al (1984) energy budget. Shallow-Adapted Deep-Adapted Parameter Minimum Value % NIA Maximum Value % NIA Steady State (NIA = 8.4%) Minimum Value % NIA Maximum Value % NIA Steady State (NIA = 1.7%) Host Biomass (biomass units) BH 25 0% 27 0.5% 26 8 0.7% 9 0% 8.1 Algal Biomass (biomass units) BA3 0.85 0% 1.6 1.9% 1.5 0.628 0.7% 0.7 0% 0.632 Host APC %BH 0.95% 0% 0.99% 0.1-5.7% 0.98% -0.19% 0.7-8.4% -0.07% 0% -0.19% Algal APC %BA 1% 0% 2% 4.7-7.3% 1.9% -0.19% 0.7-8.4% -0.07% 0% -0.19% Average Carbon Translocated (C units) CTA 15 0% 29 0.4% 27 1.6 0.7% 1.7 0% 1.6 Average Required Nitrogen Translocated (N units) NTH1 0 * 0 0 * 0 Average Available Nitrogen Translocated (N units) NTH2 0 0.5-8.5% 0.0082 0% 0 0.2266 0.7% 0.2277 0% 0.2272 Average Excess Host Carbon Production (C units) CEH 0.15 0% 8.4 0.8% 7.1 0 * 0 Average Algal N itrogen Excretion (N units) NEA 0 0-0.1% 1.4 8.4% 1.4 0.22 0% 0.93 8.4% 0.38 refers to instances that continually occu r throughout the 100 -iteration period.

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67 Shallow-Adapted Coral The final host biomass was a minimum 25 biomass units with DIN uptake rate of 0.7%, reached a maximum of 27 biomass units at the DIN uptake rate of 0.4%, then slowly declined to 26 until it maintained a steady state at 8.4% NIA. The final algal biomass followed the same trend by beginni ng with the minimum biomass of 0.85 biomass units with no DIN uptake, peaking at 1.6 biomass units at the DIN uptake rate of 0.4%, and slowly declining to 1.5 biomass units at 8.4% NIA, which was steady state (Fig. 9a). The host average percent change per itera tion initially increased from a minimum of 0.95% with no DIN uptake to a maximum of 1% at DIN uptake rates between 0.1% and 5.7% NIA, then maintained a slight decrease in growth with an increase in nitrogen uptake. The algal average percent change per iteration initially increased from a minimum of 1% with no DIN uptake to a ma ximum of 2% at DIN uptake rates between 4.7% and 7.3% NIA then maintained its steady state at 1.9% at DIN uptak e rates of 7.4% NIA and higher (Fig. 9b). The minimum amount of carbon translocated to the host was 15 C units with no DIN uptake (NIA = 0%), but with DIN available to support algal growth, the carbon translocated reached a maximum of 29 C units at 0.4% NIA. As DIN uptake became excessive, allowing the zooxanthellae to reta in their photosynthates for growth, the amount of carbon translocated to the host decr eased to 27 C units at its steady state, which was reached at 8.4% NIA (Fig. 9c). With no DIN uptake (NIA = 0%), there was a minimal amount (0.000018 N units) of required nitrogen (NTH1) translocated to the algae, which decreased to 0 with input of DIN upt ake. The maximum amount of available

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68 0 5 10 15 20 25 300 % 0.5% 1% 1. 5% 2 % 2.5% 3% 3. 5% 4% 4.5% 5% 5. 5% 6% 6 .5% 7% 7.5 % 8% 8 .5%NIAHost Biomass (biomass units)0 0.5 1 1.5 2 2.5 3Algal Biomass (biomass units) Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted) Figure 9a. Final host (BH) and algal (BA) biomass with an increase in algal nitrogen uptake rate (% NIA) for shallowand deepadapted corals over 100 iterati ons using default parameters from Falkowsk i et al. (1984) with host feeding rate (BIH) set at 1% for the shallow-adapted coral and 2.35% for the deep-adapted coral.

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69 -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5%0 % 0 .5 % 1% 1. 5 % 2% 2. 5 % 3% 3. 5 % 4% 4.5% 5% 5 .5 % 6 % 6 .5 % 7 % 7. 5 % 8% 8. 5 %NIAAverage Percent Change Host (Shallow-Adapted) Algal (Shallow-Adapted) Host (Deep-Adapted) Algal (Deep-Adapted) Figure 9b. Average host (%BH) and algal (%BA) percent change with an increase in algal nitrogen uptake rate (NIA) for shallowand deep-adapted corals over 100 iterations using parameters from Falkowski et al. ( 1984) as defined in Fig. 9a.

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70 0 2 4 6 8 10 12 14 16 18 200% 0. 5 % 1% 1.5% 2% 2.5% 3% 3 5% 4 % 4 5% 5% 5. 5 % 6% 6.5% 7% 7.5% 8% 8.5%NIAAverage Carbon Translocated to the Host (C units) Shallow-Adapted Deep-Adapted Figure 9c. Average in carbon translocated (CTA) with an increase in alga l nitrogen uptake rate (NIA) for shallowand deep-adapted corals over 100 iterations using pa rameters from Falkowski et al (1984) as defined in Fig. 9a.

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71 nitrogen (NTH2) translocated to the zooxanthellae was 0.0082 N units with no DIN uptake (NIA = 0%) and decreased to 0 N units at the DIN uptake rate of 0.5% (Fig. 9d). Since the shallow-adapted coral was in itially nitrogen limited, excess carbon was produced at a minimum of 0.15 C units with no DIN uptake (NIA = 0%) but quickly increased to a maximum of 8.4 C units at a DIN uptake rate of 0.8% (Fig. 9e). With the increase of DIN uptake, the amount of carbon translocated decrea sed to 7.1 C units at higher rates of nitrogen uptake (8.4% NIA). Nitrogen excretion di d not occur at low DIN uptake rates (0-0.1% NIA) but increased linearly to 1.4 N units with an increase in DIN uptake until steady state (NIA = 8.4%) occurred, which was when the coral-algal symbiosis switched from nitroge n limitation to carbon limitation. Deep-Adapted Coral Because the default values for the deep -adapted coral maintained light-limited nutrition, the final host biomass of the deep-a dapted coral was its maximum at 9 biomass units with no DIN uptake, then decreased a nd maintained a minimum of 8 biomass units at 1.7% NIA and higher (Fig. 9a). The final algal biomass of the deep-adapted coral followed the same trend. The maximum al gal biomass was 0.7 biomass units with no DIN uptake and decreased and maintained a minimum of 0.63 biomass units at steady state (1.7% NIA). The host average percent change per ite ration was always negative, indicating biomass consumption or negative growth (F ig. 9b). The minimum amount of biomass consumption was -0.07% with no DIN upt ake, reaching and maintaining maximum biomass consumption of -0.19% when it reached steady state at 1.7% NIA. The average

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72 0 0.05 0.1 0.15 0.2 0.250% 0 5% 1 % 1 .5 % 2 % 2.5% 3 % 3 5% 4 % 4 5% 5% 5 .5 % 6 % 6 .5 % 7 % 7.5% 8 % 8 5%NIAAverage Nitrogen Translocated to the Algae (N units) Required N (Shallow-Adapted) Required N (Deep-Adapted) Available N (Shallow-Adapted) Available N (Deep-Adapted) Figure 9d. Average required (NTH1) and available (NTH2) nitrogen translocated with an increa se in algal nitrogen uptake rate (NIA) for shallowand deep-adapted corals over 100 iterations using pa rameters from Falkowski et al (1984) as defined in Fig. 9a.

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73 0 1 2 3 4 5 6 7 8 90 % 0.5% 1% 1.5% 2% 2 .5 % 3% 3. 5 % 4% 4. 5 % 5 % 5. 5 % 6 % 6.5% 7% 7.5% 8% 8 .5 %NIAAverage Excess Carbon Production (C units)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Average Nitrogen Excretion (N units) Carbon (Shallow-Adapted) Carbon (Deep-Adapted) Nitrogen (Shallow-Adapted) Nitrogen (Deep-Adapted) Figure 9e. Average excess carbon production (CEH) and nitrogen excretion (NEA) with an increase in algal nitrogen uptake rate (NIA) for shallowand deep-adapted corals over 100 iterations using parameters from Falkow ski et al. (1984) as defined in Fig. 9a.

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74 algal percent change per iteration followed the same trend. Carbon translocation followed a similar tr end as biomass for the deep-adapted coral. The maximum average amount of carbo n translocated to the host was 1.7 C units with no DIN uptake, but decreased to a mini mum of 1.6 C units with input of DIN at rates of 0.7%. Once steady state was reached at 1.7% NIA, average carbon translocated remained at 1.6 C units (Fig. 9c). There was no required nitrogen (NTH1) translocated to the zooxanthellae with the increase in DIN uptake rates due to the holobiont being ov erall carbon limited using the default values. The maximum average amount of available nitrogen translocated to the zooxanthellae was 0.2277 N units with no DIN up take, decreasing slightly to a minimum of 0.2266 N units at the DIN uptake rate of 0.7%, then remained stable at 0.2272 N units at steady state (NIA = 1.7%) and higher rates of DIN uptake (Fig. 9d). Overall, the deep-adapted coral was car bon-limited; therefore, no excess carbon was produced with an increase in DIN uptake (Fig. 9e). However, there was an increase in nitrogen excretion with the increase in nitrogen uptake (Fig. 9e ), since the DIN from the environment could not be utilized as a c onsequence of light (i.e ., carbon) limitation. The minimum average amount of nitrogen excretion was 0.22 N units with no DIN uptake, and the maximum average of nitr ogen excretion was 0.93 N units at maximum DIN uptake (NIA = 8.4%). Comparison of Results The shallowand deep-adapted corals responded in an opposite manner from each other with an increase in DIN uptake by the z ooxanthellae (Fig. 9a). There was an initial

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75 increase in biomass of the shallow-adapte d coral because the corals and zooxanthellae were nitrogen limited. Because the deep-adapt ed coral was carbon limited, the input of DIN was of no advantage to the symbiosis. The biomass of the shallow-adapted coral peaked at low DIN uptake (NIA = 0.4%), decreasing with highe r rates of nitrogen uptake; whereas, the deep-adapted coral decreased wi th the input of DIN because, as shown in Trial 1, the default values used were insu fficient to maintain the holobiont. In the shallow-adapted coral, the host biomass (BH) increased by 7%, and the algal biomass (BA) increased by 47% with low rates of DIN up take, but as DIN uptake increased past a rate of 0.4% NIA, the host biomass decreased by 4% and the algal biomass decreased by 6% until steady state (8.4% NIA) was reached. In the deep-adapted coral, there was an overall decrease in biomass for both the host (BH) and algal (BA) by 10% with the increase in uptake of DIN. As DIN uptake increased past a rate of 0.7% NIA, the host and algal biomass decreased by 2% and 1%, respectively, until steady state (1.7% NIA) was reached (Fig. 9a). As a direct result of the increase in biom ass, the average host percent change of the shallow-adapted coral incr eased exponentially with the in itial input of DIN, peaking between 0.4% and 0.5% NIA, and remaining stable at above 1.2% NIA (Fig. 9b). The average algal percent change al so increased exponen tially with input of DIN, peaking at slightly higher DIN uptake rates (4.7% to 5.5% NIA), stabilizing with the continued increase in DIN uptake. With decreasing host and algal biomass, the host and algal percent change of the deep-adapted coral initially decreased to 0.7% NIA, then stabilized (Fig. 9b).

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76 Carbon translocation followed a similar tr end because the shallow-adapted coral was initially nitrogen limited, and therefore co uld benefit from the slight increase in DIN uptake. On the other hand, the deep-adapted coral was carbon limited using the default values (Falkowski et al., 1984), so the i nput of DIN only increased algal biomass as photosynthates were retained for algal grow th. There was abundant carbon within the symbiosis of the shallow-adapted coral, and the amount of carbon translocated (CTA) exponentially increased with the initial input of dissolved inorgani c nitrogen, peaked at algal nitrogen uptake rate s between 0.4% and 0.5% NIA, and then dropped slightly at minimal nitrogen uptake (1.2% NIA) remaining stable when the symbiosis became carbon limited. In the deep-adapted coral, the amount of carbon translocated (CTA) decreased exponentially at DIN uptake rate of 0.6% (Fig. 9c). A small increase in DIN uptake by the zooxanthellae resulted in some growth of the shallow-adapted coral initially because default values reflected nitrogen limitation. But when DIN became abundant, the symbiosis became carbon limited, compromising growth. Above the DIN uptake rate of 0.4%, there was no required nitrogen (NTH1) translocation in the shallow-adapted coral, because nitrogen was available to the zooxanthellae from the environment. However, there was available ni trogen translocated (NTH2) in the deep-adapted coral indicating th at the coral must utilize some of its heterotrophic input for respiration a nd other metabolic needs (Fig. 9d). Excess carbon was produced in the shallow-adapted coral, which initially increased exponentially until the DIN uptake ra te of 0.4%, then declined until stabilizing at an extremely high nitrogen uptake rate (NIA = 8.4% and higher). There was no excess carbon production in the deep-adapted coral. Nitrogen excretion in both the shallowand

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77 deep-adapted coral increased linearly with the increase in DIN uptake due to carbon limitation (Fig. 9e).

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78 Discussion Each parameter within the coral-algal sy mbiosis can have a significant effect on growth rates, mucus, skeletal, and lipid produ ction, as well as the translocation of carbon and nitrogen between the coral host and its symbiotic algae. Within my model, all parameters such as respiration rates (e.g., as a proxy for temperature), mucus production (e.g., as a proxy for sediment loads), skel etal production (e.g., as a proxy for water chemistry), and lipid production (indicating reproductive success) can be manipulated. However, for the purpose of my thesis, only host feeding rates, photosynthesis rates (as a proxy for light), and DIN uptake rates (as a pr oxy for DIN availability) were examined individually. Host/Algal Biomass Ratio Host/algal biomass ratio built into th e model restrict the maximum holobiont to 105% for the shallow-adapted co ral and 104% for the deep-adapt ed coral. As noted in the Comparison of Results for each trial, default values of the shallow-adapted coral result in nitrogen limitation, and those for the deep-adapted coral result in carbon limitation. The minimum and ma ximum biomass ratios are necessary assumptions for the model to lim it the zooxanthellae from outgrowing the host or the host from outgrowing the algae. Figure 10 shows the results without this assumption of functional biomass ratios. Over 100 iterations, the host exhausts the

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79 organic input from host feeding for its grow th, leaving the zooxant hellae nitrogen limited and remaining at the default value. The assu mption of the biomass ra tios requires either nitrogen be translocated when the zooxanthe llae falls below the minimum ratio or limits algal growth, resulting in nitrogen excretion fr om the holobiont. Another possible reality would be continued algal growth, with hos t expulsion of algal cells above a fixed concentration. The minimum biomass ratio prevents th e host from outgrowing the zooxanthellae in trials where the holobiont was nitrogen limited, i.e., in the trial examined the increase in host feeding in the shallow-adapted cora l (Fig. 11). In other trials, the maximum biomass ratio prevented the zooxanthellae from outgrowing the host, e.g., an increase in host feeding for the deep-adapted coral (Fi g. 12) and the increase in nitrogen uptake for both the shallow-adapted and deep-adapted coral (Fig. 13). Lastly, trials with increased algal photosynthesis rates used both minimum and maximum biomass ratios to maintain a functional symbiosis for both the shallowand deep-adapted corals. Initially, the zooxanthellae were prevented from outgrowing the host by the maximum biomass ratio up to photosynthetic saturation. Photosynthetic saturation occurred at the at which carbon limitation to nitrogen limita tion. Algal biomass fluctuated during this transition to steady state, resulting in a nitrogen-limite d symbiosis, under which the biomass-ratio assumption maintained the minimum algal biom ass (Fig. 14). An a dditional modification to the model could be to allow the algal biom ass to rapidly drop to simulate bleaching,

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80 1 10 100 1000 10000 110192837465564738291100Iteration (time, x)Host Biomass (biomass units) in logarithmic scale0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50Algal Biomass (biomass units) Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted) Figure 10. Host (BH) and algal (BA) biomass for shallowand deep-adapted corals over 100 iterations w ithout the assumption of maintaining functional biomass ratios.

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81 0 10 20 30 40 50 60 70 80 90 100 110192837465564738291100Iterations (time x)Host Biomass (biomass units)0 50 100 150 200 250 300 350Algal Biomass (biomass units) Host (Shallow-Adapted) Host (Deep-Adapted) Algal (Shallow-Adapted) Algal (Deep-Adapted) Figure 11. Host (BH) and algal (BA) biomass for shallowand deep-adapted corals over 100 iterations w ithout the assumption of maintaining functional biomass ratios. DIN was held constant at 8.5% to show how the zooxanthellae will outgrow the host witho ut if a maximum biomass ratio is not maintained.

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82 0 50 100 150 200 250 300 350 4000% 0. 5 % 1.0% 1.5% 2 .0% 2 .5% 3. 0 % 3. 5 % 4.0% 4.5% 5 .0% 5 .5% 6 .0 % 6. 5 %BIHHost/Algal Biomass Ratio and Algal Biomass (biomass units) in a Shallow-Adapted Coral0 5 10 15 20 25 30 35 40 45 50Host/Algal Biomass Ratio and Algal Biomass (biomass units) in a Deep-Adapted Coral Algal (Shallow-Adapted) Minimum Host/Algal Biomass Ratio (Shallow-Adapted) Maximum Host/Algal Biomass Ratio (Shallow-Adapted) Algal (Deep-Adapted) Minimum Host/Algal Biomass Ratio (Deep-Adapted) Maximum Host/Algal Biomass Ratio (Deep-Adapted) Figure 12. Minimum and maximum biomass ratios ex amining the increase in host feeding rates (BIH) of the shallowand deepadapted coral.

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83 0 0.5 1 1.5 2 2.5 3 3.50 % 0.5% 1% 1 .5 % 2 % 2.5% 3% 3 .5% 4 % 4.5% 5% 5 .5% 6% 6. 5 % 7 % 7.5% 8% 8. 5 %NIAHost/Algal Biomass Ratio and Algal Biomass (biomass units) in a Shallow-Adapted Coral0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Host/Algal Biomass Ratio and Algal Biomass (biomass units) in a Deep-Adapted Coral Algal (Shallow-Adapted) Minimum Host/Algal Biomass Ratio (Shallow-Adapted) Maximum Host/Algal Biomass Ratio (Shallow-Adapted) Algal (Deep-Adapted) Minimum Host/Algal Biomass Ratio (Deep-Adapted) Maximum Host/Algal Biomass Ratio (Deep-Adapted) Figure 13. Minimum and maximum biomass ratios examini ng the increase in algal nitrogen uptake rates (NIA) of the shallowand deep-adapted coral.

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84 0 0.5 1 1.5 2 2.5 30% 0 .5% 1 % 1. 5% 2% 2. 5% 3% 3.5% 4% 4.5% 5% 5.5% 6 % 6. 5% 7% 7. 5% 8%CPAHost/Algal Biomass Ratio and Algal Biomass (biomass units) in a Shallow-Adapted Coral0 1 2 3 4 5 6 7 8 9Host/Algal Biomass Ratio and Algal Biomass (biomass units) in a Deep-Adapted Coral Algal (Shallow-Adapted) Minimum Host/Algal Biomass Ratio (Shallow-Adapted) Maximum Host/Algal Biomass Ratio (Shallow-Adapted) Algal (Deep-Adapted) Minimum Host/Algal Biomass Ratio (Deep-Adapted) Maximum Host/Algal Biomass Ratio (Deep-Adapted) 4.3% CPA2.6% CPA Figure 14. Minimum and maximum biomass ratios examin ing the increase in al gal photosynthesis rates (CPA) of the shallowand deep-adapted coral.

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85 for example, if photosynthesis and respirat ion rates were both randomized and set to trigger bleaching when both rates simultaneously exceeded set thresholds. Heterotrophic Feeding Due to the difficulties associated with analysis of consumed prey (Ferrier-Pages et al., 2003), heterotrophic feeding is probably th e least-understood charact eristic in corals. Ferrier-Pages et al. (2003) showed that Stylophora pistillata fed mainly on copepods in their experiment, despite the sm all size of the polyps. Unfort unately, there are relatively few studies on this topic. Food sources re ported for coral are mainly bacteria and zooplankton (Johannes et al., 1970; Sorokin, 1993; Lewis, 1992; Sebens et al., 1996, Ferrier-Pages et al., 2003), a nd others (Ferrier-Pages et al., 2003) have suggested that both dissolved and particulate organic matter can be consumed by coral. The holobiont cannot grow without nutrient inputs; therefor e, heterotrophic feed ing is considered a source of “new” nitrogen, as compared to “recycled” nitrogen, to the coral-algal symbiosis (Ferrier-Pages et al., 2003). Nitrogen from heterotrophic feeding is assumed to be available to the host first (Piniak, 2003; Piniak and Li pschultz, 2004), and is translocated when necessary to maintain algal densities. Piniak et al. (2003) reported that w ithin a few hours after feeding, approximately 20% of the nitrogen assi milated was present in the zooxanthellae. This does not allow sufficient time for digest ion, synthesis into protein or biomass, catabolism, or excretion by the host. To acc ount for this, the zooxanthellae may take up nitrogen as the prey is being digested by th e host within the coelenteron, most likely as ammonia (Piniak and Lipschultz, 2002; Piniak et al., 2003; Piniak and Lipschultz, 2004),

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86 which supports the assumption that the initia l translocation of nitr ogen is necessary to maintain minimal biomass ratios. If no nitr ogen is needed by the zooxanthellae directly, I assume the nitrogen is assimilated by the hos t to biomass until all nitrogen or carbon is exhausted. The surplus, or available (NTH2) nitrogen from host feeding and metabolism, if any, is translocated to the algae to be utilized for growth; if the zooxanthellae are carbon-limited, the excess nitrogen (NEA) is excreted from the holobiont. With further studies of th e coral-algal symbiosis, the earlier assumption of nitrogen being recycled between the cora l and algae (e.g., Muscatine and Porter, 1977; Hallock, 1981) is being explor ed. Traditionally, the zoox anthellae were assumed to assimilate the host’s wastes pr oducts in the form of compounds such as amino acids, and return some percentage of these products to the coral host (Piniak and Lipschultz, 2004). Muscatine et al. (1972) and Fal kowski et al. (1984) showed that nitrogenous products are minor components of the translocated materi al from the zooxanthellae, which supports the translocation of only carbon within my model. In other previous studies, nitrogen was observed to be translocated from the hos t to the zooxanthellae, but not the reverse (Piniak, 2001; Piniak and Lipschultz, 2002; Pi niak et al., 2003; Piniak and Lipschultz, 2004). Kelty (2000) showed that phosphorus was translocated from the host to the zooxanthellae, which also supports the assump tion in my model that primarily carbon is translocated from the algae to the host, while major nutrients assimilated from heterotrophic feeding can be translocated from the host to the algae. Wang and Douglas (1998) suggested that nitrogen conservation is linked to car bon supply rather than to the presence and abundance of the zooxanthellae. In my model, I assume that if there is not

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87 enough carbon to utilize all nitrogen available for algal growth, the excess nitrogen is excreted. Szmant-Froelich and Pilson ( 1977, 1984) showed that feeding frequency affects nitrogen excretion; my model for the deep-adapted coral similarly shows an increase in nitrogen excretion with the increase in host feedin g rate (Fig. 7e). Overall, an increase in feeding can in fluence algal density, which indirectly affects photosynthesis rates (Muscatine et al., 19 89; Titlyanov et al., 2000). In my model, total assimilation of carbon by photosynthesis is based on algal biomass; therefore, the more the zooxanthellae grow, the more the algal can photosynthesize, creating a positive correlation between heterotrophic feeding, algal biomass, and photosynthesis due to nitrogen limitation. The shallow-adapted coral, as seen in Figures 7a and 7c, exhibit these increases due to the tr anslocation of required nitr ogen, assimilated from host feeding, for algal growth. Ferrier-Pages et al. (2003) reported that heterotrophi c feeding increased tissue growth by 2 and 8 times. In my models, the e xponential growth of shallowand deep-adapted coral with the in crease in host feeding rates reflects this reality. Studies have shown that deeper corals acquire most of their metabolic energy from feeding. Muscatine and Kaplan (1994), Grottoli and Wellington (1999), and Grottoli (2000) demonstrated a strong zoopla nkton isotopic signature in deep corals. In my model for the shallow-adapted coral, th e zooxanthellae directly consume nitrogen from the host to maintain a minimum biomass ra tio; whereas, in a deep-adapted coral, the host translocates the excess nitrogen to the zo oxanthellae while restraining algal growth to the maximum biomass ratio as seen in Figure 11.

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88 Starvation of corals causes a reduction in host biomass (Szmant-Froelich and Pilson, 1980; Cook et al., 1988), calcification ra tes (Reynaud et al., 2002; Houlbreque et al., 2003; Ferrier-Pages et al., 2003), algal division rates, ch lorophyll content (Cook et al., 1988; McAuley and Cook, 1994; Reynaud et al., 2002) and photosynthe sis rates (SzmantFroelich, 1981; Cook et al., 1992; McAuley and Cook, 1994; H oulbreque et al., 2003). But starvation also can increase rates of hete rotrophic feeding (Ferrier -Pages et al., 2003) and the uptake of inorganic nitrogen by th e algae (Wilkerson and Muscatine, 1984; Muller-Parker et al., 1988, 1994; D’Elia and Cook, 1988). For starved corals in my model, nitrogen becomes availa ble by the catabolism of biomass and is translocated. If there is available carbon in combination w ith the translocated nitrogen, biomass is assimilated, and nitrogen excretion rates are lo wer (Piniak and Lipschultz, 2004). This is seen in Figure 7e, where low amounts of n itrogen were excreted from the symbiosis at low rates of host feeding and increase with the increase in feeding rate. Light Light plays an important role in the bioe nergetics of hermatypic corals due to the symbiotic relationship between coral and its alg ae (Odum, 1971). Photosynthetic carbon (photosynthate) produced by the zooxanthellae is one of several possible sources of reduced carbon available to corals as an ener gy source. Variations in irradiance reaching the benthos are caused by season, varying cloud cover, turbidity, and sedimentation loads (Anthony and Hoegh-Guldberg, 2002), all of whic h can potentially influence the rate of algal photosynthesis and potential ly the amount of photosynthate that is translocated to the coral host. Light also varies with wa ter transparency and latitude (Kirk, 1994), but

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89 mainly with depth (Chalker, Dunlap, and Oliver, 1983; Oliver, Chalker, and Dunlap, 1983), as do associated responses in photosynthesis and growth. In my model, I used photosynthesis rates as a proxy for light. Reduced rates of photosynthesis reduce the amount of photosyntha te translocated to the host (Fig. 8c, lower rates of photosynthesis). In contrast, excess light can result in a surplus of photosynthate, which may be transferred to ca rbon storage products, su ch as wax esters (McCloskey and Muscatine, 1984), free sugars glycerol, which minimizes the energy consumption inside the chloroplasts, and glucos e, (Titlyanov et al., 2000), or excreted as mucus (Hallock, 2001). Within my model, phot osynthesis rates are assumed to increase in direct proportion to increas ing irradiance, but eventually photosynthesis rates becomes saturated (Fig. 8c), peaking at a maximum gross photosynthetic rate (CPA = 4.2% for the shallow-adapted coral, CPA = 2.6% for the deep-adapted coral). At higher irradiance, photoinhibition and bleaching occurs (Winters et al., 2003), and, as not ed above, could be simulated with some modifications to my model. Not only can excess irradiance induce photoinhibition (Fig. 8c, high rates of photos ynthesis), but other factors that are associated with high irradian ce, such as high temperature and elevated oxygen tensions can significantly reduce photosynthe sis rates of the zooxanthellae. Several studies have shown differences between lightand shade-adapted (shallowand deep-adapted, respectively) corals ; for example, the Falkowski et al. (1984) energy budget used as the default values in my model. Anthony and Hoegh-Guldberg (2003) demonstrated that photo synthesis varies significan tly across habitats when normalized to surface area and that daily rate s of net photosynthesis are likely to cover only maintenance costs of shade-adapted cora ls. My default values for photosynthesis

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90 rate of the deep-adapted coral could not sust ain the host metabolic needs; and therefore, consumed organic carbon to satisfy the re maining demand (Fig. 6a). McCloskey and Muscatine (1984) showed that light-adapted corals are potentially photoautotrophic with respect to photosynthate satisfying their maintenance respiration; while shade-adapted corals require additional heterotrophic sources to maintain their meta bolism, as seen in my model (Fig. 6a). McCloskey and Muscatine (1984) dem onstrated that both gross and net photosynthesis in corals decreased by more than 75% between 3 and 35 m due to decreased irradiance with depth, not as a c onsequence of reduced coral-tissue thickness or biomass. The default value used for phot osynthesis rate of deep-adapted coral (CPA = 1.6%) is five times lower than the photosynt hesis rate of the shallow-adapted coral (CPA = 8.4%). Wethey and Porter (1976) demonstrated that deeper-dwelling individuals saturate their photosynthetic machinery at lower radiat ion intensities when compared to shallowdwelling individuals. In my model, the deep-adapted coral reached photosynthetic saturation (CPA = 2.6%) at lower photosynthesis rate s than the shallow-adapted coral (CPA = 4.2%). Anthony and Fabricius (2000) demonstrated that during periods of reduced irradiance, the energy balance of zooxanthellae may become compromised. Franklin et al. (1996) and Hoegh-Guldberg a nd Jones (1999) demonstrated that exposure to high irradiances can stress or damage the photosystems of the zooxanthellae, but overall, hermatypic corals show a wide varian ce in light tolerances, not only at various depths, but between shaded and non-shaded in dividuals (Fricke and Schuhmacker, 1983; Titlyanov and Latypov, 1991).

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91 Studies have reached different conclu sions as to whether light affects zooxanthellae densities. Studies focusing on changing light regimes that have reported either no change or an increas e in zooxanthellae density wi th shading or depth include Drew (1972); Redalje (1976); Davies (1977); Svoboda and Poorman (1980); and Falkowski and Dubinsky (1981). However, T itlyanov et al. (1980) and Muscatine et al. (1984) reported some decrease in zooxanthellae de nsity in shade-adapted or deep corals. In my model with respect to depth or shad e versus non-shaded individuals, zooxanthellae densities are dependent on nitr ogen and carbon availability w ithin the symbiosis and are maintained by minimum and maximum bioma ss ratios (Fig. 12). However, as noted previously, high rate of excess nitrogen excr etion can functionally include expulsion of zooxanthellae when the zooxanthellae out grow the host (Jones and Yellowlees, 1997). McCloskey and Muscatine (1984) reported that the translocated photosynthate seems to be released to the host only af ter the zooxanthellae needs are satisfied, suggesting that the zooxanthellae control phot osynthate translocati on independently of host’s demands, which is an assumption of my model. With depth, a shift toward heterotrophy is apparent as symbiont photos ynthesis becomes limited by light (Muscatine et al., 1984; Porter et al., 1984). This is al so assumed in my model by having a higher feeding rate for the deep-adapted coral (BIH = 2.4%) when compared to the shallowadapted coral (BIH = 1%). There are several possible mechanisms of photoadaptation or photoacclimation suggested by Titlyanov et al. (2000), wh ich include acclimating to excess light by decreasing the zooxanthellae density and the photosynthetic pigments of the zooxanthellae, and oppositely for the reduction in light, increasing z ooxanthellae density

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92 and photosynthetic pigments of the zooxanthe llae. In reduced light, zooxanthellae densities (Drew, 1972; Titlyanov et al., 1980; McCloskey and Muscatine, 1984; Porter et al., 1984) and chlorophyll concentrations (Titlyanov et al., 1980; Falkowski and Dubinsky, 1981) tend to increase, but algal di vision rates decrease (Titlyanov et al., 1996). McCloskey and Muscatine (1984) and Anthony and Hoegh-Guldberg (2003) reported an increase in photosynthesis rates wi th low light availability, which is not an expected reaction to decrea sed chlorophyll and zooxanthella e densities, but may be explained by a survival reaction to increase chlorophyll accumulation to allow for sustained photosynthetic capabilit ies stimulated by the decrease in algal metabolism. The inverse relationship between zooxanthellae de nsity and algal division rates was also reported by Titlyanov et al. (2000), and may be used as a mechanism to minimize selfshading of the zooxanthellae (M cCloskey and Muscatine, 1984). Nutrients Past studies have documented the ability of corals to remove inorganic nutrients from seawater (Franzisket, 1974; D’Elia 1977; D’Elia and Webb, 1977; Muscatine and D’Elia, 1978; Burris, 1983; Bythell, 1990). Nu trient concentrations range from 0.1 to 0.5 M nitrate, 0.2 to 0.5 M ammonium, and le ss than 0.3 M phosphorus in reef waters (Furnas, 1991). The presence and abundance of nutrients influences the coral-algal symbiosis, mainly affecting the translocation of carbon from the algae to the host. The coral-zooxanthellae symbiosis is energetically most advantageous in nutrient-deplete (oligotrophic) environments, as seen in Figur e 9a, and with the continued increase of nutrients to the marine environment, nutri ent-loving organisms can out compete corals

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93 (Falkowski, 1977; Smith et al., 1981). Mortalit y, reduced growth rates, reduced gamete production and larvae settlement and reduced skeletal density are all consequences of nutrient enrichment on corals (Hoegh-Guldbe rg and Smith, 1989; Muscatine et al., 1991; Stimson and Kinzie, 1991; Muller-Parker et al., 1994; Stambler et al., 1994; HoeghGuldberg, 1999; many others), which are sim ilar to the implications of my model. Effects of nutrient enrichment are dependent on chemical composition and concentrations (Ferrier-Pages et al., 2000) and include the increase of zooxanthellae densities and chlorophyll concentrations (Wiebe, 1975; D’Elia and Webb, 1977; Muscatine, et al., 1991; Titlyanov et al., 2000) which was indicated by my model. When excess nitrogen is available to the zooxanthe llae, the photosynthate is retained for their own growth (Dubinsky et al., 1990), and only a minimal amount of photosynthate, if any, is translocated to the coral, as seen in my model even with low levels of DIN uptake by the zooxanthellae of the shallow-water coral (Fi g. 9a). As a consequence, the coral must consume carbon from its heterotrophic resour ces to provide energy for respiration and other metabolic costs, allowing for nitrogen to be translocated to the algae, which may be used for algal growth or excreted (Fig. 9d). Grover et al. (2002) reported that nitrogen uptake rates were influenced by the amount of heterotrophic f eeding. For example, wellfed individuals showed an inhibition of nitrogen uptake since there is significant translocated nitrogen to the algae (Cook et al., 1988; D’Elia and Cook, 1988; and MullerParker et al, 1988). Critical parameters for the nitrogen budget within the coral-al gal symbiosis are the assimilation efficiencies of the coral taking nitrogen from i ngested prey and the zooxanthellae absorbing DIN from the environm ent. There are a num ber of factors that

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94 influence the assimilation of nitrogen, wh ich include the amount and frequency of heterotrophic feeding (Anthony, 1999), the a bundance of zooxanthellae (Steen, 1986; Piniak et al., 2003), whether the nitrogen is organic or inorganic, and metabolic rates (Piniak and Lipschultz, 2004). Rates of 80-100% nitrogen assimilation from fine, suspended, particulate matter and 40-100% for de posited natural, part iculate matter were observed by Mills (2000) and Mills et al. (2004) for corals found in Bermuda. Piniak et al. (2003) reported nearly 100% assi milation for the temperate coral Oculina carbuncular but when zooxanthellae densities were low, reported only 50% assimilation of ingested nitrogen. If there is abundant dissolved inorganic nitr ogen available in the environment, the excess nitrogen should co mpensate for lack of organic nitrogen, reducing the assimilation efficiency for inge sted food. It was also reported that the assimilation efficiency was higher in starved corals than fed corals, but between the nutrient regimes, there was no differe nce (Piniak and Li pschultz, 2004). Growth rates of S. pistillata are influenced greatly by the abundance of nitrogen. At slightly increased levels of ammonia (10 M), the growth rates of S. pistillata were unaffected, but at higher concentrations ( 20 M), they were rapidly reduced. Both nitrogen and phosphorus reduced growth rate (Ferrier-Pages et al., 2000). At 15 M ammonia, skeletal growth rates of Porites damicornis decreased (Stambler et al., 1991). Nitrate most often induces a decrease in grow th and calcification (F errier-Pages et al., 2000). At low concentrations of amm onia (1 M), the growth rates of Porites furcata were enhanced (Meyer and Schultz, 1985).

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95 Recommendations for Future Work There are many possibilities of varia tions, situations, circumstances, and conditions that can create di rect and indirect impacts in the environment, a community, population, or species. My study summarizes th e effects of several basic parameters, such as feeding rates as a proxy for food availability, photos ynthesis rates as a proxy for light, and nitrogen uptake rates for a proxy of dissolved inorganic nitrogen availability, upon the transfer of energy and nutrients within the host and algal symbiosis. There are numerous other variables that can be manipulated, such as respiration rates as a proxy for water temperature and mucus production as a proxy for sediment load. Other possibilities that could be included are the expuls ion of algal biomass as seen in bleaching events and include the associ ated energy consumption, energy use for the active uptake of other inorganic nutrien ts, such as phosphorus and iron, energy consumption during translocation of carbon a nd nitrogen, the reliance on lipid storage during starvation, and many others, to define mechanisms with more detail and accurately determine metabolic demands within the symbiosis. As previously discussed, manipulating feeding, photosynthetic, and nitrogen uptake rates as proxies for va rying environmental conditions were ways to immediately explore my model, but there are many other appr oaches to derive insi ght from my model. Because zooxanthellate scleractinian corals likely follow the conceptual theory, my model can be applied to different species besides S. pistillata simply by changing biomass rations and other species-sensitive energetic rates. Another subject for discussion would be to apply values that maintain neutral or positive growth in shade-adapted corals by increasing the input of carbon, whether from

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96 host feeding, algal photosynthesis, or a comb ination of both, in an amount adequate to meet energy demands. Since the default values for S. pistillata were insufficient to meet its energy demands (Fig. 6a), the increase in feeding rate to 2.5% (Fig. 15) or photosynthesis rate of 1.7% would assim ilate adequate carbon to suffice the host metabolic demands (Fig. 16). Using the hi gher default values also might change interpretations of responses to, e.g., DIN uptake. Varying multiple parameters simultaneously is another capability within my model. The trends which I observed by vary ing one parameter independently have been discussed previously. By varying combinat ions of parameters, the trends can be comparatively altered among the parameters. Detailed analysis manipulating two pa rameters simultaneously are beyond the scope of this thesis. However, Figures 17 and 18 were generated for the shallow-adapted corals respectively to demonstrate the po tential for two-parameter manipulations. Increased feeding rates alone caused exponential growth with in the symbiosi s (Fig. 7a), but concurrently altering phot osynthetic rate caused photosynth etic saturation to occur at various levels (Fig. 17 ). Increased rates of dissolved nitrogen uptake restricted biomass growth with the increase in photosynthesis rates for both the shallow-adapted and deepadapted corals (Fig. 18). An approach that I recommend for future st udies is to utilize the equations I have developed using software that is better desi gned for modeling applic ations. Programming macros in EXCEL worked reasonably well for single parameter runs, but as the macros started interfacing with multiple files, th e program would freeze. Other software

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97 8 8.5 9 9.5 10 10.5 11 110192837465564738291100Iterations (time x)Host Biomass (biomass units)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Algal Biomass (biomass units) Host (2.4% BIH) Host (2.5% BIH) Algal (2.4% BIH) Algal (2.5% BIH) Figure 15. Final host and algal biom ass with host feeding rate (BIH) set at 2.4% and 2.5% to show change from negative to positive growth.

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98 0 2 4 6 8 10 12 14 110192837465564738291100Iterations (time x)Host Biomass (biomass units)0 0.2 0.4 0.6 0.8 1 1.2Algal Biomass (biomass units) Host (1.6% CPA) Host (1.7% CPA) Algal (1.6% CPA) Algal (1.7% CPA) Figure 16. Final host and algal biom ass with the photosynthesis rate (CPA) set at 2.4% and 2.5% to show change from negative to positive growth.

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99 16% CPA14% CPA12% CPA10% CPA8% CPA6% CPA0% CPA2% CPA4% CPA3% BIH2% BIH1% BIH0.1% BIH0.01% BIH0.001% BIH0% BIH-10% -8% -6% -4% -2% 0% 2% 4%Average Percent Change per Iteration0% CPA2% CPA0.01% BIH0.001% BIH1% BIH Figure 17. Trends associated w ith increasing host feeding (BIH) and algal photosynthesis (CPA) rates simultaneously in a shallowadapted coral.

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100 8% NIA9% NIA10% NIA0% NIA0.1% NIA1% NIA2% NIA3% NIA4% NIA5% NIA6% NIA7% NIA16% CPA14% CPA12% CPA10% CPA8% CPA6% CPA4% CPA2% CPA0% CPA-8% -7% -6% -5% -4% -3% -2% -1% 0% 1% 2%Average Percent Change per Iteration Figure 18. Trends associated with increasing algal photosynthesis (CPA) and nitrogen uptake (NIA) rates simultaneously in a shallowadapted coral.

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101 possibilities include MATLAB, SIMULINK, which is a relative of MATLAB, or STELLA. These software packages have friendlier interface for the user and can represent the data in better graphical detail. Other soft ware manufactures, such as ECOBEAKER or ECOSIM, can develop modules based on this model for educational packages.

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102 References Anthony, K.R.N., 1999. Coral suspension feedi ng on fine particulate matter. J. Exp. Mar. Biol. Ecol. 232, 85-106. Anthony, K.R.N., 2000. Enhanced particle-fee ding capacity of cora ls on turbid reefs (Great Barrier Reef, Austra lia). Coral Reefs 19, 59-67. Anthony, K.R.N., Connolly, S.R., Willis, B.L ., 2002. Comparative analysis of energy allocation to tissue and skeletal growth in corals. Limnol. Oceanogr. 47(5), 1417-1429. Anthony, K.R.N., Fabricius, K.E., 2000. Shifting roles of heterotrophy and autotrophy in coral energetic s under varying turbidity. Journal of Experimental Marine Biology and Ecology 252, 221-253. Anthony, K.R.N., Hoegh-Guldberg, O., 2002. Ki netics of photoacclimation in corals. Oecologia 134(1), 23-31. Anthony, K.R.N., Hoegh-Guldberg, O., 2003. Variations in coral photosynthesis, respiration, and growth characteristic s in contrasting light microhabitats: an analogue to plants in forest gaps and understoreys. Functional Ecology 17, 246-259. Atkinson, M.J., Smith, S.V., 1983. C:N:P ra tios of benthic marine plants. Limnol. Oceanogr. 28, 568-574.

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103 Belda, C.A., Cuff, C., Yellowlees, D., 1993. Modification of shell formation in the giant clam Tridacna gigas at elevated nutrient levels in sea water. Mar. Biol. 117, 251-257. Birkeland, C., 1997. Introduction, in: Life and Death of Coral Reefs (C. Birkeland, ed.), Chapman and Hall, New York, pp. 1-10. Bryant, D., Burke, L., McManus, J., Spalding, M., 1998. Reefs at Risk: A Map-Based Indicator of Potential Threats to the World’s Coral Reefs World Resources Institute, Washington DC. Burris, R.H., 1983. Uptake and assimilation of 15NH3 + by a variety of corals. Mar. Biol. 75, 151-156. Bythell, J.C., 1990. Nutrient upt ake in the reef-building coral Acropora palmata at natural environmental concentrations. Mar. Ecol. Prog. Ser. 68, 65-69. Chalker, B.E., Dunlap, W.C., Oliver, J.K ., 1983. Bathymetric adaptation of reefbuilding corals Acropora variabilis and Stylophora pistillata in different light regimes. Coral Reefs 6, 35-42. Cook, C.B., D’Elia, C.F., Muller-Parker, G., 1988. Host feeding and nutrient sufficiency for zooxanthellae in the sea anemone Aiptasia pallida Mar. Biol. 98, 253-262. Cook, C.B., Muller-Parker, G., D’Elia, C.F ., 1992. Ammonium enhancement of dark carbon fixation and nitrogen limitation in symbiotic zooxanthellae: effects of feeding and starvation of the sea anemone Aiptasia pallida. Limnol. Oceanogr. 37, 131-139.

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104 Davies, P.S., 1977. Carbon budgets and vertical zonation of Atlantic reef corals. In: Gabrie C., et al. (eds) Proc. 3rd Int. Coral Reef C ongr. Vol. 1 Antenne Museum-EPHE, Moorea, French Polynesia, pp. 391-396. D’Elia, C.F., 1977. The uptake and release of dissolved phosphorus by reef corals. Limnol. Oceanogr. 22(2), 301-315. D’Elia, C.F., Cook, C.B., 1988. Methylamin e uptake by zooxanthellae-invertebrate symbioses: Insights into host ammonium environment and nutrition. Limnol. Oceanogr. 33, 1153-1165. D’Elia, C.F., Webb, K.L., 1977. The dissolved nitrogen flux on reef corals. Proc. 3rd Int. Coral Reef Symp. 1, 325-330. Durnford, D.G., Falkowski, P.G., 1997. Chlo roplast redox regulation of nuclear gene transcription during photoacclimati on. Photosynthesis Research 53, 229-241. Drew, E.A., 1972. The biology and physiology of al ga-invertebrate symbioses. J. Exp. Mar. Biol. Ecol. 9, 71-75. Dubinsky, Z., Berman-Frank, I., 2001. Un coupling primary production from population growth in photosynthesizing organisms in aquatic ecosystems. Aquatic Sciences 63, 4-17. Dubinsky, Z., Stambler, N., Ben-Zion, M. McCloskey, L.R., Muscatine, L., Falkowski, P.G., 1990. The effect of ex ternal nutrient res ources on the optical properties and photosynthetic efficiency of Stylophora pistillata. Proc. R. Soc. Lond. Ser. B 239, 231-246.

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105 Falkowski, P.G., 1977. The adenylate energy charge in marine phytoplankton: The effect of temperature on the physiological state of Skeletonema costatum (Grev.) Cleve. Journal of Experimental Marine Biology and Ec ology 27(1), 37-45. Falkowski, P.G., Dubinsky, Z., 198 1. Light-shade adaptation of Stylophora pistillata a hermatypic coral from the Gu lf of Elat. Nature 289, 172-174. Falkowski, P.G., Dubinsky, Z., Muscatin e, L., Porter, J.W., 1984. Light and bioenergetics of a symbiotic coral. BioScience 34, 705-709. Ferrier-pages, C., Allemand, D., Gattuso, J.P., Jaubert J., 1998. Mi croheterotrophy in the zooxanthellae coral Stylophora pi stillata: Effects of light and ciliate density. Limnol. Oceanogr. 43(7): 1639-1648. Ferrier-Pages, C., Gattuso, J.P., Dallot, S., Jaubert, J., 2000. Effect of nutrient enrichment on growth and photosynth esis of the zooxanthellate coral Stylophora pistillata Coral Reefs 19: 103-113. Ferrier-Pages, C., Gattuso, J.P., Dallot, S., Jaubert, J., Rassoulzadegan, F., 1998. Microheterotrophy in th e zooxanthellate coral Stylophora pistillata : Effects of light and ciliate density. Limnol. Oceanogr. 43(7), 1639-1648. Ferrier-Pages, C., Witting, J., Tambutte, E., 2003. Effect of natural zooplankton feeding on the tissue and skeletal growth of the scleractinian coral Stylophora pistillata Coral Reefs 22: 229-240. Fong, P., Zedler, J.B., Donohoe, R.M., 1993. Nitrogen versus phosphorus limitation of algal biomass in shallow coastal lagoons. Limnol. Oceanogr. 38, 906-923.

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106 Franklin, L.A., Seaton, G.G.R., Love lock, C.A., Larkum, A.W.D., 1996. Photoinhibition of photosynthesis on a co ral reef. Plant Cell Environ. 19, 825836. Franzisket, L., 1974. Nitrate uptake by reef corals. Int. Rev. Ges. Hydrobiol. 59, 1-7. Frick, H.W., Schuhmacher, H., 1983. The dept h limits of the Red Sea stony corals: an ecophysiological problem (a deep diving survey by submersible). Publ. Staz. Zool. Napoli.(I Mar. Ecol.) 4, 163-194. Furnas, M.J., 1991. Nutrient status and tre nd in the Great Barrier Reef Marine Park, pp. 162-179 in D. Yellowlees (ed.). Land Uses, Patterns, and Nutrient Loadings of the Great Barrier Reef Region, James Cook University. Gattuso, J., Allemand, D., Frankignoulle, M ., 1999. Photosynthesis and Calcification at Cellular, Organismal and Community Levels in Coral Reefs: A Review on Interactions and Control by Carbonate Chemistry. American Zoologist 39(1), 160-183. Gattuso, J.P., Frankignoulle, M., Bourge, I ., Romaine, S., Buddemeier, R.W., 1998. Effect of calcium carbonate saturation of seawater on coral calcification. Global and Planetary Change 18, 37-46. Gattuso, J.P., Pichon, M., Jaubert, J., 1991. Physiology and taxonomy of scleractinian corals: a case study in the genus Stylophora. Coral Reefs 9, 173-182. Goreau, J.T., 1992. Control of atmosphe ric carbon dioxide. Global Environment Change 2(1), 5-11. Grottoli, A.G., 2000. Stable carbon isotope s in coral skeletons. Oceanographie 13, 93-97.

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118 APPENDICES

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119 Appendix A. Macros written for Excel program. Sub Questions() Dim K As Integer Dim repeat As Integer 'Clear out any previous calculations. Dim ClearRange As Range Set ClearRange = Range("A5:Z2000") ClearRange.ClearContents UserInput = InputBox("Enter the Biomass of Host in prot ein units as an integer number (default=10):", "Host Biomass", "10") Cells(5, 2) = UserInput 'UserInput = InputBox("How many times do you want the model to run? (default = 180 times)", "Model", "180") UserInput = InputBox("HOW MANY TIMES DO YOU WANT THE MODEL TO RUN? (default = 180 times, minimum 2, ma ximum 180)", "Model", "180") Cells(4, 1) = UserInput repeat = Cells(4, 1) 'End of input. 'Begin first-time calculations: 'Int((Upperbound Lowerbound + 1) RND + Lowerbound 'BIH = BH %(RND)BIH Cells(5, 3) = IIf((Worksheets("Table").Cells(15, 2) < 0), (Int((Worksheets("Table").Cells(17, 2) / 100 Worksheets("Table").Cells(16, 2) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 2) / 100)) Cells(5, 2), Worksheets("Table").Cells(15, 2) / 100 Cells(5, 2)) 'BA = BH %(RND)BA Cells(5, 4) = IIf(Worksheets("Table").Cells(15, 4) < 0, (Int((Worksheets("Table").Cells(17, 4) / 100 Worksheets("Table").Cells(16, 4) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 4) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 2) / 100 Cells(5, 2)) 'CP = BH %(RND)CP Cells(5, 5) = IIf((Worksheets("Table").Cells(15, 5) < 0), (Int((Worksheets("Table").Cells(17, 5) / 100 Worksheets("Table").Cells(16, 5) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 5) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 5) / 100 Cells(5, 2)) 'CRA = BH %(RND)CRA Cells(5, 6) = IIf(Worksheets("Table").Cells(15, 6) < 0, (Int((Worksheets("Table").Cells(17, 6) / 100 Worksheets("Table").Cells(16, 6) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 6) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 6) / 100 Cells(5, 2)) 'DIN Cells(5, 7) = IIf(Worksheets("Table").Cells(15, 7) < 0, (Int((Worksheets("Table").Cells(17, 7) / 100 Worksheets("Table").Cells(16, 7) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 7) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 7)) 'NIA = DIN %(RND)NIA Cells(5, 8) = IIf(Worksheets("Table").Cells(15, 8) < 0, (Int((Worksheets("Table").Cells(17, 8) / 100 Worksheets("Table").Cells(16, 8) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 8) / 100)) Cells(5, 4), Worksheets("Table").Cells(14, 8) / 100 Cells(5, 7)) 'CGA = (CP CRA)/6.6 Cells(5, 9) = (Cells(5, 5) Cells(5, 6)) / 6.6 'NGA = NIA Cells(5, 10) = Cells(5, 8) 'BGA = If CGA >= NGA, use NGA. If not, use CGA. Cells(5, 11) = IIf(Cells(5, 9) >= Cells(5, 10), Cells(5, 10), Cells(5, 9)) 'CT = CP CRA (CGA 6.6) Cells(5, 13) = Cells(5, 5) Cells(5, 6) (Cells(5, 11) 6.6) 'CIH = BIH 6.6 Cells(5, 14) = Cells(5, 3) 6.6 'NIH = BIH 1 Cells(5, 15) = Cells(5, 3) 1

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120 Appendix A. cont. 'CRH = BH %(RND)CRH Cells(5, 16) = IIf(Worksheets("Table").Cells(15, 3) < 0, (Int((Worksheets("Table").Cells(17, 3) / 100 Worksheets("Table").Cells(16, 3) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 3) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 3) / 100 Cells(5, 2)) 'CMH = BH %(RND)CMH Cells(5, 17) = IIf(Worksheets("Table").Cells(15, 9) < 0, (Int((Worksheets("Table").Cells(17, 9) / 100 Worksheets("Table").Cells(16, 9) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 9) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 9) / 100 Cells(5, 2)) 'CSH = BH %(RND)CSH Cells(5, 18) = IIf(Worksheets("Table").Cells(15, 10) < 0, (Int((Worksheets("Table").Cells(17, 10) / 100 Worksheets("Table").Cells(16, 10) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 10) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 10) / 100 Cells(5, 2)) 'CLH = BH %(RND)CLH Cells(5, 19) = IIf(Worksheets("Table").Cells(15, 11) < 0, (Int((Worksheets("Table").Cells(17, 11) / 100 Worksheets("Table").Cells(16, 11) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 11) / 100)) Cells(5, 2), Worksheets("Table").Cells(14, 11) / 100 Cells(5, 2)) 'CGH = If CT (CRH + CMH + CSH + CLH) > 0, use CIH. If not, use (CT + CIH) (CRH + CMH + CSH + CLH). Cells(5, 20) = IIf(Cells(5, 13) (Cells(5, 16) + Cells(5, 17) + Cells(5, 18) + Cells(5, 19)) >= 0, Cells(5, 14) / 6.6, ((Cells(5, 14) + Cells(5, 12)) (Cells(5, 16) + Cells(5, 17) + Cells(5, 18) + Cells(5, 19)) / 6.6)) 'NGH = NIH Cells(5, 21) = IIf(Cells(5, 3) >= (Cells(5, 2) (4.72 / 100) ), Cells(5, 15), Cells(5, 15) ((Cells(5, 2) (4.72 / 100)) Cells(5, 4))) 'Now do BGH (Column 22) If C GH>=NGH, use NGH else use CGH Cells(5, 22) = IIf(Cells(5, 20) >= Cells(5, 21), Cells(5, 21), Cells(5, 20)) 'NT = NIH BGH Cells(5, 24) = IIf((Worksheets("Table").Cells( 15, 12) < 0), ((Cells(5, 15) Cells(5, 22)) (Int((Worksheets("Table").Cells(17, 12) / 100 Work sheets("Table").Cells(16, 12) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 12) / 100))), Cells(5, 15) Cells(5, 22)) 'Display the first repeat count value in (5,1) Cells(5, 1) = 1 For K = 1 To repeat 1 'nxt = next row (starting at row 6 (K+5 or 1+5=6)) 'prv = previous row (starting at row 5 (K+4 or 1+4=5)) nxt = K + 5 prv = K + 4 'Display the repeat count value in (nxt,1) Cells(nxt, 1) = K + 1 'Next do BH (Column 2) BH(nxt)=BH(prv)+BGH(prv) Cells(nxt, 2) = Cells(prv, 2) + Cells(prv, 22) 'Next do BIH (Column 3) BIH=BH*BIH Cells(nxt, 3) = IIf((Worksheets("Table ").Cells(15, 2) < 0), (Int((Worksh eets("Table").Cells(17, 2) / 100 Worksheets("Table").Cells(16, 2) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 2) / 100)) Cells(nxt, 2), Worksheets("Table").Cells(14, 2) / 100 Cells(nxt, 2)) 'Next do BA (column 4) BA=BA+BGA Cells(nxt, 4) = IIf(Worksheets("Table ").Cells(15, 4) < 0, (Int((Worksh eets("Table").Cells(17, 4) / 100 Worksheets("Table").Cells(16, 4) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 4) / 100)) Cells(nxt, 2), (Cells(prv, 4) + Cells(prv, 11))) 'Next do CP (Column 5) CP=CP*BH Cells(nxt, 5) = IIf((Worksheets("Table ").Cells(15, 5) < 0), (Int((Worksh eets("Table").Cells(17, 5) / 100 Worksheets("Table").Cells(16, 5) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 5) / 100)) Cells(nxt, 2), Worksheets("Table").Cells(14, 5) / 100 Cells(nxt, 2)) 'Next do CRA (Column 6) CRA=CRA*BH Cells(nxt, 6) = IIf(Worksheets("Table ").Cells(15, 6) < 0, (Int((Worksh eets("Table").Cells(17, 6) / 100 Worksheets("Table").Cells(16, 6) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 6) / 100)) Cells(nxt, 4), Worksheets("Table").Cells(14, 6) / 100 Cells(nxt, 2)) 'Next do DIN (Column 7)DIN

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121 Appendix A. cont. Cells(nxt, 7) = IIf(Worksheets("Table ").Cells(15, 7) < 0, (Int((Worksh eets("Table").Cells(17, 7) / 100 Worksheets("Table").Cells(16, 7) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 7) / 100)) Cells(nxt, 4), Worksheets("Table").Cells(14, 7)) 'Next do NIA (Column 8) NIA=NIA*DIN Cells(nxt, 8) = IIf(Worksheets("Table ").Cells(15, 8) < 0, (Int((Worksh eets("Table").Cells(17, 8) / 100 Worksheets("Table").Cells(16, 8) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 8) / 100)) Cells(nxt, 4), Worksheets("Table").Cells(14, 8) / 100 Cells(nxt, 7)) 'Next do CGA (Column 9) CGA=(CP-CRA)/6.6 Cells(nxt, 9) = (Cells(nxt, 5) Cells(nxt, 6)) / 6.6 'Next do NGA (Column 10) NGA=NIA+NT(prv) Cells(nxt, 10) = Cells(nxt, 8) + Cells(prv, 24) 'Next do BGA (Column 11) Cells(nxt, 11) = IIf(Cells(nxt, 9) >= Cells( nxt, 10), Cells(nxt, 10), Cells(nxt, 9)) 'Next do CT (Column 13) Cells(nxt, 13) = Cells(nxt, 5) Cells (nxt, 6) (Cells(nxt, 11) 6.6) 'Next do CIH (Column 14) Cells(nxt, 14) = Cells(nxt, 3) 6.6 'Now do NIH (Column 15) NIH=BIH*1 Cells(nxt, 15) = Cells(nxt, 3) 1 'Now do CRH (Column 16) CRH=CRH*BH Cells(nxt, 16) = IIf(Worksheets("Table") .Cells(15, 3) < 0, (Int((Worksh eets("Table").Cells(17, 3) / 100 Worksheets("Table").Cells(16, 3) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 3) / 100)) Cells(nxt, 2), Worksheets("Table").Cells(14, 3) / 100 Cells(nxt, 2)) 'Now do CMH (Column 17) CMH=CMH*BH Cells(nxt, 17) = IIf(Worksheets("Table") .Cells(15, 9) < 0, (Int((Worksh eets("Table").Cells(17, 9) / 100 Worksheets("Table").Cells(16, 9) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 9) / 100)) Cells(nxt, 2), Worksheets("Table").Cells(14, 9) / 100 Cells(nxt, 2)) 'Now do CSH (Column 18) CSH=CSH*BH Cells(nxt, 18) = IIf(Worksheets("Table") .Cells(15, 10) < 0, (Int((Worksheet s("Table").Cells(17, 10) / 100 Worksheets("Table").Cells(16, 10) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 10) / 100)) Cells(nxt, 2), Worksheets("Table").Cells(14, 10) / 100 Cells(nxt, 2)) 'Now do CLH (Column 19) CLH=CLH*BH Cells(nxt, 19) = IIf(Worksheets("Table") .Cells(15, 11) < 0, (Int((Worksheet s("Table").Cells(17, 11) / 100 Worksheets("Table").Cells(16, 11) / 100 + 1) Rnd + Wo rksheets("Table").Cells(16, 11) / 100)) Cells(nxt, 2), Worksheets("Table").Cells(14, 11) / 100 Cells(nxt, 2)) 'Now do CGH (Column 20) (see formulas below) testit = Cells(nxt, 13) (Ce lls(nxt, 16) + Cells(nxt, 17) + Cells(nxt, 18) + Cells(nxt, 19)) result = ((Cells(nxt, 14) + Cells(nxt, 13) ) (Cells(nxt, 16) + Cells(nxt, 17) + Cells(nxt, 18) + Cells(nxt, 19))) / 6.6 Cells(nxt, 20) = IIf(testit >= 0, (Cells(nxt, 14) / 6.6), result) 'Now do NGH: NGH=NIH Cells(nxt, 21) = IIf(Cells(nxt, 3) >= (Cells (nxt, 2) (4.72 / 100)), Cells(nxt, 15), Cells(nxt, 15) ((Cells(nxt, 2) (4.72 / 100)) Cells(nxt, 4))) 'Now do BGH (Column 22) If C GH>=NGH, use NGH else use CGH Cells(nxt, 22) = IIf(Cells(nxt, 20) >= Cells(nxt, 21), Cells (nxt, 21), Cells(nxt, 20)) 'Now do NT (Column 24) NT=NIH-BGH Cells(nxt, 24) = IIf((Worksheets("Tab le").Cells(15, 12) < 0), ((Cel ls(nxt, 15) Cells(nxt, 22)) (Int((Worksheets("Table").Cells(17, 12) / 100 Work sheets("Table").Cells(16, 12) / 100 + 1) Rnd + Worksheets("Table").Cells(16, 12) / 100))), Cells(nxt, 15) Cells(nxt, 22)) Next K For K = 1 To repeat 1 'nxt = next row (starting at row 6 (K+5 or 1+5=6)) 'prv = previous row (starting at row 5 (K+4 or 1+4=5)) nxt = K + 5 prv = K + 4 Cells(prv, 25) = Cells(prv, 24) Cells(nxt, 11)

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122 Appendix A. cont. Next K Call percent_change End Sub Sub percent_change() Range("Z6").Select ActiveCell.FormulaR1C1 = "=R[-1]C[-24]/RC[-24]" Range("AA6").Select ActiveCell.FormulaR1C1 = "=RC[-23]/R[-1]C[-23]" Range("AA6").Select ActiveCell.FormulaR1C1 = "=RC[-23]/R[-1]C[-23]" Range("AB6").Select ActiveCell.FormulaR1C1 = "=1-RC[-2]" Range("AC6").Select ActiveCell.FormulaR1C1 = "=1-RC[-2]" Range("AB4").Select ActiveCell.FormulaR1C1 = "Host % Change" Range("AC4").Select ActiveCell.FormulaR1C1 = "Algal % Change" Range("AB4:AC4").Select With Selection .Horizont alAlignment = xlGeneral .Vertical Alignment = xlBottom .WrapText = True .Orientation = 0 .AddIndent = False .IndentLevel = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With Columns("AB:AC").Select Selection.NumberFormat = "0.00%" Range("Z6:AC6").Select Selection.AutoFill Destination: =Range("Z6:AC184"), Type:=xlFillDefault Range("Z6:AC184").Select ActiveWindow.ScrollRow = 170 ActiveWindow.ScrollRow = 169 ActiveWindow.ScrollRow = 168 ActiveWindow.ScrollRow = 166 ActiveWindow.ScrollRow = 165 ActiveWindow.ScrollRow = 163 ActiveWindow.ScrollRow = 161 ActiveWindow.ScrollRow = 160 ActiveWindow.ScrollRow = 159 ActiveWindow.ScrollRow = 158 ActiveWindow.ScrollRow = 157 ActiveWindow.ScrollRow = 156 ActiveWindow.ScrollRow = 155 ActiveWindow.ScrollRow = 154 ActiveWindow.ScrollRow = 153 ActiveWindow.ScrollRow = 152 ActiveWindow.ScrollRow = 151 ActiveWindow.ScrollRow = 150 ActiveWindow.ScrollRow = 149 ActiveWindow.ScrollRow = 148 ActiveWindow.ScrollRow = 147 ActiveWindow.ScrollRow = 146

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123 Appendix A. cont. ActiveWindow.ScrollRow = 145 ActiveWindow.ScrollRow = 144 ActiveWindow.ScrollRow = 143 ActiveWindow.ScrollRow = 142 ActiveWindow.ScrollRow = 141 ActiveWindow.ScrollRow = 140 ActiveWindow.ScrollRow = 139 ActiveWindow.ScrollRow = 138 ActiveWindow.ScrollRow = 137 ActiveWindow.ScrollRow = 136 ActiveWindow.ScrollRow = 135 ActiveWindow.ScrollRow = 134 ActiveWindow.ScrollRow = 133 ActiveWindow.ScrollRow = 132 ActiveWindow.ScrollRow = 131 ActiveWindow.ScrollRow = 130 ActiveWindow.ScrollRow = 128 ActiveWindow.ScrollRow = 127 ActiveWindow.ScrollRow = 125 ActiveWindow.ScrollRow = 122 ActiveWindow.ScrollRow = 120 ActiveWindow.ScrollRow = 118 ActiveWindow.ScrollRow = 116 ActiveWindow.ScrollRow = 113 ActiveWindow.ScrollRow = 111 ActiveWindow.ScrollRow = 108 ActiveWindow.ScrollRow = 104 ActiveWindow.ScrollRow = 98 ActiveWindow.ScrollRow = 93 ActiveWindow.ScrollRow = 87 ActiveWindow.ScrollRow = 82 ActiveWindow.ScrollRow = 77 ActiveWindow.ScrollRow = 73 ActiveWindow.ScrollRow = 69 ActiveWindow.ScrollRow = 66 ActiveWindow.ScrollRow = 64 ActiveWindow.ScrollRow = 61 ActiveWindow.ScrollRow = 59 ActiveWindow.ScrollRow = 56 ActiveWindow.ScrollRow = 53 ActiveWindow.ScrollRow = 51 ActiveWindow.ScrollRow = 47 ActiveWindow.ScrollRow = 44 ActiveWindow.ScrollRow = 42 ActiveWindow.ScrollRow = 40 ActiveWindow.ScrollRow = 39 ActiveWindow.ScrollRow = 38 ActiveWindow.ScrollRow = 37 ActiveWindow.ScrollRow = 36 ActiveWindow.ScrollRow = 35 ActiveWindow.ScrollRow = 34 ActiveWindow.ScrollRow = 33 ActiveWindow.ScrollRow = 32 ActiveWindow.ScrollRow = 31 ActiveWindow.ScrollRow = 30 ActiveWindow.ScrollRow = 29 ActiveWindow.ScrollRow = 28 ActiveWindow.ScrollRow = 27 ActiveWindow.ScrollRow = 26

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124 Appendix A. cont. ActiveWindow.ScrollRow = 24 ActiveWindow.ScrollRow = 22 ActiveWindow.ScrollRow = 21 ActiveWindow.ScrollRow = 19 ActiveWindow.ScrollRow = 17 ActiveWindow.ScrollRow = 15 ActiveWindow.ScrollRow = 14 ActiveWindow.ScrollRow = 13 ActiveWindow.ScrollRow = 12 ActiveWindow.ScrollRow = 11 ActiveWindow.ScrollRow = 9 ActiveWindow.ScrollRow = 8 ActiveWindow.ScrollRow = 7 ActiveWindow.ScrollRow = 6 ActiveWindow.ScrollRow = 5 Range("AC6").Select ActiveCell.FormulaR1C1 = "=RC[-2]-1" Range("Z6:AC6").Select Selection.AutoFill Destination: =Range("Z6:AC184"), Type:=xlFillDefault Range("Z6:AC184").Select 'Now re-generate the chart. Call CreateChartSheet End Sub Sub CreateChartSheet() Dim Axs As Axis Dim NewChart As Chart Dim RC As String Dim RC1 As String Dim SelectChart As Chart ThisWorkbook.Activate Charts("ModelChart").Delete Set NewChart = ThisWorkbook.Charts.Add() ActiveChart.Name = "ModelChart" NewChart.ChartType = xlLineMarkers 'Convert repeat count to a string RC = Worksheets("MainSheet").Cells(4, 1) + 4 'RC = "B5:B" + RC 'Start at the label BH followed by the data for the series RC = "B4:B" + RC RC1 = Worksheets("MainSheet").Cells(4, 1) + 4 'RC1 = "D5:D" + RC1 'Start at teh label BA followed by the data for the series RC1 = "D4:D" + RC1 With NewChart .ChartType = xlLineMarkers .SetSourceData Source:=Worksheets("MainS heet").Range(RC), PlotBy:=xlColumns .SeriesCollection.Add Source:=Worksheets("MainSheet").Range(RC1) .SeriesCollection(2).AxisGroup = 2 .HasTitle = True .ChartTitle.Text = "Host an d Algal Biomass over Time" '.HasLegend = True End With Set Axs = Charts("ModelChart").Axes(xlValue)

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125 Appendix A. cont. With Axs .HasTitle = True .AxisTitle.Text = "Host Biomass" End With With ActiveChart .Axes(xlValue, xlSecondary).HasTitle = True .Axes(xlValue, xlSecondary).Ax isTitle.Characters.Text = "Algal Biomass" End With Set Axs = Charts("ModelC hart").Axes(xlCategory) With Axs .HasTitle = True .AxisTitle.Text = "Time in Days" End With ActiveChart.PlotArea.Select With Selection.Border .ColorIndex = 16 .Weight = xlThin .LineStyle = xlContinuous End With Selection.Interior.ColorIndex = xlNone ActiveChart.Axes(xlCategory).Select With Selection.TickLabels .Alignment = xlCenter .Offset = 100 .Orientation = -45 End With With ActiveChart.Axes(xlCategory) .CrossesAt = 1 .TickLabelSpacing = 13 .TickMarkSpacing = 1 .AxisBetweenCategories = True .ReversePlotOrder = False End With ActiveChart.Legend.Select With Selection.Border .Weight = xlHairline .LineStyle = xlNone End With Selection.Shadow = False Selection.Interior.ColorIndex = xlAutomatic Selection.Position = xlBottom ActiveChart.Legend.LegendEn tries(1).LegendKey.Select With Selection.Border .ColorIndex = 5 .Weight = xlThin .LineStyle = xlContinuous End With With Selection .MarkerBackgroundColorIndex = xlAutomatic .MarkerForegroundColorIndex = xlAutomatic .MarkerStyle = xlNone .Smooth = False

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126 Appendix A. cont. .MarkerSize = 5 .Shadow = False End With ActiveChart.Legend.Lege ndEntries(2).LegendKey.Select With Selection.Border .ColorIndex = 10 .Weight = xlThin .LineStyle = xlContinuous End With With Selection .MarkerBackgroundColorIndex = xlAutomatic .MarkerForegroundColorIndex = xlAutomatic .MarkerStyle = xlNone .Smooth = False .MarkerSize = 5 .Shadow = False End With ActiveChart.Deselect Call summary_sheet End Sub Function WorkbookOpen(WorkBookN ame As String) As Boolean WorkbookOpen = False On Error GoTo WorkBookNotOpen If Len(Application.Wor kbooks(WorkBookName).N ame) > 0 Then WorkbookOpen = True Exit Function End If WorkBookNotOpen: End Function Sub summary_sheet() 'The first row of the Summary sheet is rese rved for saving the 180th day of the test cycle. '(which is Row 184 of the MainSheet). 'The second row contains in Cells (2,1) the Starting Value of BioMass of the Host and Cells (2,2) contains the "Next" free row to save the test cycle data to. 'Test if Summary Workbook Exists and create it if it does not exist: 'TestFileName = Application.OpenFilename("Su mmary.xls", 1, "Does Summary.xls exist?", False) 'If (Not TestFileName) Then 'FullFileN ameS = "Summary.xls" 'Sheets.Add After:=Sheets(Sheets.Count) 'Sheets(Sheets.Count).Name = "Summary" 'ThisWorkbook.SaveAs Filename:=Fu llFileNameS 'End If 'Start to save data from current workboook MultiTrials MainSheet to the Summary Sheet: Sheets("MainSheet").Select Rows("184:184").Select Selection.Copy Cells52 = Sheets("MainSheet").Cells(5, 2) 'Test if Summary Workbook is opened; if not, open it: If Not WorkbookOpen("Summary.xls") Then Workbooks.Open Filename:="Summary.xls" End If 'Activate Summary and paste the saved data in Rows 1 and 2:

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127 Appendix A. cont. Workbooks("Summary").Activate Sheets("Summary").Select 'Paste the saved data into the Summary.xls workbook: Rows(1).Select ActiveSheet.Paste 'Save the Starting value of BioMass of the Host: Cells(2, 1) = Cells52 'Now save the current workbook xls file: FullFileNameTR = Applicatio n.GetSaveAsFilename("De fault.xls", 1, "Save Trial File Name.") ThisWorkbook.SaveAs Filename:=FullFileNameTR 'Now move/copy the saved data in Rows 1 and 2 to the "NEXT" row in the Summary sheet: Workbooks("Summary").Activate Sheets("Summary").Select 'If Cells (2,2) are not >=1 then this is the first test cycle. If (Cells(2, 2) >= 1) Then Cells(2, 2) = Cells(2, 2) + 1 Else 'This is the first time. Set the next free row to row 5. Cells(2, 2) = 5 End If nxt = Cells(2, 2) 'Select and copy the saved data in Row 1 to the "nxt" row: Rows("1:1").Select Selection.Copy Rows(nxt).Select ActiveSheet.Paste UserInput = InputBox("Do you want to run another trial?", "y") If UserInput = "y" Then 'Close the newly saved workbook: 'This code closes all workbooks except Summary.xls and the current active workbook: Dim Wkbk As Workbook For Each Wkbk In Workbooks If Wkbk.Name <> ThisWorkbook.Na me And Wkbk.Name <> "Summary.xls" Then Wkbk.Close SaveChanges:=True End If Next Wkbk Else Call Create_Summary_Chart End If 'Switch from the Summary.xls back to the standard MultiTrials workbook to run the next trial: Workbooks.Open Filename:="MultiTrials.xls" Workbooks("MultiTrials").Activate Sheets("MainSheet").Select End Sub Sub Create_Summary_Chart() Charts.Add ActiveChart.ChartType = xlLine ActiveChart.SetSourceData Source:=Sh eets("Summary").Range("A1:K13"), PlotBy :=xlRows ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete

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128 Appendix A. cont. ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection(3).Delete ActiveChart.SeriesCollection( 1).XValues = "=Summary!R3C1:R13C1" ActiveChart.SeriesCollection( 1).Values = "=Summary!R3C2:R13C2" ActiveChart.SeriesCo llection(1).Name = "=""Host Biomass (protein units)""" ActiveChart.SeriesCollection( 2).XValues = "=Summary!R3C1:R13C1" ActiveChart.SeriesCollection( 2).Values = "=Summary!R3C4:R13C4" ActiveChart.SeriesCo llection(2).Name = "=""Algal Biomass (protein units)""" ActiveChart.SeriesCollection(1).Name = "=""Host Biomass""" ActiveChart.SeriesCollecti on(2).Name = "=""Algal Biomass""" ActiveChart.Location Where:=xlLocationAsNewSheet, Name:="B-BIH" With ActiveChart .HasTitle = True .ChartTitle.Characters.Text = "Host and Algal Biomass w ith an Increase in Host Feeding (BIH)" .Axes(xlCategory, xlPrimary).HasTitle = True .Axes(xlCategory, xlPr imary).AxisTitle.Characters.Text = "Host Feeding (BIH)" .Axes(xlValue, xlPrimary).HasTitle = True .Axes(xlValue, xlPrimary).AxisTitle.Characters.Text = "Host Biomass (protein units)" End With ActiveChart.PlotArea.Select With Selection.Border .Weight = xlThin .LineStyle = xlAutomatic End With Selection.Interior.ColorIndex = xlNone ActiveChart.Legend.Select With Selection.Border .Weight = xlHairline .LineStyle = xlNone End With Selection.Shadow = False Selection.Interior.ColorIndex = xlAutomatic Selection.Position = xlBottom ActiveChart.Legend.Lege ndEntries(1).LegendKey.Select With Selection.Border .ColorIndex = 5 .Weight = xlThin .LineStyle = xlContinuous End With With Selection .MarkerBackgroundColorIndex = xlNone .MarkerForegroundColorIndex = xlNone .MarkerStyle = xlNone .Smooth = False .MarkerSize = 3 .Shadow = False End With ActiveChart.Legend.Lege ndEntries(2).LegendKey.Select With Selection.Border .ColorIndex = 10 .Weight = xlThin .LineStyle = xlContinuous End With

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129 Appendix A. cont. With Selection .MarkerBackgroundColorIndex = xlNone .MarkerForegroundColorIndex = xlNone .MarkerStyle = xlNone .Smooth = False .MarkerSize = 3 .Shadow = False End With ActiveChart.SeriesCollection(2).Select ActiveChart.SeriesCollection(2).AxisGroup = 2 ActiveChart.Axes(xlV alue, xlSecondary).Select Selection.TickLabe ls.NumberFormat = "0.0" ActiveChart.Axes(xlValue).Select Selection.TickLa bels.NumberFormat = "0" ActiveChart.ChartTitle.Select Selection.Characters.Text = "Host and Algal Biomass w ith an Increase in Host Feeding (BIH)" Selection.AutoScaleFont = False With Selection.Characters(Start:=1, Length:=58).Font .Name = "Arial" .FontStyle = "Bold" .Size = 12 .Strikethrough = False .Superscript = False .Subscript = False .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With Selection.AutoScaleFont = False With Selection.Characters(Start:=59, Length:=2).Font .Name = "Arial" .FontStyle = "Bold" .Size = 12 .Strikethrough = False .Superscript = False .Subscript = True .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With Selection.AutoScaleFont = False With Selection.Characters(Start:=61, Length:=1).Font .Name = "Arial" .FontStyle = "Bold" .Size = 12 .Strikethrough = False .Superscript = False .Subscript = False .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With ActiveChart.Axes(xlCategory).AxisTitle.Select Selection.Characters.Text = "Host Feeding (BIH)" Selection.AutoScaleFont = False

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130 Appendix A. cont. With Selection.Characters(Start:=1, Length:=15).Font .Name = "Arial" .FontStyle = "Bold" .Size = 10 .Strikethrough = False .Superscript = False .Subscript = False .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With Selection.AutoScaleFont = False With Selection.Characters(Start:=16, Length:=2).Font .Name = "Arial" .FontStyle = "Bold" .Size = 10 .Strikethrough = False .Superscript = False .Subscript = True .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With Selection.AutoScaleFont = False With Selection.Characters(Start:=18, Length:=1).Font .Name = "Arial" .FontStyle = "Bold" .Size = 10 .Strikethrough = False .Superscript = False .Subscript = False .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With ActiveChart.PlotArea.Select With ActiveChart .Axes(xlValue, xlSecondary).HasTitle = True .Axes(xlValue, xlSec ondary).AxisTitle.Characters.Text = "Algal Biomass (protein units)" End With Sheets("MainSheet").Select Application.Wi ndowState = xlMinimized Sheets("Summary").Select Charts.Add ActiveChart.ChartType = xlColumnClustered ActiveChart.SetSourceData Source:=Sh eets("Summary").Range("A1:K13"), PlotBy :=xlRows ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection(1).Delete

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131 Appendix A. cont. ActiveChart.SeriesCollection(1).Delete ActiveChart.SeriesCollection( 1).XValues = "=Summary!R3C1:R13C1" ActiveChart.SeriesCollection( 1).Values = "=Summary!R3C28:R13C28" ActiveChart.SeriesCollection(1).Name = "=""Host Biomass""" ActiveChart.SeriesCollection( 2).XValues = "=Summary!R3C1:R13C1" ActiveChart.SeriesCollection( 2).Values = "=Summary!R3C29:R13C29" ActiveChart.SeriesCollecti on(2).Name = "=""Algal Biomass""" ActiveChart.Location Where:=xlLocationAsNewSheet, Name:="BIH-B%" With ActiveChart .HasTitle = True .ChartTitle.Characters.Text = "Percent Change in Host and Algal Biomass with an Increase in Host Feeding" .Axes(xlCategory, xlPrimary).HasTitle = True .Axes(xlCategory, xlPr imary).AxisTitle.Characters.Text = "Host Feeding (BIH)" .Axes(xlValue, xlPrimary).HasTitle = True .Axes(xlValue, xlPrimary).AxisTitle.Characters.Text = "Biomass (% change)" End With ActiveChart.PlotArea.Select With Selection.Border .ColorIndex = 16 .Weight = xlThin .LineStyle = xlContinuous End With Selection.Interior.ColorIndex = xlNone ActiveChart.Legend.Select With Selection.Border .Weight = xlHairline .LineStyle = xlNone End With Selection.Shadow = False Selection.Interior.ColorIndex = xlAutomatic Selection.Position = xlBottom ActiveChart.Legend.Lege ndEntries(1).LegendKey.Select With Selection.Border .Weight = xlThin .LineStyle = xlAutomatic End With Selection.Shadow = False Selection.InvertIfNegative = False With Selection.Interior .ColorIndex = 5 .Pattern = xlSolid End With ActiveChart.Legend.Lege ndEntries(2).LegendKey.Select With Selection.Border .Weight = xlThin .LineStyle = xlAutomatic End With Selection.Shadow = False Selection.InvertIfNegative = False With Selection.Interior .ColorIndex = 10 .Pattern = xlSolid End With ActiveChart.Axes(xlCategory).AxisTitle.Select Selection.Characters.Text = "Host Feeding (BIH)" Selection.AutoScaleFont = False With Selection.Characters(Start:=1, Length:=15).Font

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132 Appendix A. cont. .Name = "Arial" .FontStyle = "Bold" .Size = 10 .Strikethrough = False .Superscript = False .Subscript = False .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With Selection.AutoScaleFont = False With Selection.Characters(Start:=16, Length:=2).Font .Name = "Arial" .FontStyle = "Bold" .Size = 10 .Strikethrough = False .Superscript = False .Subscript = True .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With Selection.AutoScaleFont = False With Selection.Characte rs(Start:=18, Le ngth:=1).Font .Name = "Arial" .FontStyle = "Bold" .Size = 10 .Strikethrough = False .Superscript = False .Subscript = False .OutlineFont = False .Shadow = False .Underline = xlUnderlineStyleNone .ColorIndex = xlAutomatic End With End Sub

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133 Appendix B. Final values of the 100-iteration peri od with the increase in host feeding rate (BIH) for the shallow-adapted coral. BIH BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 0% 9.87 9.87 9.87 0.4660 0 0 0.60 0.60 6.98 0.0119 0 0 0.1% 11 11 10 0.5145 0 0 0.60 0.60 6.99 0.0119 0 0 0.2% 12 12 11 0.5675 0 0 0.61 0.61 7.10 0.0121 0 0 0.3% 13 13 11 0.6233 0 0 0.67 0.67 7.77 0.0132 0 0.0055 0.4% 14 14 12 0.6843 0 0 0.74 0.74 8.60 0.0146 0 0.0079 0.5% 16 16 13 0.7518 0 0 0.81 0.81 9.48 0.0161 0 0 0.6% 17 17 13 0.8253 0 0 0.90 0.90 10 0.0178 0 0.0027 0.7% 19 19 14 0.9072 0 0 0.97 0.97 11 0.0192 0 0 0.8% 21 21 15 1.00 0 0 1.09 1.09 13 0.0215 0 0.0013 0.9% 23 23 16 1.09 0 0 1.17 1.17 14 0.0232 0 0.0000 1.0% 25 25 17 1.20 0 0 1.27 1.27 15 0.0252 0 0.0395 1.1% 28 28 17 1.32 0 0 1.45 1.45 17 0.0288 0 0 1.2% 31 31 18 1.45 0 0 1.58 1.58 18 0.0312 0 0 1.3% 34 34 20 1.59 0 0 1.67 1.67 19 0.0330 0 0.0508 1.4% 37 37 21 1.74 0 0 1.88 1.88 22 0.0372 0 0.0000 1.5% 41 41 22 1.91 0 0 2.00 2.00 23 0.0396 0 0.0446 1.6% 44 44 23 2.09 0 0 2.20 2.20 26 0.0436 0 0.1049 1.7% 49 49 25 2.29 0 0.0001 2.50 2.50 29 0.0494 0 0.1099 1.8% 53 53 26 2.52 0 0.0001 2.75 2.75 32 0.0544 0 0.1225 1.9% 59 59 28 2.76 0 0.0001 3.08 3.08 36 0.0610 0 0.0164 2.0% 64 64 29 3.03 0 0.0001 3.42 3.42 40 0.0678 0 0 2.1% 70 70 31 3.33 0 0.0001 3.68 3.68 43 0.0730 0 0 2.2% 77 77 33 3.65 0 0.0001 4.05 4.05 47 0.0801 0 0 2.3% 85 85 35 4.00 0 0.0001 4.42 4.42 52 0.0876 0 0 2.4% 93 93 38 4.39 0 0.0001 4.73 4.73 55 0.0936 0 0 2.5% 102 102 40 4.81 0 0.0001 5.24 5.24 61 0.1037 0 0 2.6% 112 112 43 5.27 0 0.0001 5.72 5.72 67 0.1133 0 0 2.7% 123 123 45 5.79 0 0.0001 6.14 6.14 72 0.1215 0 0 2.8% 134 134 48 6.35 0 0.0001 6.63 6.63 77 0.1312 0 0 2.9% 147 147 52 6.95 0 0.0001 7.34 7.34 86 0.1453 0 0 3.0% 161 161 55 7.61 0 0.0001 8.06 8.06 94 0.1596 0 0 3.1% 177 177 59 8.35 0 0.0001 8.73 8.73 102 0.1728 0 0 3.2% 194 194 63 9.14 0 0.0001 9.37 9.37 109 0.1855 0 0.2775

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134 Appendix B cont. BIH BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 3.3% 212 212 67 10 0 0.0001 10 10 118 0.2000 0 0.5817 3.4% 232 232 72 11 0 0.0001 11 11 129 0.2188 0 0.6857 3.5% 255 255 77 12 0 0.0001 12 12 143 0.2422 0 0.4402 3.6% 279 279 82 13 0 0.0001 13 13 156 0.2642 0 0.5572 3.7% 305 305 88 14 0 0.0001 14 14 168 0.2857 0 0.9287 3.8% 333 333 94 16 0 0.0002 16 16 187 0.3181 0 1.76 3.9% 364 364 100 17 0 0.0002 18 18 206 0.3496 0 2.18 4.0% 399 399 108 19 0 0.0002 19 19 226 0.3830 0 2.51 4.1% 437 437 115 21 0 0.0003 21 21 246 0.4182 0 2.74 4.2% 478 478 124 23 0 0.0007 26 26 303 0.5147 0 0.6180 4.3% 525 525 132 25 0 0.0033 27 27 321 0.5442 0 0 4.4% 577 577 142 27 0 0.0042 29 29 336 0.5708 0 0 4.5% 632 632 153 30 0 0.0047 30 30 349 0.5931 0 1.32 4.6% 689 689 164 33 0 0.0057 33 33 382 0.6485 0 4.02 4.7% 753 753 176 36 0 0.0089 38 38 438 0.7439 0 4.93 4.8% 825 825 189 39 0 0.0097 45 45 525 0.8921 0 1.00 4.9% 905 905 203 43 0 0.0129 48 48 561 0.9531 0 0 5.0% 994 994 218 47 0 0.0142 50 50 582 0.9887 0 0 5.1% 1091 1091 235 51 0 0.0165 52 52 607 1.03 0 1.09 5.2% 1191 1190 253 56 0.7256 0.0258 55 56 656 1.11 0 6.48 5.3% 1299 1299 272 61 0 0.0241 66 66 770 1.31 0 8.68 5.4% 1424 1424 293 67 0 0.0510 76 76 890 1.51 0 3.31 5.5% 1551 1551 314 73 0 0.0317 85 85 987 1.68 0 1.02 5.6% 1696 1696 337 80 0 0.0344 92 92 1078 1.83 0 1.24 5.7% 1855 1855 363 88 0 0.0375 101 101 1178 2.00 0 1.48 5.8% 2029 2029 391 96 0 0.0408 110 110 1286 2.18 0 1.75 5.9% 2219 2219 421 105 0 0.0444 120 120 1404 2.38 0 2.07 6.0% 2452 2452 456 116 0 0.0972 116 116 1354 2.30 0 15 6.1% 2678 2678 491 126 0 0.1054 129 129 1507 2.56 0 17 6.2% 2932 2932 530 138 0 0.1349 153 153 1785 3.03 0 11 6.3% 3209 3209 571 151 0 0.1585 169 169 1969 3.34 0 9.73 6.4% 3529 3529 617 167 0 0.1460 177 177 2070 3.51 0 0 6.5% 3867 3865 665 183 1.15 0.1715 181 183 2128 3.61 0 5.07

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135 Appendix B cont. BIH CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 0% 6.97 1.06 0 0 0.9321 0.5985 0.5966 10 6.97 6.94 0 0 0.1% 6.98 1.06 0 0 1.03 0.5994 0.5974 11 6.98 6.95 0 0 0.2% 7.09 1.07 0 0 1.13 0.6089 0.5987 13 7.09 6.97 0 0 0.3% 7.76 1.18 0.0055 0.0055 1.25 0.6664 0.6123 14 7.75 7.13 0 0 0.4% 8.58 1.30 0.0079 0.0079 1.37 0.7372 0.6350 15 8.58 7.39 0 0 0.5% 9.46 1.43 0 0 1.50 0.8129 0.6628 17 9.46 7.71 0 0 0.6% 10 1.58 0.0027 0.0027 1.65 0.8973 0.6939 18 10 8.07 0 0 0.7% 11 1.71 0 0 1.81 0.9687 0.7283 20 11 8.47 0 0 0.8% 13 1.92 0.0013 0.0013 1.99 1.09 0.7655 22 13 8.91 0 0 0.9% 14 2.06 0 0 2.19 1.17 0.8058 24 14 9.37 0 0 1.0% 15 2.24 0.0395 0.0395 2.40 1.27 0.8487 27 15 9.87 0 0 1.1% 17 2.56 0 0 2.63 1.45 0.8956 29 17 10 0 0 1.2% 18 2.78 0 0 2.89 1.58 0.9457 32 18 11 0 0 1.3% 19 2.94 0.0508 0.0508 3.17 1.67 1.00 35 19 12 0 0 1.4% 22 3.32 0 0 3.48 1.88 1.06 39 22 12 0 0 1.5% 23 3.53 0.0446 0.0446 3.82 2.00 1.12 43 23 13 0 0 1.6% 26 3.89 0.1049 0.1049 4.19 2.20 1.18 47 26 14 0 0 1.7% 29 4.40 0.1099 0.1099 4.59 2.50 1.25 51 29 15 0 0 1.8% 32 4.85 0.1225 0.1225 5.03 2.75 1.33 56 32 15 0 0 1.9% 36 5.43 0.0164 0.0164 5.53 3.08 1.41 62 36 16 0 0 2.0% 40 6.04 0 0 6.06 3.42 1.50 68 40 17 0 0 2.1% 43 6.50 0 0 6.65 3.68 1.59 74 43 19 0 0 2.2% 47 7.14 0 0 7.29 4.05 1.69 81 47 20 0 0 2.3% 52 7.80 0 0 8.00 4.42 1.80 89 52 21 0 0 2.4% 55 8.34 0 0 8.78 4.73 1.91 98 55 22 0 0 2.5% 61 9.24 0 0 9.62 5.24 2.04 107 61 24 0 0 2.6% 67 10 0 0 11 5.72 2.17 117 67 25 0 0 2.7% 71 11 0 0 12 6.14 2.31 129 71 27 0 0 2.8% 77 12 0 0 13 6.63 2.46 141 77 29 0 0 2.9% 85 13 0 0 14 7.34 2.63 155 85 31 0 0 3.0% 94 14 0 0 15 8.06 2.81 169 94 33 0 0 3.1% 102 15 0 0 17 8.73 2.99 186 102 35 0 0 3.2% 109 17 0.2775 0.2775 18 9.37 3.20 203 109 37 0 0

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136 Appendix B cont. BIH CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 3.3% 118 18 0.5817 0.5817 20 10 3.41 222 117 40 0 0 3.4% 129 19 0.6857 0.6857 22 11 3.64 243 128 42 0 0 3.5% 142 22 0.4402 0.4402 24 12 3.90 267 142 45 0 0 3.6% 155 24 0.5572 0.5572 26 13 4.17 292 155 48 0 0 3.7% 168 25 0.9287 0.9287 29 14 4.45 320 167 52 0 0 3.8% 187 28 1.76 1.76 31 16 4.77 349 185 55 0 0 3.9% 206 31 2.18 2.18 34 18 5.10 382 203 59 0 0 4.0% 225 34 2.51 2.51 38 19 5.46 418 223 63 0 0 4.1% 246 37 2.74 2.74 41 21 5.85 458 243 68 0 0 4.2% 303 46 0.6180 0.6180 45 26 6.28 504 302 73 0 0 4.3% 320 48 0 0 50 27 6.75 553 320 78 0 0 4.4% 336 51 0 0 54 29 7.23 605 336 84 0 0 4.5% 349 53 1.32 1.32 60 30 7.73 662 347 90 0 0 4.6% 381 58 4.02 4.02 65 33 8.27 722 377 96 0 0 4.7% 437 66 4.93 4.93 71 38 8.88 790 432 103 0 0 4.8% 525 79 1.00 1.00 78 45 9.56 870 524 111 0 0 4.9% 560 85 0 0 85 48 10 953 560 119 0 0 5.0% 581 88 0 0 94 50 11 1044 581 128 0 0 5.1% 606 92 1.09 1.09 103 52 12 1143 605 138 0 0 5.2% 655 99 6.48 6.48 112 56 13 1247 648 147 0 0 5.3% 768 116 8.68 8.68 123 66 14 1365 760 158 0 0 5.4% 888 135 3.31 3.31 134 76 15 1501 885 171 0 0 5.5% 986 149 1.02 1.02 146 85 16 1636 985 183 0 0 5.6% 1077 163 1.24 1.24 160 92 17 1789 1075 197 0 0 5.7% 1176 178 1.48 1.48 175 101 18 1956 1174 212 0 0 5.8% 1284 194 1.75 1.75 192 110 20 2139 1282 227 0 0 5.9% 1402 212 2.07 2.07 209 120 21 2339 1399 245 0 0 6.0% 1351 205 15 15 231 116 23 2568 1336 263 0 0 6.1% 1504 228 17 17 253 129 24 2808 1487 284 0 0 6.2% 1782 270 11 11 277 153 26 3085 1771 306 0 0 6.3% 1966 298 9.73 9.73 303 169 29 3378 1956 330 0 0 6.4% 2066 313 0 0 333 177 31 3706 2066 357 0 0 6.5% 2125 322 5.07 5.07 365 183 33 4048 2120 383 0 0

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137 Appendix B cont. BIH BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 0% 0 0 0 4.24 0.2867 0.8146 0.4887 5.83 0.1731 0 0 0 0.1% 0.0109 0.0719 0.0109 4.68 0.3165 0.8992 0.5395 6.43 0.0939 0.0719 0.0109 0.0109 0.2% 0.0240 0.1587 0.0240 5.16 0.3491 0.9919 0.5951 7.09 0.0235 0.1587 0.0240 0.0235 0.3% 0.0396 0.2614 0.0396 5.66 0.3835 1.09 0.6536 7.79 0.0338 0.2614 0.0396 0.0338 0.4% 0.0580 0.3827 0.0580 6.22 0.4210 1.20 0.7176 8.55 0.0612 0.3827 0.0580 0.0580 0.5% 0.0796 0.5256 0.0796 6.83 0.4626 1.31 0.7884 9.40 0.0896 0.5256 0.0796 0.0796 0.6% 0.1049 0.6924 0.1049 7.50 0.5078 1.44 0.8655 10 0.1243 0.6924 0.1049 0.1049 0.7% 0.1345 0.8880 0.1345 8.25 0.5582 1.59 0.9514 11 0.1250 0.8880 0.1345 0.1250 0.8% 0.1687 1.11 0.1687 9.04 0.6122 1.74 1.04 12 0.2011 1.1131 0.1687 0.1687 0.9% 0.2085 1.38 0.2085 9.94 0.6729 1.91 1.15 14 0.2001 1.38 0.2085 0.2001 1.0% 0.2541 1.68 0.2541 11 0.7379 2.10 1.26 15 0.2206 1.68 0.2541 0.2206 1.1% 0.3067 2.02 0.3067 12 0.8097 2.30 1.38 16 0.3776 2.02 0.3067 0.3067 1.2% 0.3675 2.43 0.3675 13 0.8893 2.53 1.52 18 0.4095 2.43 0.3675 0.3675 1.3% 0.4370 2.88 0.4370 14 0.9763 2.77 1.66 20 0.3673 2.88 0.4370 0.3673 1.4% 0.5166 3.41 0.5166 16 1.07 3.04 1.83 22 0.5329 3.41 0.5166 0.5166 1.5% 0.6077 4.01 0.6077 17 1.18 3.34 2.01 24 0.5067 4.01 0.6077 0.5067 1.6% 0.7101 4.69 0.7101 19 1.29 3.66 2.20 26 0.6140 4.69 0.7101 0.6140 1.7% 0.8265 5.46 0.8265 21 1.41 4.01 2.41 29 0.8679 5.46 0.8265 0.8265 1.8% 0.9598 6.33 0.9598 23 1.55 4.40 2.64 31 1.03 6.33 0.9598 0.9598 1.9% 1.11 7.34 1.11 25 1.70 4.83 2.90 35 1.31 7.34 1.11 1.11 2.0% 1.28 8.47 1.28 28 1.86 5.29 3.18 38 1.58 8.47 1.28 1.28 2.1% 1.48 9.76 1.48 30 2.05 5.81 3.49 42 1.68 9.76 1.48 1.48 2.2% 1.70 11 1.70 33 2.24 6.37 3.82 46 1.93 11 1.70 1.70 2.3% 1.95 13 1.95 36 2.46 6.99 4.19 50 2.18 13 1.95 1.95 2.4% 2.23 15 2.23 40 2.70 7.67 4.60 55 2.26 15 2.23 2.23 2.5% 2.55 17 2.55 44 2.96 8.41 5.04 60 2.68 17 2.55 2.55 2.6% 2.90 19 2.90 48 3.24 9.22 5.53 66 3.01 19 2.90 2.90 2.7% 3.31 22 3.31 53 3.56 10 6.07 72 3.18 22 3.31 3.18 2.8% 3.76 25 3.76 58 3.90 11 6.65 79 3.44 25 3.76 3.44 2.9% 4.27 28 4.27 63 4.28 12 7.29 87 4.05 28 4.27 4.05 3.0% 4.84 32 4.84 69 4.68 13 7.99 95 4.64 32 4.84 4.64 3.1% 5.48 36 5.48 76 5.14 15 8.75 104 5.07 36 5.48 5.07 3.2% 6.20 41 6.20 83 5.62 16 9.59 114 5.37 41 6.20 5.37

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138 Appendix B cont. BIH BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 3.3% 7.00 46 7.00 91 6.16 17 10 125 5.77 46 7.00 5.77 3.4% 7.90 52 7.90 100 6.74 19 11 137 6.53 52 7.90 6.53 3.5% 8.91 59 8.91 109 7.39 21 13 150 7.67 59 8.91 7.67 3.6% 10 66 10 120 8.09 23 14 164 8.57 66 10 8.57 3.7% 11 75 11 131 8.86 25 15 180 9.33 75 11 9.33 3.8% 13 84 13 143 9.67 27 16 197 11 84 13 11 3.9% 14 94 14 156 11 30 18 215 12 94 14 12 4.0% 16 105 16 171 12 33 20 235 14 105 16 14 4.1% 18 118 18 187 13 36 22 258 16 118 18 16 4.2% 20 133 20 205 14 39 24 282 23 133 20 20 4.3% 23 149 23 225 15 43 26 310 24 149 23 23 4.4% 25 167 25 247 17 48 29 340 25 167 25 25 4.5% 28 188 28 271 18 52 31 373 25 188 28 25 4.6% 32 209 32 296 20 57 34 407 27 209 32 27 4.7% 35 233 35 323 22 62 37 444 34 233 35 34 4.8% 40 261 40 354 24 68 41 487 45 261 40 40 4.9% 44 293 44 388 26 75 45 534 48 293 44 44 5.0% 50 328 50 427 29 82 49 587 49 328 50 49 5.1% 56 367 56 468 32 90 54 644 50 367 56 50 5.2% 62 409 62 511 35 98 59 702 54 409 62 54 5.3% 69 454 69 557 38 107 64 766 68 454 69 68 5.4% 77 508 77 611 41 117 70 840 84 508 77 77 5.5% 85 563 85 665 45 128 77 915 96 563 85 85 5.6% 95 627 95 728 49 140 84 1001 106 627 95 95 5.7% 106 698 106 796 54 153 92 1095 118 698 106 106 5.8% 118 777 118 870 59 167 100 1197 131 777 118 118 5.9% 131 864 131 952 64 183 110 1309 145 864 131 131 6.0% 147 971 147 1052 71 202 121 1447 130 971 147 130 6.1% 163 1078 163 1149 78 221 133 1580 149 1078 163 149 6.2% 182 1200 182 1258 85 242 145 1730 188 1200 182 182 6.3% 202 1335 202 1377 93 265 159 1894 212 1335 202 202 6.4% 226 1491 226 1514 102 291 175 2082 223 1491 226 223 6.5% 251 1658 251 1658 112 319 191 2281 227 1658 251 227

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139 Appendix B cont. BIH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 0% 0 0.0007 0 1.142612 1.1227 0.0% 0.0% 0.0% 0.3% 0.0% 0.2% 0.1% 0 0.0007 0 0.5475303 0.8324 0.1% 0.1% 0.0% 0.3% 0.1% 0.3% 0.2% 0.0006 0.0008 0.0006 0 0.5274 0.2% 0.2% 0.0% 0.3% 0.2% 0.5% 0.3% 0.0058 0.0015 0.0058 0 0.3542 0.3% 0.3% 0.3% 0.4% 0.5% 0.6% 0.4% 0 0.0021 0 0.0212 0.2704 0.3% 0.4% 1.2% 0.5% 1.5% 0.8% 0.5% 0 0.0028 0 0.0660 0.2239 0.5% 0.5% 0.0% 0.6% 0.5% 1.0% 0.6% 0 0.0037 0 0.1276 0.1942 0.6% 0.6% 1.9% 0.7% 2.5% 1.2% 0.7% 0.0095 0.0045 0.0095 0 0.1756 0.7% 0.7% 0.0% 0.7% 0.7% 1.4% 0.8% 0 0.0056 0 0.2140 0.1633 0.8% 0.8% 2.4% 0.9% 3.2% 1.6% 0.9% 0.0085 0.0065 0.0085 0 0.1560 0.9% 0.9% 0.0% 0.9% 0.9% 1.8% 1.0% 0.0335 0.0082 0.0335 0 0.1502 0.8% 0.9% 1.3% 1.0% 2.1% 2.0% 1.1% 0 0.0093 0.0000 0.4682 0.1531 1.1% 1.0% 2.7% 1.2% 3.8% 2.2% 1.2% 0 0.0105 0.0000 0.2774 0.1569 1.2% 1.1% 0.0% 1.2% 1.2% 2.4% 1.3% 0.0698 0.0127 0.0698 0 0.1712 1.1% 1.2% 0.7% 1.3% 1.9% 2.5% 1.4% 0 0.0136 0 0.107407 0.1728 1.4% 1.3% 0.0% 1.4% 1.4% 2.8% 1.5% 0.1010 0.0162 0.1010 0 0.1738 1.4% 1.4% 0.0% 1.5% 1.4% 2.9% 1.6% 0.0962 0.0189 0.0962 0 0.1832 1.4% 1.5% 1.9% 1.6% 3.2% 3.1% 1.7% 0 0.0209 0 0.2727 0.1936 1.5% 1.6% 5.1% 1.7% 6.5% 3.3% 1.8% 0 0.0236 0 0.4313 0.2116 1.6% 1.7% 5.6% 1.8% 7.2% 3.5% 1.9% 0 0.0258 0 1.31 0.2374 1.9% 1.8% 5.6% 1.9% 7.5% 3.8% 2.0% 0 0.0291 0 1.98 0.2632 2.0% 1.9% 4.5% 2.1% 6.5% 4.0% 2.1% 0 0.0318 0 1.33 0.2919 2.1% 2.0% 0.0% 2.1% 2.1% 4.1% 2.2% 0 0.0354 0 1.53 0.3214 2.2% 2.1% 0.0% 2.2% 2.2% 4.3% 2.3% 0 0.0392 0 1.52 0.3472 2.3% 2.2% 0.9% 2.3% 3.2% 4.5% 2.4% 0 0.0423 0 0.18 0.3686 2.4% 2.3% 0.0% 2.4% 2.4% 4.7% 2.5% 0 0.0474 0 0.86 0.4255 2.5% 2.4% 0.0% 2.5% 2.5% 4.9% 2.6% 0 0.0523 0 0.71 0.4585 2.6% 2.5% 0.0% 2.6% 2.6% 5.1% 2.7% 0.1293 0.0578 0.1293 0 0.4964 2.7% 2.6% 0.0% 2.7% 2.7% 5.2% 2.8% 0.3261 0.0648 0.3261 0 0.5116 2.8% 2.7% 0.0% 2.8% 2.8% 5.4% 2.9% 0.2198 0.0708 0.2198 0 0.5930 2.9% 2.8% 0.0% 2.9% 2.9% 5.6% 3.0% 0.2040 0.0780 0.2040 0 0.6597 3.0% 2.8% 0.0% 3.0% 3.0% 5.8% 3.1% 0.4121 0.0868 0.4121 0 0.6907 3.1% 2.9% 0.0% 3.1% 3.1% 6.0% 3.2% 0.8324 0.1003 0.8324 0 0.7652 3.1% 3.0% 0.0% 3.1% 3.1% 6.2%

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140 Appendix B cont. BIH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 3.3% 1.23 0.1148 1.2251 0 0.7889 3.0% 3.1% 0.0% 3.2% 3.0% 6.4% 3.4% 1.37 0.1269 1.3708 0 0.8616 3.1% 3.2% 0.2% 3.3% 3.3% 6.6% 3.5% 1.24 0.1350 1.2383 0 1.01 3.3% 3.3% 0.0% 3.4% 3.3% 6.8% 3.6% 1.46 0.1496 1.4594 0 1.09 3.4% 3.4% 0.0% 3.5% 3.4% 6.9% 3.7% 1.96 0.1694 1.9625 0 1.14 3.4% 3.5% 0.0% 3.6% 3.4% 7.1% 3.8% 1.70 0.1917 1.6995 0 1.27 3.3% 3.6% 4.3% 3.7% 7.5% 7.3% 3.9% 1.75 0.2126 1.7543 0 1.35 3.3% 3.7% 5.6% 3.8% 8.9% 7.5% 4.0% 1.92 0.2345 1.9159 0 1.47 3.3% 3.8% 6.1% 3.9% 9.5% 7.7% 4.1% 2.21 0.2576 2.2080 0 1.62 3.5% 3.9% 5.9% 4.0% 9.3% 7.9% 4.2% 0 0.2627 0 20 1.69 4.1% 4.0% 12.2% 4.2% 16.2% 8.2% 4.3% 0 0.2689 0 10 1.96 4.3% 4.1% 0.0% 4.3% 4.3% 8.4% 4.4% 0.6893 0.2886 0.6893 0 1.96 4.4% 4.2% 0.0% 4.4% 4.4% 8.5% 4.5% 3.84 0.3445 3.8353 0 1.94 4.3% 4.3% 0.0% 4.4% 4.3% 8.7% 4.6% 4.46 0.4054 4.4571 0 1.98 4.0% 4.4% 4.2% 4.5% 8.2% 8.9% 4.7% 1.75 0.4328 1.7525 0 2.07 4.1% 4.5% 10.0% 4.6% 14.1% 9.1% 4.8% 0 0.4501 0.0000 37 2.41 4.7% 4.6% 13.2% 4.8% 17.9% 9.4% 4.9% 0 0.4679 0.0000 26 2.70 4.9% 4.7% 2.1% 4.9% 7.0% 9.6% 5.0% 0.8047 0.4929 0.8047 0 2.71 5.0% 4.8% 0.0% 4.9% 5.0% 9.7% 5.1% 5.89 0.5741 5.8940 0 2.72 5.0% 4.9% 0.0% 5.0% 5.0% 9.8% 5.2% 8.22 0.6852 8.9496 4.79 2.74 4.6% 4.9% 3.9% 5.1% 8.4% 10.0% 5.3% 1.01 0.7349 1.0105 0 2.68 4.6% 5.0% 12.6% 5.2% 17.2% 10.3% 5.4% 0 0.7478 0 45 3.28 5.2% 5.1% 13.0% 5.4% 18.2% 10.5% 5.5% 0 0.8285 0 70 3.76 5.4% 5.2% 13.2% 5.5% 18.6% 10.8% 5.6% 0 0.9066 0 74 3.95 5.5% 5.3% 13.2% 5.6% 18.7% 10.9% 5.7% 0 0.9920 0 79 4.15 5.6% 5.4% 13.2% 5.7% 18.8% 11.1% 5.8% 0 1.0852 0 85 4.35 5.7% 5.5% 13.2% 5.8% 18.9% 11.3% 5.9% 0 1.1870 0 90 4.57 5.8% 5.6% 13.2% 5.9% 19.0% 11.5% 6.0% 17 1.3913 16.7782 0 4.09 5.4% 5.7% 5.6% 5.8% 11.1% 11.6% 6.1% 14 1.5050 14.0826 0 4.33 5.6% 5.8% 7.7% 6.0% 13.3% 11.8% 6.2% 0 1.5187 0 41 4.63 5.8% 5.9% 12.9% 6.1% 18.7% 12.0% 6.3% 0 1.6396 0 62 5.03 6.0% 6.0% 12.8% 6.2% 18.8% 12.2% 6.4% 2.40 1.6655 2.4004 0 5.25 6.4% 6.1% 0.4% 6.3% 6.8% 12.4% 6.5% 24 1.9641 25.5337 7.58 5.22 6.3% 6.2% 0.6% 6.3% 7.0% 12.5%

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141 Appendix C. Final values of the 100-iteration peri od with the increase in host feeding rate (BIH) for the deep-adapted coral. BIH BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 0% 0.8462 0.8462 3.57 0.0329 0 0 0.0891 0.0891 0.1803 0.0005 0 0.0211 0.1% 0.9369 0.9369 3.69 0.0364 0 0 0.0985 0.0985 0.1996 0.0005 0 0.0233 0.2% 1.04 1.04 3.82 0.0403 0 0 0.1089 0.1089 0.2210 0.0006 0 0.0257 0.3% 1.15 1.15 3.95 0.0447 0 0 0.1204 0.1204 0.2446 0.0006 0 0.0285 0.4% 1.27 1.27 4.09 0.0494 0 0 0.1330 0.1330 0.2708 0.0007 0 0.0315 0.5% 1.41 1.41 4.24 0.0547 0 0 0.1470 0.1470 0.2997 0.0008 0 0.0348 0.6% 1.56 1.56 4.40 0.0605 0 0 0.1625 0.1625 0.3316 0.0009 0 0.0384 0.7% 1.72 1.72 4.56 0.0670 0 0 0.1796 0.1796 0.3669 0.0010 0 0.0425 0.8% 1.91 1.91 4.73 0.0741 0 0 0.1984 0.1984 0.4060 0.0011 0 0.0470 0.9% 2.11 2.11 4.92 0.0820 0 0 0.2192 0.2192 0.4491 0.0012 0 0.0519 1.0% 2.33 2.33 5.11 0.0907 0 0 0.2422 0.2422 0.4968 0.0013 0 0.0573 1.1% 2.58 2.58 5.32 0.1003 0 0 0.2675 0.2675 0.5495 0.0015 0 0.0633 1.2% 2.85 2.85 5.54 0.1110 0 0 0.2955 0.2955 0.6077 0.0016 0 0.0699 1.3% 3.15 3.15 5.77 0.1227 0 0 0.3263 0.3263 0.6720 0.0018 0 0.0773 1.4% 3.49 3.49 6.02 0.1357 0 0 0.3603 0.3603 0.7430 0.0020 0 0.0853 1.5% 3.86 3.86 6.28 0.1500 0 0 0.3979 0.3979 0.8214 0.0022 0 0.0942 1.6% 4.26 4.26 6.56 0.1658 0 0 0.4392 0.4392 0.9081 0.0024 0 0.1040 1.7% 4.71 4.71 6.86 0.1833 0 0 0.4849 0.4849 1.00 0.0027 0 0.1148 1.8% 5.21 5.21 7.18 0.2026 0 0 0.5352 0.5352 1.11 0.0029 0 0.1268 1.9% 5.75 5.75 7.51 0.2239 0 0 0.5907 0.5907 1.23 0.0033 0 0.1399 2.0% 6.36 6.36 7.87 0.2474 0 0 0.6519 0.6519 1.35 0.0036 0 0.1545 2.1% 7.03 7.03 8.25 0.2733 0 0 0.7194 0.7194 1.50 0.0040 0 0.1705 2.2% 7.76 7.76 8.66 0.3020 0 0 0.7938 0.7938 1.65 0.0044 0 0.1881 2.3% 8.58 8.58 9.09 0.3336 0 0 0.8757 0.8757 1.83 0.0048 0 0.2075 2.4% 9.47 9.47 9.55 0.3685 0 0 0.9661 0.9661 2.02 0.0054 0 0.2290 2.5% 10 10 10 0.4070 0 0 1.07 1.07 2.23 0.0059 0 0.2526 2.6% 12 12 11 0.4494 0 0 1.18 1.18 2.46 0.0065 0 0.2786 2.7% 13 13 11 0.4963 0 0 1.30 1.30 2.72 0.0072 0 0.3073 2.8% 14 14 12 0.5480 0 0 1.43 1.43 3.00 0.0080 0 0.3389 2.9% 16 16 12 0.6050 0 0 1.58 1.58 3.31 0.0088 0 0.3737 3.0% 17 17 13 0.6678 0 0 1.74 1.74 3.66 0.0097 0 0.4121 3.1% 19 19 14 0.7372 0 0 1.92 1.92 4.04 0.0107 0 0.4543 3.2% 21 21 15 0.8136 0 0 2.11 2.11 4.46 0.0118 0 0.5008

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142 Appendix C cont. BIH BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 3.3% 23 23 15 0.8979 0 0 2.33 2.33 4.92 0.0130 0 0.5521 3.4% 25 25 16 0.9908 0 0 2.56 2.56 5.43 0.0144 0 0.6085 3.5% 28 28 17 1.09 0 0 2.83 2.83 5.99 0.0159 0 0.6706 3.6% 31 31 18 1.21 0 0 3.11 3.11 6.61 0.0175 0 0.7390 3.7% 34 34 20 1.33 0 0 3.43 3.43 7.29 0.0193 0 0.8142 3.8% 38 38 21 1.47 0 0 3.78 3.78 8.04 0.0213 0 0.8970 3.9% 42 42 22 1.62 0 0 4.16 4.16 8.86 0.0235 0 0.9882 4.0% 46 46 23 1.78 0 0 4.59 4.59 9.77 0.0259 0 1.09 4.1% 51 51 25 1.97 0 0 5.05 5.05 11 0.0286 0 1.20 4.2% 56 56 27 2.17 0 0 5.56 5.56 12 0.0315 0 1.32 4.3% 61 61 28 2.39 0 0 6.12 6.12 13 0.0347 0 1.45 4.4% 68 68 30 2.64 0 0 6.74 6.74 14 0.0383 0 1.60 4.5% 75 75 32 2.91 0 0 7.42 7.42 16 0.0422 0 1.76 4.6% 82 82 34 3.20 0 0 8.17 8.17 18 0.0465 0 1.94 4.7% 91 91 37 3.53 0 0 8.99 8.99 19 0.0513 0 2.14 4.8% 100 100 39 3.89 0 0 9.90 9.90 21 0.0565 0 2.35 4.9% 110 110 42 4.29 0 0 11 11 23 0.0622 0 2.59 5.0% 121 121 45 4.72 0 0.0001 12 12 26 0.0686 0 2.85 5.1% 134 134 48 5.20 0 0.0001 13 13 28 0.0755 0 3.13 5.2% 147 147 51 5.73 0 0.0001 15 15 31 0.0832 0 3.45 5.3% 162 162 55 6.31 0 0.0001 16 16 35 0.0917 0 3.79 5.4% 179 179 59 6.95 0 0.0001 18 18 38 0.1009 0 4.17 5.5% 197 197 63 7.66 0 0.0001 19 19 42 0.1112 0 4.59 5.6% 217 217 68 8.43 0 0.0001 21 21 46 0.1224 0 5.05 5.7% 239 239 72 9.28 0 0.0001 23 23 51 0.1348 0 5.55 5.8% 263 263 78 10 0 0.0001 26 26 56 0.1484 0 6.10 5.9% 289 289 84 11 0 0.0001 28 28 62 0.1633 0 6.71 6.0% 318 318 90 12 0 0.0001 31 31 68 0.1798 0 7.38 6.1% 350 350 96 14 0 0.0001 34 34 75 0.1978 0 8.11 6.2% 385 385 104 15 0 0.0001 37 37 82 0.2177 0 8.92 6.3% 424 424 112 16 0 0.0001 41 41 90 0.2396 0 9.80 6.4% 467 467 120 18 0 0.0001 45 45 99 0.2636 0 11 6.5% 513 513 129 20 0 0.0001 50 50 109 0.2900 0 12

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143 Appendix C cont. BIH CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 0% 0.1798 0.0272 0.0211 0.0211 0.0658 0.0658 0.2727 0.9121 0.1588 0.6558 0.0232 0.0955 0.1% 0.1991 0.0302 0.0233 0.0233 0.0729 0.0729 0.2819 1.01 0.1758 0.6783 0.0256 0.0983 0.2% 0.2204 0.0334 0.0257 0.0257 0.0807 0.0807 0.2917 1.12 0.1947 0.7019 0.0282 0.1012 0.3% 0.2440 0.0370 0.0285 0.0285 0.0893 0.0893 0.3020 1.24 0.2155 0.7269 0.0310 0.1043 0.4% 0.2700 0.0409 0.0315 0.0315 0.0989 0.0989 0.3129 1.37 0.2386 0.7532 0.0342 0.1075 0.5% 0.2989 0.0453 0.0348 0.0348 0.1094 0.1094 0.3243 1.52 0.2641 0.7810 0.0376 0.1109 0.6% 0.3307 0.0501 0.0384 0.0384 0.1211 0.1211 0.3365 1.68 0.2923 0.8103 0.0414 0.1145 0.7% 0.3660 0.0554 0.0425 0.0425 0.1340 0.1340 0.3493 1.86 0.3235 0.8414 0.0456 0.1183 0.8% 0.4049 0.0613 0.0470 0.0470 0.1483 0.1483 0.3628 2.05 0.3579 0.8742 0.0502 0.1223 0.9% 0.4479 0.0679 0.0519 0.0519 0.1640 0.1640 0.3772 2.27 0.3960 0.9090 0.0552 0.1265 1.0% 0.4955 0.0751 0.0573 0.0573 0.1814 0.1814 0.3923 2.51 0.4381 0.9458 0.0608 0.1309 1.1% 0.5480 0.0830 0.0633 0.0633 0.2007 0.2007 0.4084 2.78 0.4847 0.9848 0.0669 0.1356 1.2% 0.6061 0.0918 0.0699 0.0699 0.2219 0.2219 0.4255 3.07 0.5361 1.03 0.0736 0.1405 1.3% 0.6702 0.1015 0.0773 0.0773 0.2454 0.2454 0.4436 3.40 0.5929 1.07 0.0809 0.1458 1.4% 0.7410 0.1123 0.0853 0.0853 0.2713 0.2713 0.4628 3.76 0.6557 1.12 0.0890 0.1513 1.5% 0.8193 0.1241 0.0942 0.0942 0.3000 0.3000 0.4832 4.16 0.7251 1.17 0.0979 0.1572 1.6% 0.9057 0.1372 0.1040 0.1040 0.3316 0.3316 0.5049 4.59 0.8017 1.22 0.1076 0.1634 1.7% 1.00 0.1517 0.1148 0.1148 0.3666 0.3666 0.5280 5.08 0.8863 1.27 0.1183 0.1700 1.8% 1.11 0.1676 0.1268 0.1268 0.4051 0.4051 0.5525 5.61 0.9797 1.33 0.1301 0.1770 1.9% 1.22 0.1853 0.1399 0.1399 0.4477 0.4477 0.5787 6.20 1.08 1.40 0.1430 0.1844 2.0% 1.35 0.2047 0.1545 0.1545 0.4948 0.4948 0.6065 6.85 1.20 1.47 0.1572 0.1923 2.1% 1.49 0.2262 0.1705 0.1705 0.5467 0.5467 0.6361 7.57 1.32 1.54 0.1727 0.2006 2.2% 1.65 0.2499 0.1881 0.1881 0.6040 0.6040 0.6677 8.37 1.46 1.61 0.1898 0.2095 2.3% 1.82 0.2761 0.2075 0.2075 0.6672 0.6672 0.7015 9.24 1.61 1.70 0.2086 0.2189 2.4% 2.01 0.3049 0.2290 0.2290 0.7369 0.7369 0.7374 10 1.78 1.78 0.2291 0.2289 2.5% 2.22 0.3368 0.2526 0.2526 0.8139 0.8139 0.7759 11 1.97 1.88 0.2517 0.2396 2.6% 2.45 0.3720 0.2786 0.2786 0.8989 0.8989 0.8169 12 2.18 1.98 0.2765 0.2509 2.7% 2.71 0.4107 0.3073 0.3073 0.9926 0.9926 0.8608 14 2.40 2.08 0.3036 0.2630 2.8% 2.99 0.4535 0.3389 0.3389 1.10 1.10 0.9077 15 2.65 2.20 0.3334 0.2758 2.9% 3.30 0.5007 0.3737 0.3737 1.21 1.21 0.9578 17 2.93 2.32 0.3661 0.2895 3.0% 3.65 0.5527 0.4121 0.4121 1.34 1.34 1.01 19 3.24 2.45 0.4019 0.3041 3.1% 4.03 0.6101 0.4543 0.4543 1.47 1.47 1.07 20 3.57 2.59 0.4412 0.3196 3.2% 4.44 0.6733 0.5008 0.5008 1.63 1.63 1.13 23 3.94 2.74 0.4842 0.3362

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144 Appendix C cont. BIH CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 3.3% 4.90 0.7431 0.5521 0.5521 1.80 1.80 1.20 25 4.35 2.90 0.5314 0.3539 3.4% 5.41 0.8200 0.6085 0.6085 1.98 1.98 1.27 27 4.80 3.07 0.5832 0.3727 3.5% 5.97 0.9047 0.6706 0.6706 2.19 2.19 1.34 30 5.30 3.25 0.6398 0.3929 3.6% 6.59 0.9981 0.7390 0.7390 2.41 2.41 1.42 33 5.85 3.45 0.7020 0.4144 3.7% 7.27 1.10 0.8142 0.8142 2.66 2.66 1.51 37 6.45 3.66 0.7700 0.4373 3.8% 8.02 1.21 0.8970 0.8970 2.93 2.93 1.61 41 7.12 3.89 0.8445 0.4619 3.9% 8.84 1.34 0.9882 0.9882 3.24 3.24 1.71 45 7.85 4.14 0.9262 0.4881 4.0% 9.75 1.48 1.09 1.09 3.57 3.57 1.81 49 8.66 4.40 1.02 0.5161 4.1% 11 1.63 1.20 1.20 3.94 3.94 1.93 55 9.55 4.68 1.11 0.5461 4.2% 12 1.80 1.32 1.32 4.34 4.34 2.06 60 11 4.99 1.22 0.5782 4.3% 13 1.98 1.45 1.45 4.78 4.78 2.19 66 12 5.31 1.34 0.6125 4.4% 14 2.18 1.60 1.60 5.27 5.27 2.33 73 13 5.67 1.47 0.6492 4.5% 16 2.41 1.76 1.76 5.81 5.81 2.49 81 14 6.04 1.61 0.6886 4.6% 17 2.65 1.94 1.94 6.41 6.41 2.66 89 16 6.45 1.76 0.7307 4.7% 19 2.92 2.14 2.14 7.06 7.06 2.84 98 17 6.89 1.93 0.7758 4.8% 21 3.22 2.35 2.35 7.78 7.78 3.03 108 19 7.37 2.11 0.8241 4.9% 23 3.55 2.59 2.59 8.57 8.57 3.24 119 21 7.88 2.32 0.8759 5.0% 26 3.91 2.85 2.85 9.45 9.45 3.47 131 23 8.42 2.54 0.9314 5.1% 28 4.31 3.13 3.13 10 10 3.71 144 25 9.02 2.78 0.9909 5.2% 31 4.74 3.45 3.45 11 11 3.97 159 28 9.66 3.04 1.05 5.3% 34 5.22 3.79 3.79 13 13 4.26 175 31 10 3.33 1.12 5.4% 38 5.75 4.17 4.17 14 14 4.56 193 34 11 3.65 1.20 5.5% 42 6.34 4.59 4.59 15 15 4.89 212 37 12 3.99 1.28 5.6% 46 6.98 5.05 5.05 17 17 5.25 234 41 13 4.37 1.36 5.7% 51 7.68 5.55 5.55 19 19 5.63 257 45 14 4.78 1.45 5.8% 56 8.46 6.10 6.10 20 20 6.05 283 50 15 5.23 1.55 5.9% 61 9.31 6.71 6.71 22 22 6.49 312 55 16 5.72 1.65 6.0% 68 10 7.38 7.38 25 25 6.98 343 60 17 6.26 1.76 6.1% 74 11 8.11 8.11 27 27 7.50 377 66 18 6.85 1.89 6.2% 82 12 8.92 8.92 30 30 8.06 415 73 20 7.49 2.01 6.3% 90 14 9.80 9.80 33 33 8.67 457 80 21 8.19 2.15 6.4% 99 15 11 11 36 36 9.33 503 88 23 8.96 2.30 6.5% 109 17 12 12 40 40 10 553 97 24 9.80 2.46

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145 Appendix C cont. BIH BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 0% 0 0 0 0.1765 0.0424 0.0335 0.0419 0.2943 -0.0205 0 0 -0.0205 0.1% 0.0009 0.0062 0.0009 0.1954 0.0470 0.0371 0.0464 0.3259 -0.0218 0.0062 0.0009 -0.0218 0.2% 0.0021 0.0137 0.0021 0.2163 0.0520 0.0411 0.0513 0.3608 -0.0231 0.0137 0.0021 -0.0231 0.3% 0.0034 0.0227 0.0034 0.2395 0.0576 0.0455 0.0568 0.3994 -0.0244 0.0227 0.0034 -0.0244 0.4% 0.0051 0.0336 0.0051 0.2651 0.0637 0.0503 0.0629 0.4421 -0.0257 0.0336 0.0051 -0.0257 0.5% 0.0070 0.0464 0.0070 0.2934 0.0706 0.0557 0.0696 0.4892 -0.0271 0.0464 0.0070 -0.0271 0.6% 0.0093 0.0616 0.0093 0.3246 0.0781 0.0616 0.0770 0.5414 -0.0284 0.0616 0.0093 -0.0284 0.7% 0.0121 0.0796 0.0121 0.3592 0.0864 0.0682 0.0853 0.5991 -0.0297 0.0796 0.0121 -0.0297 0.8% 0.0152 0.1006 0.0152 0.3974 0.0956 0.0755 0.0943 0.6628 -0.0309 0.1006 0.0152 -0.0309 0.9% 0.0190 0.1252 0.0190 0.4397 0.1057 0.0835 0.1043 0.7332 -0.0321 0.1252 0.0190 -0.0321 1.0% 0.0233 0.1539 0.0233 0.4863 0.1170 0.0923 0.1154 0.8111 -0.0332 0.1539 0.0233 -0.0332 1.1% 0.0284 0.1872 0.0284 0.5379 0.1294 0.1021 0.1277 0.8971 -0.0341 0.1872 0.0284 -0.0341 1.2% 0.0342 0.2259 0.0342 0.5949 0.1431 0.1130 0.1412 0.9921 -0.0349 0.2259 0.0342 -0.0349 1.3% 0.0410 0.2706 0.0410 0.6578 0.1582 0.1249 0.1561 1.10 -0.0354 0.2706 0.0410 -0.0354 1.4% 0.0488 0.3222 0.0488 0.7274 0.1749 0.1381 0.1726 1.21 -0.0356 0.3222 0.0488 -0.0356 1.5% 0.0578 0.3817 0.0578 0.8042 0.1934 0.1527 0.1909 1.34 -0.0355 0.3817 0.0578 -0.0355 1.6% 0.0682 0.4501 0.0682 0.8890 0.2138 0.1688 0.2110 1.48 -0.0350 0.4501 0.0682 -0.0350 1.7% 0.0801 0.5286 0.0801 0.9826 0.2363 0.1866 0.2332 1.64 -0.0339 0.5286 0.0801 -0.0339 1.8% 0.0937 0.6186 0.0937 1.09 0.2612 0.2062 0.2578 1.81 -0.0323 0.6186 0.0937 -0.0323 1.9% 0.1093 0.7217 0.1093 1.20 0.2887 0.2279 0.2849 2.00 -0.0299 0.7217 0.1093 -0.0299 2.0% 0.1272 0.8394 0.1272 1.33 0.3190 0.2518 0.3148 2.21 -0.0266 0.8394 0.1272 -0.0266 2.1% 0.1476 0.9739 0.1476 1.47 0.3524 0.2782 0.3478 2.44 -0.0224 0.9739 0.1476 -0.0224 2.2% 0.1708 1.1272 0.1708 1.62 0.3894 0.3074 0.3843 2.70 -0.0169 1.13 0.1708 -0.0169 2.3% 0.1972 1.3018 0.1972 1.79 0.4301 0.3396 0.4245 2.98 -0.0101 1.30 0.1972 -0.0101 2.4% 0.2273 1.5004 0.2273 1.98 0.4751 0.3751 0.4689 3.29 -0.0016 1.50 0.2273 -0.0016 2.5% 0.2615 1.7262 0.2615 2.18 0.5248 0.4143 0.5179 3.64 0.0087 1.73 0.2615 0.0087 2.6% 0.3004 1.9826 0.3004 2.41 0.5795 0.4575 0.5719 4.02 0.0213 1.98 0.3004 0.0213 2.7% 0.3445 2.2735 0.3445 2.66 0.6399 0.5052 0.6315 4.44 0.0363 2.27 0.3445 0.0363 2.8% 0.3944 2.6032 0.3944 2.94 0.7066 0.5578 0.6973 4.90 0.0542 2.60 0.3944 0.0542 2.9% 0.4510 2.9766 0.4510 3.24 0.7801 0.6159 0.7698 5.41 0.0755 2.98 0.4510 0.0755 3.0% 0.5150 3.3992 0.5150 3.58 0.8611 0.6798 0.8498 5.97 0.1006 3.40 0.5150 0.1006 3.1% 0.5874 3.8772 0.5874 3.95 0.9505 0.7504 0.9380 6.59 0.1300 3.88 0.5874 0.1300 3.2% 0.6693 4.4172 0.6693 4.36 1.0491 0.8282 1.0353 7.27 0.1645 4.42 0.6693 0.1645

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146 Appendix C cont. BIH BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 3.3% 0.7617 5.03 0.7617 4.81 1.16 0.9140 1.14 8.03 0.2047 5.03 0.7617 0.2047 3.4% 0.8660 5.72 0.8660 5.31 1.28 1.01 1.26 8.86 0.2515 5.72 0.8660 0.2515 3.5% 0.9836 6.49 0.9836 5.86 1.41 1.11 1.39 9.77 0.3057 6.49 0.9836 0.3057 3.6% 1.12 7.37 1.12 6.47 1.56 1.23 1.53 11 0.3684 7.37 1.12 0.3684 3.7% 1.27 8.35 1.27 7.13 1.72 1.35 1.69 12 0.4407 8.35 1.27 0.4407 3.8% 1.43 9.46 1.43 7.87 1.89 1.49 1.87 13 0.5240 9.46 1.43 0.5240 3.9% 1.62 11 1.62 8.68 2.09 1.65 2.06 14 0.6197 11 1.62 0.6197 4.0% 1.84 12 1.84 9.57 2.30 1.82 2.27 16 0.7295 12 1.84 0.7295 4.1% 2.07 14 2.07 11 2.54 2.00 2.50 18 0.8552 14 2.07 0.8552 4.2% 2.34 15 2.34 12 2.80 2.21 2.76 19 0.9989 15 2.34 0.9989 4.3% 2.64 17 2.64 13 3.08 2.44 3.04 21 1.16 17 2.64 1.16 4.4% 2.98 20 2.98 14 3.40 2.68 3.36 24 1.35 20 2.98 1.35 4.5% 3.36 22 3.36 16 3.75 2.96 3.70 26 1.56 22 3.36 1.56 4.6% 3.79 25 3.79 17 4.13 3.26 4.08 29 1.81 25 3.79 1.81 4.7% 4.27 28 4.27 19 4.55 3.59 4.49 32 2.08 28 4.27 2.08 4.8% 4.80 32 4.80 21 5.02 3.96 4.95 35 2.39 32 4.80 2.39 4.9% 5.40 36 5.40 23 5.53 4.36 5.46 38 2.75 36 5.40 2.75 5.0% 6.07 40 6.07 25 6.09 4.81 6.01 42 3.15 40 6.07 3.15 5.1% 6.82 45 6.82 28 6.71 5.30 6.62 47 3.60 45 6.82 3.60 5.2% 7.66 51 7.66 31 7.39 5.83 7.29 51 4.12 51 7.66 4.12 5.3% 8.60 57 8.60 34 8.14 6.43 8.03 56 4.70 57 8.60 4.70 5.4% 9.65 64 9.65 37 8.96 7.08 8.85 62 5.35 64 9.65 5.35 5.5% 11 71 11 41 9.87 7.79 9.74 68 6.09 71 11 6.09 5.6% 12 80 12 45 11 8.58 11 75 6.93 80 12 6.93 5.7% 14 90 14 50 12 9.45 12 83 7.87 90 14 7.87 5.8% 15 101 15 55 13 10 13 91 8.92 101 15 8.92 5.9% 17 113 17 60 15 11 14 101 10 113 17 10 6.0% 19 126 19 66 16 13 16 111 11 126 19 11 6.1% 21 141 21 73 18 14 17 122 13 141 21 13 6.2% 24 158 24 80 19 15 19 134 15 158 24 15 6.3% 27 176 27 88 21 17 21 148 17 176 27 17 6.4% 30 197 30 97 23 18 23 162 19 197 30 19 6.5% 33 220 33 107 26 20 25 179 21 220 33 21

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147 Appendix C cont. BIH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 0% 0.0205 0.0890 0.0205 0 0 -2.4% -2.5% -2.4% -1.7% -4.9% -4.1% 0.1% 0.0227 0.0919 0.0227 0 0 -2.3% -2.4% -2.3% -1.6% -4.7% -3.9% 0.2% 0.0252 0.0949 0.0252 0 0 -2.2% -2.3% -2.2% -1.5% -4.5% -3.7% 0.3% 0.0279 0.0981 0.0279 0 0 -2.1% -2.2% -2.1% -1.4% -4.3% -3.5% 0.4% 0.0308 0.1015 0.0308 0 0 -2.0% -2.1% -2.0% -1.3% -4.1% -3.3% 0.5% 0.0341 0.1051 0.0341 0 0 -1.9% -2.0% -1.9% -1.2% -3.9% -3.1% 0.6% 0.0377 0.1089 0.0377 0 0 -1.8% -1.9% -1.8% -1.1% -3.6% -2.9% 0.7% 0.0418 0.1128 0.0418 0 0 -1.7% -1.8% -1.7% -1.0% -3.4% -2.7% 0.8% 0.0462 0.1171 0.0462 0 0 -1.6% -1.7% -1.6% -0.9% -3.2% -2.5% 0.9% 0.0511 0.1215 0.0511 0 0 -1.5% -1.6% -1.5% -0.8% -3.0% -2.3% 1.0% 0.0565 0.1263 0.0565 0 0 -1.4% -1.5% -1.4% -0.7% -2.8% -2.1% 1.1% 0.0625 0.1313 0.0625 0 0 -1.3% -1.4% -1.3% -0.6% -2.6% -1.9% 1.2% 0.0691 0.1366 0.0691 0 0 -1.2% -1.3% -1.2% -0.4% -2.4% -1.7% 1.3% 0.0764 0.1422 0.0764 0 0 -1.1% -1.2% -1.1% -0.3% -2.2% -1.5% 1.4% 0.0844 0.1482 0.0844 0 0 -1.0% -1.1% -1.0% -0.2% -2.0% -1.3% 1.5% 0.0933 0.1545 0.0933 0 0 -0.9% -1.0% -0.9% -0.1% -1.8% -1.1% 1.6% 0.1032 0.1613 0.1032 0 0 -0.8% -0.9% -0.8% 0.0% -1.6% -0.9% 1.7% 0.1140 0.1684 0.1140 0 0 -0.7% -0.8% -0.7% 0.1% -1.4% -0.7% 1.8% 0.1260 0.1760 0.1260 0 0 -0.6% -0.7% -0.6% 0.2% -1.2% -0.5% 1.9% 0.1392 0.1841 0.1392 0 0 -0.5% -0.6% -0.5% 0.3% -1.0% -0.3% 2.0% 0.1538 0.1928 0.1538 0 0 -0.4% -0.5% -0.4% 0.4% -0.8% -0.1% 2.1% 0.1699 0.2020 0.1699 0 0 -0.3% -0.4% -0.3% 0.5% -0.6% 0.1% 2.2% 0.1877 0.2118 0.1877 0 0 -0.2% -0.3% -0.2% 0.6% -0.4% 0.3% 2.3% 0.2073 0.2222 0.2073 0 0 -0.1% -0.2% -0.1% 0.7% -0.2% 0.5% 2.4% 0.2289 0.2334 0.2289 0 0 0.0% -0.1% 0.0% 0.8% 0.0% 0.7% 2.5% 0.2528 0.2453 0.2528 0 0 0.1% 0.0% 0.1% 0.9% 0.2% 0.9% 2.6% 0.2791 0.2580 0.2791 0 0 0.2% 0.1% 0.2% 1.0% 0.4% 1.1% 2.7% 0.3082 0.2716 0.3082 0 0 0.3% 0.2% 0.3% 1.1% 0.6% 1.3% 2.8% 0.3402 0.2861 0.3402 0 0 0.4% 0.3% 0.4% 1.2% 0.8% 1.5% 2.9% 0.3755 0.3017 0.3755 0 0 0.5% 0.4% 0.5% 1.3% 1.0% 1.7% 3.0% 0.4145 0.3183 0.4145 0 0 0.6% 0.5% 0.6% 1.4% 1.2% 1.9% 3.1% 0.4574 0.3361 0.4574 0 0 0.7% 0.6% 0.7% 1.5% 1.4% 2.1% 3.2% 0.5048 0.3552 0.5048 0 0 0.8% 0.7% 0.8% 1.6% 1.6% 2.3%

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148 Appendix C cont. BIH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 3.3% 0.5570 0.3756 0.5570 0 0 0.9% 0.8% 0.9% 1.7% 1.8% 2.5% 3.4% 0.6145 0.3975 0.6145 0 0 1.0% 0.9% 1.0% 1.8% 2.0% 2.7% 3.5% 0.6779 0.4210 0.6779 0 0 1.1% 1.0% 1.1% 1.9% 2.2% 2.9% 3.6% 0.7477 0.4461 0.7477 0 0 1.2% 1.1% 1.2% 2.0% 2.4% 3.1% 3.7% 0.8247 0.4731 0.8247 0 0 1.3% 1.3% 1.3% 2.1% 2.6% 3.3% 3.8% 0.9095 0.5021 0.9095 0 0 1.4% 1.4% 1.4% 2.2% 2.8% 3.5% 3.9% 1.00 0.5333 1.00 0 0.0001 1.5% 1.5% 1.5% 2.3% 3.0% 3.7% 4.0% 1.11 0.5667 1.11 0 0.0001 1.6% 1.6% 1.6% 2.4% 3.2% 3.9% 4.1% 1.22 0.6026 1.22 0 0.0001 1.7% 1.7% 1.7% 2.5% 3.4% 4.1% 4.2% 1.34 0.6413 1.34 0 0.0001 1.8% 1.8% 1.8% 2.6% 3.6% 4.3% 4.3% 1.48 0.6828 1.48 0 0.0002 1.9% 1.9% 1.9% 2.7% 3.8% 4.5% 4.4% 1.63 0.7275 1.63 0 0.0002 2.0% 2.0% 2.0% 2.8% 4.0% 4.7% 4.5% 1.80 0.7756 1.80 0 0.0002 2.1% 2.1% 2.1% 2.9% 4.2% 4.9% 4.6% 1.98 0.8274 1.98 0 0.0002 2.2% 2.2% 2.2% 3.0% 4.4% 5.1% 4.7% 2.18 0.8831 2.18 0 0.0003 2.3% 2.3% 2.3% 3.1% 4.6% 5.3% 4.8% 2.41 0.9431 2.41 0 0.0003 2.4% 2.4% 2.4% 3.2% 4.8% 5.5% 4.9% 2.65 1.01 2.65 0 0.0003 2.5% 2.5% 2.5% 3.3% 5.0% 5.7% 5.0% 2.92 1.08 2.92 0 0.0003 2.6% 2.6% 2.6% 3.4% 5.2% 5.9% 5.1% 3.22 1.15 3.22 0 0.0004 2.7% 2.7% 2.7% 3.5% 5.4% 6.1% 5.2% 3.54 1.23 3.54 0 0.0004 2.8% 2.8% 2.8% 3.6% 5.6% 6.3% 5.3% 3.90 1.32 3.90 0 0.0004 2.9% 2.9% 2.9% 3.7% 5.8% 6.5% 5.4% 4.30 1.41 4.30 0 0.0005 3.0% 3.0% 3.0% 3.8% 6.0% 6.7% 5.5% 4.73 1.52 4.73 0 0.0005 3.1% 3.1% 3.1% 3.9% 6.2% 6.9% 5.6% 5.21 1.63 5.21 0 0.0005 3.2% 3.2% 3.2% 4.0% 6.4% 7.2% 5.7% 5.73 1.74 5.73 0 0.0005 3.3% 3.3% 3.3% 4.1% 6.6% 7.4% 5.8% 6.31 1.87 6.31 0 0.0006 3.4% 3.4% 3.4% 4.2% 6.8% 7.6% 5.9% 6.95 2.01 6.95 0 0.0006 3.5% 3.5% 3.5% 4.3% 7.0% 7.8% 6.0% 7.64 2.16 7.64 0 0.0006 3.6% 3.6% 3.6% 4.4% 7.2% 8.0% 6.1% 8.41 2.32 8.41 0 0.0006 3.7% 3.7% 3.7% 4.5% 7.4% 8.2% 6.2% 9.25 2.49 9.25 0 0.0007 3.8% 3.8% 3.8% 4.6% 7.6% 8.4% 6.3% 10 2.68 10 0 0.0007 3.9% 3.9% 3.9% 4.7% 7.8% 8.6% 6.4% 11 2.88 11 0 0.0007 4.0% 4.0% 4.0% 4.8% 8.0% 8.8% 6.5% 12 3.10 12 0 0.0007 4.1% 4.1% 4.1% 4.9% 8.2% 9.0%

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149 Appendix D. Final values of the 100-iteration period with the increas e in algal photos ynthesis rate (CPA) for the shallow-adapted coral. CPA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 0% 0.0028 0.0028 1.17 0.0001 0 0 0.0003 0.0003 0 0 0 0.0003 0.1% 0.0032 0.0032 1.19 0.0002 0 0 0.0003 0.0003 0 0 0 0.0003 0.2% 0.0039 0.0039 1.22 0.0002 0 0 0.0004 0.0004 0.0001 0 0 0.0004 0.3% 0.0047 0.0047 1.24 0.0002 0 0 0.0005 0.0005 0.0002 0 0 0.0004 0.4% 0.0056 0.0056 1.27 0.0003 0 0 0.0006 0.0006 0.0003 0 0 0.0005 0.5% 0.0067 0.0067 1.30 0.0003 0 0 0.0008 0.0008 0.0004 0 0 0.0006 0.6% 0.0080 0.0080 1.34 0.0004 0 0 0.0009 0.0009 0.0006 0 0 0.0007 0.7% 0.0096 0.0096 1.37 0.0005 0 0 0.0011 0.0011 0.0009 0 0 0.0008 0.8% 0.0115 0.0115 1.40 0.0005 0 0 0.0014 0.0014 0.0012 0 0 0.0009 0.9% 0.0138 0.0138 1.44 0.0007 0 0 0.0017 0.0017 0.0017 0 0 0.0011 1% 0.0165 0.0165 1.48 0.0008 0 0 0.0020 0.0020 0.0022 0 0 0.0013 1.1% 0.0198 0.0198 1.52 0.0009 0 0 0.0024 0.0024 0.0029 0 0 0.0015 1.2% 0.0237 0.0237 1.57 0.0011 0 0 0.0030 0.0030 0.0038 0 0 0.0017 1.3% 0.0283 0.0283 1.62 0.0013 0 0 0.0036 0.0036 0.0049 0 0 0.0020 1.4% 0.0339 0.0339 1.66 0.0016 0 0 0.0044 0.0044 0.0063 0 0 0.0024 1.5% 0.0405 0.0405 1.72 0.0019 0 0 0.0053 0.0053 0.0081 0 0 0.0027 1.6% 0.0483 0.0483 1.77 0.0023 0 0 0.0065 0.0065 0.0103 0 0 0.0032 1.7% 0.0578 0.0578 1.83 0.0027 0 0 0.0078 0.0078 0.0131 0.0001 0 0.0037 1.8% 0.0690 0.0690 1.89 0.0033 0 0 0.0095 0.0095 0.0166 0.0001 0 0.0043 1.9% 0.0823 0.0823 1.96 0.0039 0 0 0.0115 0.0115 0.0209 0.0002 0 0.0049 2% 0.0983 0.0983 2.03 0.0046 0 0 0.0139 0.0139 0.0263 0.0002 0 0.0057 2.1% 0.1173 0.1173 2.11 0.0055 0 0 0.0168 0.0168 0.0329 0.0002 0 0.0066 2.2% 0.1399 0.1399 2.19 0.0066 0 0 0.0202 0.0202 0.0412 0.0003 0 0.0076 2.3% 0.1668 0.1668 2.28 0.0079 0 0 0.0245 0.0245 0.0513 0.0003 0 0.0087 2.4% 0.1989 0.1989 2.37 0.0094 0 0 0.0295 0.0295 0.0638 0.0004 0 0.0100 2.5% 0.2455 0.2455 2.50 0.0116 0 0 0.0363 0.0363 0.0821 0.0005 0 0.0118 2.6% 0.3135 0.3135 2.65 0.0148 0 0 0.0454 0.0454 0.1090 0.0006 0 0.0142 2.7% 0.4002 0.4002 2.82 0.0189 0 0 0.0567 0.0567 0.1446 0.0007 0 0.0171

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150 Appendix D cont. CPA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 2.8% 0.5107 0.5107 3.02 0.0241 0 0 0.0708 0.0708 0.1913 0.0010 0 0.0205 2.9% 0.6510 0.6510 3.24 0.0307 0 0 0.0883 0.0883 0.2526 0.0012 0 0.0245 3% 0.8293 0.8293 3.48 0.0391 0 0 0.1100 0.1100 0.3328 0.0016 0 0.0291 3.1% 1.06 1.06 3.76 0.0498 0 0 0.1369 0.1369 0.4377 0.0020 0 0.0343 3.2% 1.34 1.34 4.08 0.0634 0 0 0.1702 0.1702 0.5747 0.0025 0 0.0402 3.3% 1.71 1.71 4.44 0.0805 0 0 0.2115 0.2115 0.7533 0.0032 0 0.0468 3.4% 2.17 2.17 4.85 0.1023 0 0 0.2625 0.2625 0.9862 0.0041 0 0.0540 3.5% 2.75 2.75 5.33 0.1300 0 0 0.3256 0.3256 1.29 0.0051 0 0.0617 3.6% 3.49 3.49 5.87 0.1649 0 0 0.4034 0.4034 1.68 0.0065 0 0.0696 3.7% 4.43 4.43 6.50 0.2091 0 0 0.4992 0.4992 2.19 0.0083 0 0.0774 3.8% 5.61 5.61 7.23 0.2649 0 0 0.6172 0.6172 2.85 0.0105 0 0.0843 3.9% 7.11 7.11 8.08 0.3354 0 0 0.7621 0.7621 3.71 0.0133 0 0.0894 4% 8.98 8.98 9.05 0.4239 0 0 0.9392 0.9392 4.81 0.0168 0 0.0912 4.1% 11 11 10 0.5354 0 0 1.16 1.16 6.22 0.0212 0 0.0878 4.2% 14 14 12 0.6758 0 0 1.42 1.42 8.04 0.0268 0 0.0765 4.3% 18 18 13 0.8522 0 0 1.75 1.75 10 0.0337 0 0.0534 4.4% 22 22 15 1.05 0 0 2.09 2.09 13 0.0413 0 0.0256 4.5% 22 22 15 1.06 0 0 2.06 2.06 13 0.0409 0 0 4.6% 23 23 15 1.06 0 0 2.05 2.05 13 0.0406 0 0.0253 4.7% 23 23 15 1.07 0 0 1.98 1.98 13 0.0393 0 0.0320 4.8% 23 23 15 1.08 0 0 1.96 1.96 13 0.0389 0 0.0103 4.9% 23 23 15 1.08 0 0 1.97 1.97 14 0.0390 0 0.0020 5% 23 23 15 1.09 0 0 1.90 1.90 13 0.0377 0 0.0411 5.1% 23 23 15 1.10 0 0 1.89 1.89 14 0.0373 0 0 5.2% 23 23 15 1.10 0 0 1.88 1.88 14 0.0373 0 0.0170 5.3% 23 23 15 1.11 0 0 1.81 1.81 14 0.0359 0 0.0288 5.4% 24 24 15 1.11 0 0 1.81 1.81 14 0.0359 0 0.0047 5.5% 24 24 16 1.12 0 0 1.80 1.80 14 0.0356 0 0.0280 5.6% 24 24 16 1.12 0 0 1.74 1.74 14 0.0344 0 0.0272 5.7% 24 24 16 1.13 0 0 1.74 1.74 14 0.0345 0 0

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151 Appendix D cont. CPA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 5.8% 24 24 16 1.13 0 0 1.74 1.74 14 0.0344 0 0.0191 5.9% 24 24 16 1.14 0 0 1.67 1.67 14 0.0331 0 0.0342 6% 24 24 16 1.14 0 0 1.67 1.67 14 0.0331 0 0 6.1% 24 24 16 1.14 0 0 1.68 1.68 15 0.0333 0 0 6.2% 24 24 16 1.15 0 0 1.63 1.63 14 0.0322 0 0.0404 6.3% 24 24 16 1.15 0 0 1.59 1.59 14 0.0315 0 0.0173 6.4% 25 25 16 1.16 0 0 1.60 1.60 15 0.0317 0 0 6.5% 25 25 16 1.16 0 0 1.59 1.59 15 0.0316 0 0.0200 6.6% 25 25 16 1.17 0 0 1.53 1.53 14 0.0304 0 0.0281 6.7% 25 25 16 1.17 0 0 1.53 1.53 14 0.0302 0 0.0033 6.8% 25 25 16 1.17 0 0 1.50 1.50 14 0.0296153 0 0.0209 6.9% 25 25 16 1.17 0 0 1.49 1.49 15 0.0295108 0 0 7% 25 25 16 1.18 0 0 1.45 1.45 14 0.0287592 0 0.0192 7.1% 25 25 16 1.18 0 0 1.47 1.47 15 0.0291395 0 0.0305 7.2% 25 25 16 1.18 0 0 1.47 1.47 15 0.02913 0 0 7.3% 25 25 16 1.18 0 0 1.43 1.43 15 0.0282562 0 0 7.4% 25 25 16 1.19 0 0 1.40 1.40 15 0.0276423 0 0 7.5% 25 25 16 1.19 0 0 1.37 1.37 15 0.0271952 0 0.0446 7.6% 25 25 16 1.19 0 0 1.38 1.38 15 0.027296 0 0.0363 7.7% 25 25 16 1.19 0 0 1.37 1.37 15 0.027166 0 0 7.8% 25 25 16 1.19 0 0 1.34 1.34 15 0.0264877 0 0 7.9% 25 25 17 1.19 0 0 1.31 1.31 15 0.0259859 0 0.0422 8% 25 25 17 1.19 0 0 1.33 1.33 15 0.0263383 0 0.0342 8.1% 25 25 17 1.20 0 0 1.31 1.31 15 0.0260335 0 0 8.2% 25 25 17 1.20 0 0 1.30 1.30 15 0.0257292 0 0 8.3% 25 25 17 1.20 0 0 1.31 1.31 15 0.0259687 0 0 8.4% 25 25 17 1.20 0 0 1.28 1.28 15 0.0253933 0 0 8.5% 26 26 17 1.20 0 0 1.24 1.24 15 0.0244589 0 0.0366

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152 Appendix D cont. CPA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 0% 0 0 0.0003 0 0.0003 0.0003 0.0946 0.0030 0 0 0.0003 0.1185 0.1% 0 0 0.0003 0 0.0003 0.0003 0.0990 0.0035 0 0.0102 0.0003 0.1187 0.2% 0.0001 0 0.0004 0 0.0004 0.0004 0.1029 0.0043 0 0.0230 0.0004 0.1189 0.3% 0.0002 0 0.0004 0 0.0004 0.0004 0.1066 0.0051 0.0002 0.0367 0.0005 0.1192 0.4% 0.0003 0 0.0005 0 0.0005 0.0005 0.1103 0.0061 0.0002 0.0512 0.0005 0.1195 0.5% 0.0004 0 0.0006 0 0.0006 0.0006 0.1138 0.0073 0.0004 0.0665 0.0006 0.1197 0.6% 0.0006 0.0001 0.0007 0.0001 0.0008 0.0008 0.1174 0.0088 0.0005 0.0827 0.0007 0.1201 0.7% 0.0009 0.0001 0.0008 0.0001 0.0009 0.0009 0.1211 0.0105 0.0007 0.0999 0.0009 0.1204 0.8% 0.0012 0.0002 0.0009 0.0002 0.0011 0.0011 0.1248 0.0126 0.0010 0.1179 0.0010 0.1207 0.9% 0.0016 0.0002 0.0011 0.0002 0.0013 0.0013 0.1286 0.0151 0.0014 0.1370 0.0012 0.1211 1% 0.0022 0.0003 0.0013 0.0003 0.0016 0.0016 0.1326 0.0181 0.0018 0.1572 0.0014 0.1214 1.1% 0.0029 0.0004 0.0015 0.0004 0.0019 0.0019 0.1369 0.0216 0.0024 0.1787 0.0016 0.1218 1.2% 0.0038 0.0006 0.0017 0.0006 0.0022 0.0022 0.1414 0.0259 0.0032 0.2016 0.0019 0.1222 1.3% 0.0049 0.0007 0.0020 0.0007 0.0027 0.0027 0.1461 0.0310 0.0041 0.2260 0.0022 0.1226 1.4% 0.0063 0.0010 0.0024 0.0010 0.0032 0.0032 0.1509 0.0370 0.0053 0.2514 0.0026 0.1230 1.5% 0.0080 0.0012 0.0027 0.0012 0.0038 0.0038 0.1559 0.0443 0.0068 0.2785 0.0030 0.1235 1.6% 0.0103 0.0016 0.0032 0.0016 0.0046 0.0046 0.1612 0.0529 0.0087 0.3074 0.0035 0.1240 1.7% 0.0130 0.0020 0.0037 0.0020 0.0055 0.0055 0.1668 0.0632 0.0111 0.3382 0.0041 0.1244 1.8% 0.0165 0.0025 0.0043 0.0025 0.0065 0.0065 0.1728 0.0755 0.0140 0.3711 0.0047 0.1249 1.9% 0.0208 0.0031 0.0049 0.0031 0.0078 0.0078 0.1792 0.0901 0.0176 0.4064 0.0055 0.1254 2% 0.0261 0.0040 0.0057 0.0040 0.0093 0.0093 0.1861 0.1076 0.0222 0.4443 0.0063 0.1260 2.1% 0.0327 0.0050 0.0066 0.0050 0.0111 0.0111 0.1934 0.1283 0.0278 0.4850 0.0073 0.1265 2.2% 0.0409 0.0062 0.0076 0.0062 0.0132 0.0132 0.2012 0.1531 0.0347 0.5288 0.0084 0.1271 2.3% 0.0510 0.0077 0.0087 0.0077 0.0157 0.0157 0.2096 0.1826 0.0433 0.5761 0.0097 0.1276 2.4% 0.0635 0.0096 0.0100 0.0096 0.0188 0.0188 0.2186 0.2177 0.0539 0.6272 0.0111 0.1282 2.5% 0.0816 0.0124 0.0118 0.0118 0.0232 0.0232 0.2302 0.2687 0.0698 0.6931 0.0131 0.1289 2.6% 0.1084 0.0164 0.0142 0.0142 0.0296 0.0296 0.2448 0.3431 0.0942 0.7776 0.0158 0.1296 2.7% 0.1438 0.0218 0.0171 0.0171 0.0378 0.0378 0.2612 0.4380 0.1267 0.8736 0.0189 0.1304

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153 Appendix D cont. CPA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 2.8% 0.1903 0.0288 0.0205 0.0205 0.0482 0.0482 0.2797 0.5589 0.1698 0.9821 0.0226 0.1311 2.9% 0.2513 0.0381 0.0245 0.0245 0.0615 0.0615 0.3004 0.7125 0.2269 1.11 0.0268 0.1316 3% 0.3313 0.0502 0.0291 0.0291 0.0783 0.0783 0.3237 0.9076 0.3022 1.25 0.0317 0.1321 3.1% 0.4358 0.0660 0.0343 0.0343 0.0997 0.0997 0.3501 1.16 0.4015 1.41 0.0373 0.1323 3.2% 0.5722 0.0867 0.0402 0.0402 0.1267 0.1267 0.3800 1.47 0.5320 1.59 0.0435 0.1322 3.3% 0.7501 0.1136 0.0468 0.0468 0.1611 0.1611 0.4141 1.87 0.7033 1.80 0.0504 0.1317 3.4% 0.9821 0.1488 0.0540 0.0540 0.2047 0.2047 0.4533 2.37 0.9281 2.05 0.0578 0.1306 3.5% 1.28 0.1945 0.0617 0.0617 0.2599 0.2599 0.4982 3.01 1.22 2.34 0.0657 0.1287 3.6% 1.68 0.2539 0.0696 0.0696 0.3298 0.3298 0.5498 3.82 1.61 2.67 0.0736 0.1258 3.7% 2.18 0.3309 0.0774 0.0774 0.4182 0.4182 0.6093 4.85 2.11 3.06 0.0810 0.1216 3.8% 2.84 0.4307 0.0843 0.0843 0.5298 0.5298 0.6782 6.14 2.76 3.52 0.0873 0.1156 3.9% 3.69 0.5597 0.0894 0.0894 0.6708 0.6708 0.7582 7.78 3.60 4.07 0.0913 0.1074 4% 4.79 0.7256 0.0912 0.0912 0.8479 0.8479 0.8503 9.83 4.70 4.70 0.0913 0.0962 4.1% 6.20 0.9394 0.0878 0.0878 1.07 1.07 0.9577 12.41484 6.11 5.46 0.0852 0.0813 4.2% 8.02 1.21 0.0765 0.0765 1.35 1.35 1.08 15.66834 7.94 6.35 0.0699 0.0615 4.3% 10 1.57 0.0534 0.0534 1.70 1.70 1.23 19.75972 10.29816 7.42 0.0412 0.0356 4.4% 13 1.96 0.0256 0.0256 2.09 2.09 1.38 24.24559 12.94029 8.55 0 0.0063 4.5% 13 1.99 0 0 2.11 2.06 1.36 24.46311 13.12502 8.64 0 0.0056 4.6% 13 2.02 0.0253 0.0253 2.13 2.05 1.34 24.58504 13.28946 8.71 0 0.0052 4.7% 13 2.00 0.0320 0.0320 2.15 1.98 1.33 24.72407 13.1464 8.78 0 0.0047 4.8% 13 2.02 0.0103 0.0103 2.16 1.96 1.31 24.85954 13.30408 8.84 0 0.0044 4.9% 14 2.07 0.0020 0.0020 2.17 1.97 1.29 24.9552 13.63732 8.90 0 0.0041 5% 13 2.04 0.0411 0.0411 2.18 1.90 1.27 25.00267 13.41738 8.95 0 0.0039 5.1% 14 2.06 0 0 2.19 1.89 1.25 25.12789 13.59448 9.02 0 0.0037 5.2% 14 2.10 0.0170 0.0170 2.20 1.88 1.24 25.19375 13.82922 9.08 0 0.0035 5.3% 14 2.06 0.0288 0.0288 2.21 1.81 1.22 25.2636 13.56256 9.14 0 0.0032 5.4% 14 2.08 0.0047 0.0047 2.22 1.81 1.21 25.33054 13.7062 9.17 0 0.0031 5.5% 14 2.12 0.0280 0.0280 2.23 1.80 1.19 25.42337 13.9634 9.27 0 0.0028 5.6% 14 2.09 0.0272 0.0272 2.24 1.74 1.18 25.50207 13.74432 9.34 0 0.0025 5.7% 14 2.13 0 0 2.25 1.74 1.17 25.6029 14.03786 9.41 0 0.0023

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154 Appendix D cont. CPA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 5.8% 14 2.16 0.0191 0.0191 2.26 1.74 1.16 25.66260714.2115459.48 0 0.0021 5.9% 14 2.11 0.0342 0.0342 2.27 1.67 1.15 25.72219313.9241999.55 0 0.0018 6% 14 2.15 0 0 2.28 1.67 1.14 25.82981814.1746779.63 0 0.0016 6.1% 15 2.20 0 0 2.29 1.68 1.13 25.90291 14.51568 9.70 0 0.0014 6.2% 14 2.16 0.0404 0.0404 2.29 1.63 1.12 25.93472914.2237839.78 0 0.0011 6.3% 14 2.15 0.0173 0.0173 2.31 1.59 1.11 26.02916914.1553039.86 0 0.0009 6.4% 14 2.20 0 0 2.31 1.60 1.10 26.11682714.4961059.94 0 0.0007 6.5% 15 2.22 0.0200 0.0200 2.32 1.59 1.09 26.16703314.63090810 0 0.0004 6.6% 14 2.17 0.0281 0.0281 2.33 1.53 1.08 26.22802814.29139310 0 0.0002 6.7% 14 2.19 0.0033 0.0033 2.34 1.53 1.08 26.31850514.45989810 0 0 6.8% 14 2.18 0.0209 0.0209 2.34 1.50 1.06 26 14 10 0 0 6.9% 15 2.20 0 0 2.35 1.49 1.04 26 15 10 0 0 7% 14 2.19 0.0192 0.0192 2.36 1.45 1.02 26 14 10 0 0 7.1% 15 2.25 0.0305 0.0305 2.36 1.47 1.00 26 15 10 0 0 7.2% 15 2.29 0 0 2.36 1.47 0.9852 26 15 10 0 0 7.3% 15 2.25 0 0 2.37 1.43 0.9697 27 15 10 0 0 7.4% 15 2.23 0 0 2.37 1.40 0.9544 27 15 10 0 0 7.5% 15 2.22 0.0446 0.0446 2.37 1.37 0.9388 27 15 10 0 0 7.6% 15 2.26 0.0363 0.0363 2.38 1.38 0.9245 27 15 9.99 0 0 7.7% 15 2.28 0 0 2.38 1.37 0.9109 27 15 9.98 0 0 7.8% 15 2.25 0 0 2.39 1.34 0.8972 27 15 9.95 0 0 7.9% 15 2.24 0.0422 0.0422 2.39 1.31 0.8833 27 15 9.92 0 0 8% 15 2.28 0.0342 0.0342 2.39 1.33 0.8770 27 15 9.92 0 0 8.1% 15 2.28 0 0 2.40 1.31 0.8649 27 15 9.90 0 0 8.2% 15 2.28 0 0 2.40 1.30 0.8531 27 15 9.89 0 0 8.3% 15 2.33 0 0 2.40 1.31 0.8411 27 15 9.87 0 0 8.4% 15 2.31 0 0 2.40 1.28 0.8303 27 15 9.86 0 0 8.5% 15 2.25 0.0366 0.0366 2.41 1.24 0.8193 27 15 9.84 0 0

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155 Appendix D cont. CPA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 0% 0 0.0002 0 0.0012 0 0.0002 0.0001 0.0016 -0.0002 0.0002 0 -0.0002 0.1% 0 0.0002 0 0.0014 0 0.0003 0.0002 0.0019 -0.0003 0.0002 0 -0.0003 0.2% 0 0.0003 0 0.0017 0.0001 0.0003 0.0002 0.0023 -0.0003 0.0003 0 -0.0003 0.3% 0 0.0003 0 0.0020 0.0001 0.0004 0.0002 0.0027 -0.0003 0.0003 0 -0.0003 0.4% 0 0.0004 0 0.0024 0.0002 0.0005 0.0003 0.0033 -0.0004 0.0004 0 -0.0004 0.5% 0 0.0004 0 0.0029 0.0002 0.0006 0.0003 0.0039 -0.0005 0.0004 0 -0.0005 0.6% 0 0.0005 0 0.0034 0.0002 0.0007 0.0004 0.0047 -0.0006 0.0005 0 -0.0006 0.7% 0 0.0006 0 0.0041 0.0003 0.0008 0.0005 0.0057 -0.0006 0.0006 0 -0.0006 0.8% 0.0001 0.0008 0.0001 0.0049 0.0003 0.0010 0.0006 0.0068 -0.0008 0.0008 0.0001 -0.0008 0.9% 0.0001 0.0009 0.0001 0.0059 0.0004 0.0011 0.0007 0.0081 -0.0009 0.0009 0.0001 -0.0009 1% 0.0002 0.0011 0.0002 0.0071 0.0005 0.0014 0.0008 0.0097 -0.0010 0.0011 0.0002 -0.0010 1.1% 0.0002 0.0013 0.0002 0.0085 0.0006 0.0016 0.0010 0.0117 -0.0012 0.0013 0.0002 -0.0012 1.2% 0.0002 0.0016 0.0002 0.0101 0.0007 0.0020 0.0012 0.0140 -0.0014 0.0016 0.0002 -0.0014 1.3% 0.0003 0.0019 0.0003 0.0121 0.0008 0.0023 0.0014 0.0167 -0.0016 0.0019 0.0003 -0.0016 1.4% 0.0003 0.0022 0.0003 0.0145 0.0010 0.0028 0.0017 0.0200 -0.0019 0.0022 0.0003 -0.0019 1.5% 0.0004 0.0027 0.0004 0.0174 0.0012 0.0033 0.0020 0.0239 -0.0022 0.0027 0.0004 -0.0022 1.6% 0.0005 0.0032 0.0005 0.0207 0.0014 0.0040 0.0024 0.0285 -0.0025 0.0032 0.0005 -0.0025 1.7% 0.0006 0.0038 0.0006 0.0248 0.0017 0.0048 0.0029 0.0341 -0.0029 0.0038 0.0006 -0.0029 1.8% 0.0007 0.0046 0.0007 0.0296 0.0020 0.0057 0.0034 0.0407 -0.0034 0.0046 0.0007 -0.0034 1.9% 0.0008 0.0054 0.0008 0.0353 0.0024 0.0068 0.0041 0.0486 -0.0039 0.0054 0.0008 -0.0039 2% 0.0010 0.0065 0.0010 0.0422 0.0029 0.0081 0.0049 0.0580 -0.0044 0.0065 0.0010 -0.0044 2.1% 0.0012 0.0077 0.0012 0.0503 0.0034 0.0097 0.0058 0.0692 -0.0051 0.0077 0.0012 -0.0051 2.2% 0.0014 0.0092 0.0014 0.0600 0.0041 0.0115 0.0069 0.0825 -0.0058 0.0092 0.0014 -0.0058 2.3% 0.0017 0.0110 0.0017 0.0716 0.0048 0.0138 0.0083 0.0984 -0.0067 0.0110 0.0017 -0.0067 2.4% 0.0020 0.0131 0.0020 0.0853 0.0058 0.0164 0.0098 0.1173 -0.0076 0.0131 0.0020 -0.0076 2.5% 0.0025 0.0162 0.0025 0.1053 0.0071 0.0203 0.0122 0.1449 -0.0089 0.0162 0.0025 -0.0089 2.6% 0.0031 0.0207 0.0031 0.1345 0.0091 0.0259 0.0155 0.1850 -0.0106 0.0207 0.0031 -0.0106 2.7% 0.0040 0.0264 0.0040 0.1717 0.0116 0.0330 0.0198 0.2362 -0.0126 0.0264 0.0040 -0.0126

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156 Appendix D cont. CPA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 2.8% 0.0051 0.0337 0.0051 0.2191 0.0148 0.0421 0.0253 0.3013 -0.0148 0.0337 0.0051 -0.0148 2.9% 0.0065 0.0430 0.0065 0.2793 0.0189 0.0537 0.0322 0.3841 -0.0173 0.0430 0.0065 -0.0173 3% 0.0083 0.0547 0.0083 0.3558 0.0241 0.0684 0.0411 0.4893 -0.0201 0.0547 0.0083 -0.0201 3.1% 0.0106 0.0697 0.0106 0.4529 0.0307 0.0871 0.0523 0.6229 -0.0230 0.0697 0.0106 -0.0230 3.2% 0.0134 0.0886 0.0134 0.5760 0.0390 0.1108 0.0665 0.7922 -0.0260 0.0886 0.0134 -0.0260 3.3% 0.0171 0.1126 0.0171 0.7320 0.0496 0.1408 0.0845 1.01 -0.0289 0.1126 0.0171 -0.0289 3.4% 0.0217 0.1431 0.0217 0.9302 0.0630 0.1789 0.1073 1.28 -0.0315 0.1431 0.0217 -0.0315 3.5% 0.0275 0.1817 0.0275 1.18 0.0800 0.2272 0.1363 1.62 -0.0334 0.1817 0.0275 -0.0334 3.6% 0.0349 0.2306 0.0349 1.50 0.1015 0.2882 0.1729 2.06 -0.0340 0.2306 0.0349 -0.0340 3.7% 0.0443 0.2924 0.0443 1.90 0.1286 0.3655 0.2193 2.61 -0.0325 0.2924 0.0443 -0.0325 3.8% 0.0561 0.3704 0.0561 2.41 0.1630 0.4630 0.2778 3.31 -0.0277 0.3704 0.0561 -0.0277 3.9% 0.0711 0.4690 0.0711 3.05 0.2064 0.5862 0.3517 4.19 -0.0181 0.4690 0.0711 -0.0181 4% 0.0898 0.5928 0.0898 3.85 0.2608 0.7410 0.4446 5.30 -0.0014 0.5928 0.0898 -0.0014 4.1% 0.1134 0.7487 0.1134 4.87 0.3294 0.9359 0.5615 6.69 0.0254 0.7487 0.1134 0.0254 4.2% 0.1432 0.9449 0.1432 6.14 0.4158 1.18 0.7087 8.45 0.0663 0.9449 0.1432 0.0663 4.3% 0.1806 1.19 0.1806 7.75 0.5243 1.49 0.8937 11 0.1267 1.19 0.1806 0.1267 4.4% 0.2216 1.46 0.2216 9.51 0.6435 1.83 1.10 13 0.2012 1.46 0.2216 0.2012 4.5% 0.2240 1.48 0.2240 9.61 0.6504 1.85 1.11 13 0.2102 1.48 0.2240 0.2102 4.6% 0.2254 1.49 0.2254 9.67 0.6544 1.86 1.12 13 0.2242 1.49 0.2254 0.2242 4.7% 0.2274 1.50 0.2274 9.76 0.6604 1.88 1.13 13 0.1864 1.50 0.2274 0.1864 4.8% 0.2290 1.51 0.2290 9.82 0.6649 1.89 1.13 14 0.1978 1.51 0.2290 0.1978 4.9% 0.2299 1.52 0.2299 9.86 0.6675 1.90 1.14 14 0.2412 1.52 0.2299 0.2299 5% 0.2310 1.52 0.2310 9.91 0.6708 1.91 1.14 14 0.1990 1.52 0.2310 0.1990 5.1% 0.2324 1.53 0.2324 9.97 0.6749 1.92 1.15 14 0.2144 1.53 0.2324 0.2144 5.2% 0.2331 1.54 0.2331 10 0.6769 1.92 1.15 14 0.2446 1.54 0.2331 0.2331 5.3% 0.2345 1.55 0.2345 10 0.6810 1.93 1.16 14 0.1931 1.55 0.2345 0.1931 5.4% 0.2352 1.55 0.2352 10 0.6830 1.94 1.16 14 0.2093 1.55 0.2352 0.2093 5.5% 0.2362 1.56 0.2362 10 0.6860 1.95 1.17 14 0.2400 1.56 0.2362 0.2362 5.6% 0.2376 1.57 0.2376 10 0.6901 1.96 1.18 14 0.1958 1.57 0.2376 0.1958 5.7% 0.2386 1.57 0.2386 10 0.6929 1.97 1.18 14 0.2325 1.57 0.2386 0.2325

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157 Appendix D cont. CPA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 5.8% 0.2393 1.58 0.2393 10 0.6948 1.97 1.18 14 0.2535 1.58 0.2393 0.2393 5.9% 0.2405 1.59 0.2405 10 0.6984 1.98 1.19 14 0.2003 1.59 0.2405 0.2003 6% 0.2416 1.59 0.2416 10 0.7016 1.99 1.20 14 0.2295 1.59 0.2416 0.2295 6.1% 0.2422 1.60 0.2422 10 0.7033 2.00 1.20 14 0.2763 1.60 0.2422 0.2422 6.2% 0.2431 1.60 0.2431 10 0.7059 2.01 1.20 14 0.2251 1.60 0.2431 0.2251 6.3% 0.2444 1.61 0.2444 10 0.7097 2.02 1.21 14 0.2044 1.61 0.2444 0.2044 6.4% 0.2451 1.62 0.2451 11 0.7119 2.02 1.21 14 0.2499 1.62 0.2451 0.2451 6.5% 0.2457 1.62 0.2457 11 0.7136 2.03 1.22 14 0.2657 1.62 0.2457 0.2457 6.6% 0.2469 1.63 0.2469 11 0.7171 2.04 1.22 15 0.2047 1.63 0.2469 0.2047 6.7% 0.2479 1.64 0.2479 11 0.7200 2.05 1.23 15 0.2224 1.64 0.2479 0.2224 6.8% 0.2484 1.64 0.2484 11 0.7212 2.05 1.23 15 0.2042 1.64 0.2484 0.2042 6.9% 0.2489 1.64 0.2489 11 0.7228 2.05 1.23 15 0.2272 1.64 0.2489 0.2272 7% 0.2495 1.65 0.2495 11 0.7245 2.06 1.23 15 0.2070 1.65 0.2495 0.2070 7.1% 0.2495 1.65 0.2495 11 0.7246 2.06 1.24 15 0.2691 1.65 0.2495 0.2495 7.2% 0.2501 1.65 0.2501 11 0.7263 2.06 1.24 15 0.3000 1.65 0.2501 0.2501 7.3% 0.2508 1.66 0.2508 11 0.7283 2.07 1.24 15 0.2563 1.66 0.2508 0.2508 7.4% 0.2514 1.66 0.2514 11 0.7300 2.07 1.24 15 0.2328 1.66 0.2514 0.2328 7.5% 0.2514 1.66 0.2514 11 0.7301 2.07 1.24 15 0.2193 1.66 0.2514 0.2193 7.6% 0.2517 1.66 0.2517 11 0.7310 2.08 1.25 15 0.2561 1.66 0.2517 0.2517 7.7% 0.2524 1.67 0.2524 11 0.7329 2.08 1.25 15 0.2749 1.67 0.2524 0.2524 7.8% 0.2530 1.67 0.2530 11 0.7346 2.09 1.25 15 0.2422 1.67 0.2530 0.2422 7.9% 0.2530 1.67 0.2530 11 0.7348 2.09 1.25 15 0.2207 1.67 0.2530 0.2207 8% 0.2531 1.67 0.2531 11 0.7349 2.09 1.25 15 0.2663 1.67 0.2531 0.2531 8.1% 0.2538 1.67 0.2538 11 0.7370 2.09 1.26 15 0.2676 1.67 0.2538 0.2538 8.2% 0.2542 1.68 0.2542 11 0.7381 2.10 1.26 15 0.2658 1.68 0.2542 0.2542 8.3% 0.2543 1.68 0.2543 11 0.7384 2.10 1.26 15 0.3143 1.68 0.2543 0.2543 8.4% 0.2547 1.68 0.2547 11 0.7398 2.10 1.26 15 0.2864 1.68 0.2547 0.2547 8.5% 0.2550 1.68 0.2550 11 0.7407 2.10 1.26 15 0.2200 1.68 0.2550 0.2200

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158 Appendix D cont. CPA NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 0% 0.0002 0.1047 0.0002 0 0 -7.9% -7.9% -7.9% -7.3% -15.9% -15.2% 0.1% 0.0003 0.1050 0.0003 0 0 -7.8% -7.8% -7.8% -7.1% -15.6% -14.9% 0.2% 0.0003 0.1053 0.0003 0 0 -7.6% -7.6% -7.6% -6.9% -15.2% -14.6% 0.3% 0.0004 0.1057 0.0004 0 0 -7.4% -7.5% -7.4% -6.8% -14.9% -14.2% 0.4% 0.0005 0.1061 0.0005 0 0 -7.3% -7.3% -7.3% -6.6% -14.6% -13.9% 0.5% 0.0005 0.1065 0.0005 0 0 -7.1% -7.1% -7.1% -6.4% -14.2% -13.5% 0.6% 0.0006 0.1069 0.0006 0 0 -6.9% -6.9% -6.9% -6.2% -13.9% -13.2% 0.7% 0.0007 0.1073 0.0007 0 0 -6.8% -6.8% -6.8% -6.1% -13.5% -12.8% 0.8% 0.0009 0.1077 0.0009 0 0 -6.6% -6.6% -6.6% -5.9% -13.2% -12.5% 0.9% 0.0010 0.1082 0.0010 0 0 -6.4% -6.4% -6.4% -5.7% -12.8% -12.1% 1% 0.0012 0.1087 0.0012 0 0 -6.2% -6.3% -6.2% -5.5% -12.5% -11.8% 1.1% 0.0014 0.1092 0.0014 0 0 -6.1% -6.1% -6.1% -5.4% -12.1% -11.5% 1.2% 0.0016 0.1097 0.0016 0 0 -5.9% -5.9% -5.9% -5.2% -11.8% -11.1% 1.3% 0.0019 0.1102 0.0019 0 0 -5.7% -5.8% -5.7% -5.0% -11.5% -10.7% 1.4% 0.0022 0.1107 0.0022 0 0 -5.6% -5.6% -5.6% -4.8% -11.1% -10.4% 1.5% 0.0026 0.1113 0.0026 0 0 -5.4% -5.4% -5.4% -4.7% -10.8% -10.1% 1.6% 0.0030 0.1119 0.0030 0 0 -5.2% -5.2% -5.2% -4.5% -10.4% -9.7% 1.7% 0.0035 0.1125 0.0035 0 0 -5.0% -5.1% -5.0% -4.3% -10.1% -9.4% 1.8% 0.0040 0.1131 0.0040 0 0 -4.9% -4.9% -4.9% -4.1% -9.7% -9.0% 1.9% 0.0047 0.1137 0.0047 0 0 -4.7% -4.7% -4.7% -4.0% -9.4% -8.7% 2% 0.0054 0.1144 0.0054 0 0 -4.5% -4.6% -4.5% -3.8% -9.0% -8.3% 2.1% 0.0063 0.1151 0.0063 0 0 -4.4% -4.4% -4.4% -3.6% -8.7% -8.0% 2.2% 0.0072 0.1158 0.0072 0 0 -4.2% -4.2% -4.2% -3.4% -8.4% -7.7% 2.3% 0.0084 0.1165 0.0084 0 0 -4.0% -4.1% -4.0% -3.3% -8.0% -7.3% 2.4% 0.0096 0.1172 0.0096 0 0 -3.8% -3.9% -3.8% -3.1% -7.7% -7.0% 2.5% 0.0114 0.1181 0.0114 0 0 -3.6% -3.7% -3.6% -2.9% -7.3% -6.5% 2.6% 0.0138 0.1191 0.0138 0 0 -3.4% -3.4% -3.4% -2.6% -6.8% -6.1% 2.7% 0.0166 0.1201 0.0166 0 0 -3.1% -3.2% -3.1% -2.4% -6.3% -5.6%

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159 Appendix D cont. CPA NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 2.8% 0.0199 0.1210 0.0199 0 0 -2.9% -3.0% -2.9% -2.1% -5.8% -5.1% 2.9% 0.0238 0.1219 0.0238 0 0 -2.7% -2.7% -2.7% -1.9% -5.3% -4.6% 3% 0.0284 0.1227 0.0284 0 0 -2.4% -2.5% -2.4% -1.6% -4.8% -4.1% 3.1% 0.0335 0.1233 0.0335 0 0 -2.2% -2.2% -2.2% -1.4% -4.4% -3.6% 3.2% 0.0394 0.1237 0.0394 0 0 -1.9% -2.0% -1.9% -1.1% -3.9% -3.2% 3.3% 0.0460 0.1238 0.0460 0 0 -1.7% -1.8% -1.7% -0.9% -3.4% -2.7% 3.4% 0.0532 0.1234 0.0532 0 0 -1.5% -1.5% -1.5% -0.7% -2.9% -2.2% 3.5% 0.0610 0.1224 0.0610 0 0 -1.2% -1.3% -1.2% -0.4% -2.4% -1.7% 3.6% 0.0690 0.1204 0.0690 0 0 -1.0% -1.1% -1.0% -0.2% -1.9% -1.2% 3.7% 0.0768 0.1174 0.0768 0 0 -0.7% -0.8% -0.7% 0.1% -1.5% -0.7% 3.8% 0.0839 0.1128 0.0839 0 0 -0.5% -0.6% -0.5% 0.3% -1.0% -0.2% 3.9% 0.0891 0.1062 0.0891 0 0 -0.3% -0.3% -0.3% 0.6% -0.5% 0.2% 4% 0.0912 0.0969 0.0912 0 0 0.0% -0.1% 0.0% 0.8% 0.0% 0.7% 4.1% 0.0880 0.0843 0.0880 0 0 0. 2% 0.1% 0.2% 1.1% 0.4% 1.2% 4.2% 0.0769 0.0672 0.0769 0 0 0. 5% 0.4% 0.5% 1.3% 0.9% 1.7% 4.3% 0.0538 0.0445 0.0538 0 0 0. 7% 0.6% 0.7% 1.5% 1.4% 2.1% 4.4% 0.0204 0.0186 0.0204 0 0 0. 9% 0.8% 1.2% 1.7% 2.1% 2.6% 4.5% 0.0138 0.0174 0.0138 0 0.0065 1.0% 0.8% 0.0% 1.7% 1.0% 2.6% 4.6% 0.0012 0.0170 0.0012 0 0.0129 0.9% 0.8% 2.0% 1.7% 2.9% 2.6% 4.7% 0.0410 0.0165 0.0410 0 0.0226 0.9% 0.8% 0.6% 1.7% 1.4% 2.5% 4.8% 0.0312 0.0157 0.0312 0 0.0302 1.0% 0.8% 0.0% 1.7% 1.0% 2.5% 4.9% 0 0.0153 0 0.0752 0.0444 1. 0% 0.8% 1.5% 1.7% 2.4% 2.5% 5% 0.0320 0.0152 0.0320 0 0.0605 0.8% 0.9% 1.4% 1.6% 2.2% 2.5% 5.1% 0.0180 0.0143 0.0180 0 0.0803 1.0% 0.9% 0.0% 1.6% 1.0% 2.5% 5.2% 0 0.0142 0 0.0757 0.1024 0. 9% 0.9% 2.1% 1.6% 3.1% 2.5% 5.3% 0.0414 0.0139 0.0414 0 0.1270 0.9% 0.9% 0.4% 1.6% 1.3% 2.4% 5.4% 0.0259 0.0134 0.0259 0 0.1414 1.0% 0.9% 0.0% 1.6% 1.0% 2.4% 5.5% 0 0.0130 0 0.0246 0.1833 0. 9% 0.9% 2.3% 1.5% 3.2% 2.4% 5.6% 0.0419 0.0127 0.0419 0 0.2156 0.9% 0.9% 0.3% 1.5% 1.2% 2.4% 5.7% 0.0061 0.0120 0.0061 0 0.2494 1.0% 0.9% 0.0% 1.5% 1.0% 2.4%

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160 Appendix D cont. CPA NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 5.8% 0 0.0119 0 0.0937 0.2871 0. 9% 0.9% 2.4% 1.5% 3.3% 2.4% 5.9% 0.0402 0.0117 0.0402 0 0.3258 0.9% 0.9% 0.7% 1.4% 1.6% 2.3% 6% 0.0121 0.0109 0.0121 0 0.3683 1.0% 0.9% 0.0% 1.4% 1.0% 2.3% 6.1% 0 0.0108 0 0.2250 0.4126 1. 0% 0.9% 2.2% 1.4% 3.2% 2.3% 6.2% 0.0180 0.0107 0.0180 0 0.4564 0.8% 0.9% 2.0% 1.4% 2.8% 2.3% 6.3% 0.0400 0.0102 0.0400 0 0.5051 0.9% 0.9% 0.0% 1.4% 0.9% 2.3% 6.4% 0 0.0096 0 0.0313 0.5573 1. 0% 0.9% 0.0% 1.4% 1.0% 2.3% 6.5% 0 0.0096 0 0.1319 0.6093 0. 9% 0.9% 2.6% 1.4% 3.5% 2.3% 6.6% 0.0422 0.0094 0.0422 0 0.6647 0.9% 0.9% 0.4% 1.3% 1.3% 2.2% 6.7% 0.0255 0.0088 0.0255 0 0.7149 1.0% 0.9% 0.0% 1.3% 1.0% 2.2% 6.8% 0.0442 0.0089 0.0442 0 0.6798 0.9% 0.9% 0.0% 1.3% 0.9% 2.2% 6.9% 0.0217 0.0085 0.0217 0 0.6495 1.0% 0.9% 0.0% 1.3% 1.0% 2.2% 7% 0.0425 0.0087 0.0425 0 0.5979 0.9% 0.9% 0.0% 1.2% 0.9% 2.2% 7.1% 0 0.0087 0 0.1293 0.5534 0. 9% 0.9% 3.1% 1.2% 4.0% 2.2% 7.2% 0 0.0085 0 0.3292 0.5172 1. 0% 0.9% 2.3% 1.2% 3.3% 2.2% 7.3% 0 0.0081 0 0.0363 0.4768 1. 0% 0.9% 0.0% 1.2% 1.0% 2.1% 7.4% 0.0186 0.0081 0.0186 0 0.4368 1.0% 0.9% 0.0% 1.2% 1.0% 2.1% 7.5% 0.0322 0.0086 0.0322 0 0.3936 0.8% 0.9% 1.6% 1.1% 2.4% 2.1% 7.6% 0 0.0083 0 0.0293 0.3553 0. 9% 0.9% 2.7% 1.1% 3.6% 2.1% 7.7% 0 0.0080 0 0.1488 0.3198 1. 0% 0.9% 0.0% 1.1% 1.0% 2.1% 7.8% 0.0108 0.0078 0.0108 0 0.2822 1.0% 0.9% 0.0% 1.1% 1.0% 2.0% 7.9% 0.0324 0.0083 0.0324 0 0.2415 0.8% 0.9% 1.5% 1.1% 2.3% 2.0% 8% 0 0.0082 0 0.0873 0.2245 0. 9% 0.9% 3.0% 1.1% 3.8% 2.0% 8.1% 0 0.0077 0 0.0911 0.1942 1. 0% 0.9% 0.0% 1.1% 1.0% 2.0% 8.2% 0 0.0077 0 0.0767 0.1661 1. 0% 0.9% 0.0% 1.0% 1.0% 2.0% 8.3% 0 0.0079 0 0.3963 0.1340 1. 0% 0.9% 2.5% 1.1% 3.5% 2.0% 8.4% 0 0.0077 0 0.2091 0.1134 1. 0% 0.9% 0.2% 1.0% 1.2% 2.0% 8.5% 0.0351 0.0081 0.0351 0 0.0893 0.9% 1.0% 1.1% 1.0% 1.9% 1.9%

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161 Appendix E. Final values of the 100-iteration period with the increase in al gal photosynthesis rate (CPA) for the deep-adapted coral. CPA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 0% 0.5319 0.5319 3.18 0.0207 0 0 0.0426 0.0426 0 0.0003 0 0.0289 0.1% 0.6242 0.6242 3.32 0.0243 0 0 0.0512 0.0512 0.0083 0.0004 0 0.0328 0.2% 0.7407 0.7407 3.49 0.0288 0 0 0.0622 0.0622 0.0197 0.0004 0 0.0375 0.3% 0.8789 0.8789 3.68 0.0342 0 0 0.0754 0.0754 0.0351 0.0005 0 0.0429 0.4% 1.04 1.04 3.88 0.0406 0 0 0.0915 0.0915 0.0555 0.0006 0 0.0490 0.5% 1.24 1.24 4.11 0.0482 0 0 0.1110 0.1110 0.0824 0.0007 0 0.0559 0.6% 1.47 1.47 4.36 0.0572 0 0 0.1346 0.1346 0.1175 0.0008 0 0.0637 0.7% 1.74 1.74 4.63 0.0678 0 0 0.1629 0.1629 0.1625 0.0010 0 0.0724 0.8% 2.07 2.07 4.93 0.0804 0 0 0.1971 0.1971 0.2202 0.0012 0 0.0821 0.9% 2.45 2.45 5.26 0.0954 0 0 0.2384 0.2384 0.2938 0.0014 0 0.0929 1% 2.91 2.91 5.63 0.1131 0 0 0.2882 0.2882 0.3872 0.0016 0 0.1050 1.1% 3.45 3.45 6.03 0.1340 0 0 0.3478 0.3478 0.5046 0.0019 0 0.1182 1.2% 4.08 4.08 6.48 0.1588 0 0 0.4197 0.4197 0.6520 0.0023 0 0.1327 1.3% 4.84 4.84 6.97 0.1881 0 0 0.5061 0.5061 0.8367 0.0027 0 0.1486 1.4% 5.73 5.73 7.53 0.2229 0 0 0.6104 0.6104 1.07 0.0032 0 0.1660 1.5% 7.14 7.14 8.33 0.2777 0 0 0.7480 0.7480 1.43 0.0040 0 0.1902 1.6% 9.01 9.01 9.32 0.3506 0 0 0.9198 0.9198 1.92 0.0051 0 0.2180 1.7% 11 11 10 0.4421 0 0 1.13 1.13 2.57 0.0064 0 0.2472 1.8% 14 14 12 0.5573 0 0 1.39 1.39 3.43 0.0081 0 0.2768 1.9% 18 18 13 0.7019 0 0 1.70 1.70 4.56 0.0102 0 0.3052 2% 23 23 15 0.8843 0 0 2.08 2.08 6.05 0.0128 0 0.3298 2.1% 29 29 17 1.11 0 0 2.54 2.54 7.99 0.0161 0 0.3467 2.2% 36 36 20 1.40 0 0 3.10 3.10 11 0.0203 0 0.3506 2.3% 45 45 23 1.76 0 0 3.79 3.79 14 0.0255 0 0.3341 2.4% 57 57 27 2.21 0 0 4.62 4.62 18 0.0321 0 0.2863 2.5% 71 71 31 2.77 0 0 5.62 5.62 24 0.0403 0 0.1932 2.6% 79 79 33 3.09 0 0 6.05 6.05 27 0.0439 0 0.1319 2.7% 80 80 33 3.13 0 0 5.90 5.90 27 0.0428 0 0.1289

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162 Appendix E cont. CPA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 2.8% 81 81 34 3.16 0 0 5.75 5.75 28 0.0418 0 0.1261 2.9% 82 82 34 3.19 0 0 5.61 5.61 28 0.0408 0 0.1234 3% 83 83 34 3.22 0 0 5.48 5.48 28 0.0398 0 0.1213 3.1% 84 84 35 3.25 0 0 5.35 5.35 28 0.0389 0 0.1206 3.2% 84 84 35 3.28 0 0 5.23 5.23 29 0.0379 0 0.1224 3.3% 85 85 35 3.30 0 0 5.09 5.09 29 0.0370 0 0.1253 3.4% 86 86 35 3.33 0 0 4.95 4.95 29 0.0359 0 0.1030 3.5% 86 86 35 3.36 0 0 4.87 4.87 29 0.0354 0 0.0246 3.6% 87 87 36 3.37 0 0 4.71 4.71 29 0.0342 0 0.0780 3.7% 87 87 36 3.39 0 0 4.58 4.58 29 0.0332 0 0.1225 3.8% 87 87 36 3.40 0 0 4.48 4.48 29 0.0325 0 0.1779 3.9% 88 88 36 3.41 0 0 4.41 4.41 29 0.0320 0 0.2167 4% 88 88 36 3.42 0 0 4.36 4.36 30 0.0317 0 0.2179 4.1% 88 88 36 3.44 0 0 4.37 4.37 31 0.0317 0 0.1746 4.2% 89 89 36 3.45 0 0.0001 4.31 4.31 31 0.0313 0 0.1462 4.3% 89 89 36 3.46 0 0.0001 4.29 4.29 32 0.0311 0 0.0376 4.4% 89 89 37 3.48 0 0.0001 4.20 4.20 32 0.0305 0 0 4.5% 90 90 37 3.49 0 0.0001 4.04 4.04 31 0.0293 0 0 4.6% 90 90 37 3.50 0 0.0001 3.94 3.94 31 0.0286 0 0 4.7% 90 90 37 3.52 0 0.0001 3.81 3.81 31 0.0277 0 0.0092 4.8% 91 91 37 3.52 0 0.0001 3.71 3.71 30 0.0269 0 0.0558 4.9% 91 91 37 3.53 0 0.0001 3.61 3.61 30 0.0262 0 0.1102 5% 91 91 37 3.54 0 0.0001 3.57 3.57 31 0.0259 0 0.2111 5.1% 92 92 37 3.59 0.0310 0.0044 3.56 3.59 31 0.0261 0 0.0582 5.2% 97 97 39 3.76 0.0567 0.0227 3.70 3.76 33 0.0273 0 0.0292 5.3% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 35 0.0281 0 0 5.4% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 36 0.0281 0 0 5.5% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 36 0.0281 0 0 5.6% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 37 0.0281 0 0 5.7% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 38 0.0281 0 0

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163 Appendix E cont. CPA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 5.8% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 38 0.0281 0 0 5.9% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 39 0.0281 0 0 6% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 40 0.0281 0 0 6.1% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 40 0.0281 0 0 6.2% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 41 0.0281 0 0 6.3% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 42 0.0281 0 0 6.4% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 42 0.0281 0 0 6.5% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 43 0.0281 0 0 6.6% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 44 0.0281 0 0 6.7% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 44 0.0281 0 0 6.8% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 45 0.0281 0 0 6.9% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 46 0.0281 0 0 7% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 46 0.0281 0 0 7.1% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 47 0.0281 0 0 7.2% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 48 0.0281 0 0 7.3% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 48 0.0281 0 0 7.4% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 49 0.0281 0 0 7.5% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 50 0.0281 0 0 7.6% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 50 0.0281 0 0 7.7% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 51 0.0281 0 0 7.8% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 52 0.0281 0 0 7.9% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 52 0.0281 0 0 8% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 53 0.0281 0 0 8.1% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 54 0.0281 0 0 8.2% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 54 0.0281 0 0 8.3% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 55 0.0281 0 0 8.4% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 56 0.0281 0 0 8.5% 100 99 39 3.87 0.0888 0.0352 3.78 3.87 56 0.0281 0 0

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164 Appendix E cont. CPA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 0% -0.0003 0.0000 0.0289 0.0000 0.0414 0.0414 0.2074 0.5733 0 0 0.0301 0.1761 0.1% 0.0079 0.0012 0.0328 0.0012 0.0486 0.0486 0.2336 0.6728 0.0067 0.0324 0.0342 0.1784 0.2% 0.0193 0.0029 0.0375 0.0029 0.0576 0.0576 0.2531 0.7983 0.0164 0.0720 0.0391 0.1810 0.3% 0.0346 0.0052 0.0429 0.0052 0.0684 0.0684 0.2712 0.9473 0.0294 0.1165 0.0447 0.1839 0.4% 0.0550 0.0083 0.0490 0.0083 0.0812 0.0812 0.2894 1.12 0.0466 0.1663 0.0511 0.1869 0.5% 0.0817 0.0124 0.0559 0.0124 0.0963 0.0963 0.3084 1.33 0.0693 0.2220 0.0582 0.1900 0.6% 0.1166 0.0177 0.0637 0.0177 0.1144 0.1144 0.3291 1.58 0.0990 0.2847 0.0662 0.1932 0.7% 0.1615 0.0245 0.0724 0.0245 0.1356 0.1356 0.3510 1.88 0.1370 0.3546 0.0752 0.1965 0.8% 0.2190 0.0332 0.0821 0.0332 0.1609 0.1609 0.3750 2.23 0.1859 0.4333 0.0852 0.1998 0.9% 0.2924 0.0443 0.0929 0.0443 0.1908 0.1908 0.4015 2.64 0.2481 0.5221 0.0962 0.2032 1% 0.3855 0.0584 0.1050 0.0584 0.2262 0.2262 0.4302 3.13 0.3271 0.6220 0.1085 0.2066 1.1% 0.5026 0.0762 0.1182 0.0762 0.2681 0.2681 0.4619 3.71 0.4265 0.7348 0.1218 0.2099 1.2% 0.6497 0.0984 0.1327 0.0984 0.3176 0.3176 0.4969 4.40 0.5513 0.8627 0.1364 0.2131 1.3% 0.8340 0.1264 0.1486 0.1264 0.3762 0.3762 0.5359 5.21 0.7076 1.01 0.1522 0.2161 1.4% 1.06 0.1613 0.1660 0.1613 0.4458 0.4458 0.5794 6.18 0.9035 1.17 0.1692 0.2188 1.5% 1.42 0.2154 0.1902 0.1902 0.5554 0.5554 0.6424 7.69 1.23 1.42 0.1925 0.2218 1.6% 1.92 0.2902 0.2180 0.2180 0.7012 0.7012 0.7192 9.71 1.70 1.74 0.2186 0.2239 1.7% 2.57 0.3888 0.2472 0.2472 0.8843 0.8843 0.8086 12 2.32 2.12 0.2453 0.2244 1.8% 3.42 0.5189 0.2768 0.2768 1.11 1.11 0.9131 15 3.15 2.58 0.2712 0.2227 1.9% 4.55 0.6900 0.3052 0.3052 1.40 1.40 1.04 19 4.25 3.13 0.2942 0.2180 2% 6.04 0.9152 0.3298 0.3298 1.77 1.77 1.18 24 5.71 3.80 0.3114 0.2090 2.1% 8 1.21 0.3467 0.3467 2.22 2.22 1.35 31 7.63 4.62 0.3181 0.1946 2.2% 11 1.59 0.3506 0.3506 2.80 2.80 1.55 39 10 5.61 0.3083 0.1728 2.3% 14 2.09 0.3341 0.3341 3.51 3.51 1.78 49 13 6.82 0.2736 0.1413 2.4% 18 2.74 0.2863 0.2863 4.42 4.42 2.06 61 18 8.31 0.2015 0.0970 2.5% 24 3.59 0.1932 0.1932 5.55 5.55 2.39 77 23 10 0.0766 0.0363 2.6% 27 4.07 0.1319 0.1319 6.18 6.05 2.52 85 27 11 0 0.0030 2.7% 27 4.12 0.1289 0.1289 6.25 5.90 2.45 86 27 11 0 0.0026

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165 Appendix E cont. CPA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 2.8% 28 4.17 0.1261 0.1261 6.32 5.75 2.39 87 27 11 0 0.0022 2.9% 28 4.21 0.1234 0.1234 6.38 5.61 2.33 88 28 11 0 0.0019 3% 28 4.26 0.1213 0.1213 6.44 5.48 2.28 88 28 12 0 0.0016 3.1% 28 4.30 0.1206 0.1206 6.50 5.35 2.22 89 28 12 0 0.0012 3.2% 29 4.33 0.1224 0.1224 6.55 5.23 2.17 89 28 12 0 0.0009 3.3% 29 4.35 0.1253 0.1253 6.61 5.09 2.12 90 29 12 0 0.0006 3.4% 29 4.36 0.1030 0.1030 6.66 4.95 2.08 91 29 12 0 0.0003 3.5% 29 4.42 0.0246 0.0246 6.71 4.87 2.04 91 29 12 0 0 3.6% 29 4.39 0.0780 0.0780 6.74 4.71 1.99 91 29 12 0 0 3.7% 29 4.39 0.1225 0.1225 6.77 4.58 1.94 92 29 12 0 0 3.8% 29 4.41 0.1779 0.1779 6.80 4.48 1.90 92 29 12 0 0 3.9% 29 4.45 0.2167 0.2167 6.82 4.41 1.86 92 29 12 0 0 4% 30 4.52 0.2179 0.2179 6.85 4.36 1.82 92 30 12 0 0 4.1% 31 4.64 0.1746 0.1746 6.87 4.37 1.78 93 30 12 0 0 4.2% 31 4.69 0.1462 0.1462 6.90 4.31 1.74 93 31 12 0 0 4.3% 32 4.77 0.0376 0.0376 6.93 4.29 1.71 93 31 13 0 0 4.4% 32 4.79 0 0 6.95 4.20 1.67 94 32 13 0 0 4.5% 31 4.71 0 0 6.98 4.04 1.64 94 31 13 0 0 4.6% 31 4.70 0 0 7.01 3.94 1.61 94 31 13 0 0 4.7% 31 4.64 0.0092 0.0092 7.03 3.81 1.58 94 31 13 0 0 4.8% 30 4.61 0.0558 0.0558 7.05 3.71 1.55 94 30 13 0 0 4.9% 30 4.58 0.1102 0.1102 7.07 3.61 1.52 94 30 13 0 0 5% 30 4.62 0.2111 0.2111 7.08 3.57 1.49 95 30 13 0 0 5.1% 31 4.74 0.0582 0.0582 7.18 3.59 1.47 96 31 13 0 0 5.2% 33 5.06 0.0292 0.0292 7.52 3.76 1.50 100 33 13 0 0 5.3% 35 5.31 0 0 7.74 3.87 1.53 103 35 13 0 0 5.4% 36 5.42 0 0 7.74 3.87 1.53 103 36 13 0 0 5.5% 36 5.52 0 0 7.74 3.87 1.53 103 36 13 0 0 5.6% 37 5.62 0 0 7.74 3.87 1.53 103 37 13 0 0 5.7% 38 5.72 0 0 7.74 3.87 1.53 103 38 13 0 0

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166 Appendix E cont. CPA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 5.8% 38 5.82 0 0 7.74 3.87 1.53 103 38 13 0 0 5.9% 39 5.92 0 0 7.74 3.87 1.53 103 39 13 0 0 6% 40 6.02 0 0 7.74 3.87 1.53 103 40 13 0 0 6.1% 40 6.12 0 0 7.74 3.87 1.53 103 40 13 0 0 6.2% 41 6.22 0 0 7.74 3.87 1.53 103 41 13 0 0 6.3% 42 6.32 0 0 7.74 3.87 1.53 103 42 13 0 0 6.4% 42 6.32 0 0 7.74 3.87 1.53 103 42 13 0 0 6.5% 43 6.32 0 0 7.74 3.87 1.53 103 43 13 0 0 6.6% 44 6.32 0 0 7.74 3.87 1.53 103 44 13 0 0 6.7% 44 6.32 0 0 7.74 3.87 1.53 103 44 13 0 0 6.8% 45 6.32 0 0 7.74 3.87 1.53 103 45 13 0 0 6.9% 46 6.32 0 0 7.74 3.87 1.53 103 46 13 0 0 7% 46 6.32 0 0 7.74 3.87 1.53 103 46 13 0 0 7.1% 47 6.32 0 0 7.74 3.87 1.53 103 47 13 0 0 7.2% 48 6.32 0 0 7.74 3.87 1.53 103 48 13 0 0 7.3% 48 6.32 0 0 7.74 3.87 1.53 103 48 13 0 0 7.4% 49 6.32 0 0 7.74 3.87 1.53 103 49 13 0 0 7.5% 50 6.32 0 0 7.74 3.87 1.53 103 50 13 0 0 7.6% 50 6.32 0 0 7.74 3.87 1.53 103 50 13 0 0 7.7% 51 6.32 0 0 7.74 3.87 1.53 103 51 13 0 0 7.8% 52 6.32 0 0 7.74 3.87 1.53 103 52 13 0 0 7.9% 52 6.32 0 0 7.74 3.87 1.53 103 52 13 0 0 8% 53 6.32 0 0 7.74 3.87 1.53 103 53 13 0 0 8.1% 54 6.32 0 0 7.74 3.87 1.53 103 54 13 0 0 8.2% 54 6.32 0 0 7.74 3.87 1.53 103 54 13 0 0 8.3% 55 6.32 0 0 7.74 3.87 1.53 103 55 13 0 0 8.4% 56 6.32 0 0 7.74 3.87 1.53 103 56 13 0 0 8.5% 56 6.32 0 0 7.74 3.87 1.53 103 56 13 0 0

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167 Appendix E cont. CPA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 0% 0.0125 0.0825 0.0125 0.1109 0.0267 0.0211 0.0263 0.1850 -0.0155 0.0825 0.0125 -0.0155 0.1% 0.0147 0.0968 0.0147 0.1302 0.0313 0.0247 0.0309 0.2171 -0.0172 0.0968 0.0147 -0.0172 0.2% 0.0174 0.1149 0.0174 0.1545 0.0372 0.0293 0.0367 0.2576 -0.0191 0.1149 0.0174 -0.0191 0.3% 0.0207 0.1363 0.0207 0.1833 0.0441 0.0348 0.0435 0.3057 -0.0212 0.1363 0.0207 -0.0212 0.4% 0.0245 0.1618 0.0245 0.2176 0.0523 0.0413 0.0516 0.3628 -0.0234 0.1618 0.0245 -0.0234 0.5% 0.0291 0.1920 0.0291 0.2582 0.0621 0.0490 0.0613 0.4306 -0.0256 0.1920 0.0291 -0.0256 0.6% 0.0345 0.2280 0.0345 0.3066 0.0737 0.0582 0.0728 0.5113 -0.0279 0.2280 0.0345 -0.0279 0.7% 0.0410 0.2704 0.0410 0.3636 0.0875 0.0690 0.0863 0.6064 -0.0301 0.2704 0.0410 -0.0301 0.8% 0.0486 0.3207 0.0486 0.4313 0.1037 0.0819 0.1024 0.7192 -0.0322 0.3207 0.0486 -0.0322 0.9% 0.0576 0.3804 0.0576 0.5115 0.1230 0.0971 0.1214 0.8530 -0.0340 0.3804 0.0576 -0.0340 1% 0.0683 0.4510 0.0683 0.6065 0.1459 0.1152 0.1439 1.01 -0.0353 0.4510 0.0683 -0.0353 1.1% 0.0810 0.5344 0.0810 0.7186 0.1728 0.1364 0.1706 1.20 -0.0360 0.5344 0.0810 -0.0360 1.2% 0.0959 0.6331 0.0959 0.8513 0.2047 0.1616 0.2021 1.42 -0.0357 0.6331 0.0959 -0.0357 1.3% 0.1136 0.7499 0.1136 1.01 0.2425 0.1915 0.2393 1.68 -0.0340 0.7499 0.1136 -0.0340 1.4% 0.1347 0.8888 0.1347 1.20 0.2874 0.2269 0.2837 1.99 -0.0304 0.8888 0.1347 -0.0304 1.5% 0.1678 1.11 0.1678 1.49 0.3581 0.2827 0.3534 2.48 -0.0219 1.11 0.1678 -0.0219 1.6% 0.2118 1.40 0.2118 1.88 0.4521 0.3569 0.4461 3.13 -0.0060 1.40 0.2118 -0.0060 1.7% 0.2671 1.76 0.2671 2.37 0.5701 0.4501 0.5626 3.95 0.0195 1.76 0.2671 0.0195 1.8% 0.3367 2.22 0.3367 2.99 0.7186 0.5673 0.7091 4.98 0.0587 2.22 0.3367 0.0587 1.9% 0.4240 2.80 0.4240 3.76 0.9051 0.7145 0.8932 6.28 0.1168 2.80 0.4240 0.1168 2% 0.5342 3.53 0.5342 4.74 1.14 0.9002 1.13 7.91 0.2015 3.53 0.5342 0.2015 2.1% 0.6719 4.43 0.6719 5.96 1.43 1.13 1.42 9.94 0.3214 4.43 0.6719 0.3214 2.2% 0.8447 5.58 0.8447 7.50 1.80 1.42 1.78 13 0.4894 5.58 0.8447 0.4894 2.3% 1.06 7.01 1.06 9.42 2.27 1.79 2.24 16 0.7222 7.01 1.06 0.7222 2.4% 1.33 8.81 1.33 12 2.85 2.25 2.81 20 1.04 8.81 1.33 1.04 2.5% 1.68 11 1.68 15 3.58 2.82 3.53 25 1.48 11 1.68 1.48 2.6% 1.87 12 1.87 17 3.98 3.14 3.93 28 1.73 12 1.87 1.73 2.7% 1.89 12 1.89 17 4.03 3.18 3.98 28 1.76 12 1.89 1.76

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168 Appendix E cont. CPA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 2.8% 1.91 13 1.91 17 4.07 3.22 4.02 28 1.78 13 1.91 1.78 2.9% 1.93 13 1.93 17 4.11 3.25 4.06 29 1.80 13 1.93 1.80 3% 1.95 13 1.95 17 4.15 3.28 4.10 29 1.82 13 1.95 1.82 3.1% 1.96 13 1.96 17 4.19 3.31 4.13 29 1.84 13 1.96 1.84 3.2% 1.98 13 1.98 18 4.22 3.33 4.17 29 1.85 13 1.98 1.85 3.3% 2.00 13 2.00 18 4.26 3.36 4.20 30 1.85 13 2.00 1.85 3.4% 2.01 13 2.01 18 4.29 3.39 4.24 30 1.84 13 2.01 1.84 3.5% 2.03 13 2.03 18 4.33 3.42 4.27 30 1.90 13 2.03 1.90 3.6% 2.04 13 2.04 18 4.35 3.43 4.29 30 1.85 13 2.04 1.85 3.7% 2.05 14 2.05 18 4.37 3.45 4.31 30 1.83 14 2.05 1.83 3.8% 2.05 14 2.05 18 4.38 3.46 4.33 30 1.83 14 2.05 1.83 3.9% 2.06 14 2.06 18 4.40 3.47 4.34 31 1.86 14 2.06 1.86 4% 2.07 14 2.07 18 4.42 3.49 4.36 31 1.92 14 2.07 1.92 4.1% 2.08 14 2.08 18 4.43 3.50 4.37 31 2.03 14 2.08 2.03 4.2% 2.08 14 2.08 18 4.45 3.51 4.39 31 2.08 14 2.08 2.08 4.3% 2.09 14 2.09 19 4.47 3.53 4.41 31 2.17 14 2.09 2.09 4.4% 2.10 14 2.10 19 4.48 3.54 4.42 31 2.18 14 2.10 2.10 4.5% 2.11 14 2.11 19 4.50 3.55 4.44 31 2.09 14 2.11 2.09 4.6% 2.12 14 2.12 19 4.52 3.57 4.46 31 2.07 14 2.12 2.07 4.7% 2.12 14 2.12 19 4.53 3.58 4.47 31 2.00 14 2.12 2.00 4.8% 2.13 14 2.13 19 4.55 3.59 4.49 32 1.96 14 2.13 1.96 4.9% 2.13 14 2.13 19 4.56 3.60 4.50 32 1.91 14 2.13 1.91 5% 2.14 14 2.14 19 4.56 3.60 4.50 32 1.93 14 2.14 1.93 5.1% 2.17 14 2.17 19 4.63 3.65 4.57 32 2.04 14 2.17 2.04 5.2% 2.27 15 2.27 20 4.84 3.82 4.78 34 2.24 15 2.27 2.24 5.3% 2.34 15 2.34 21 4.99 3.94 4.92 35 2.41 15 2.34 2.34 5.4% 2.34 15 2.34 21 4.99 3.94 4.92 35 2.51 15 2.34 2.34 5.5% 2.34 15 2.34 21 4.99 3.94 4.92 35 2.61 15 2.34 2.34 5.6% 2.34 15 2.34 21 4.99 3.94 4.92 35 2.71 15 2.34 2.34 5.7% 2.34 15 2.34 21 4.99 3.94 4.92 35 2.81 15 2.34 2.34

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169 Appendix E cont. CPA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 5.8% 2.34 15 2.34 21 4.99 3.94 4.92 35 2.91 15 2.34 2.34 5.9% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.01 15 2.34 2.34 6% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.11 15 2.34 2.34 6.1% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.21 15 2.34 2.34 6.2% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.32 15 2.34 2.34 6.3% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 6.4% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 6.5% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 6.6% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 6.7% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 6.8% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 6.9% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.1% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.2% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.3% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.4% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.5% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.6% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.7% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.8% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 7.9% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 8% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 8.1% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 8.2% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 8.3% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 8.4% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34 8.5% 2.34 15 2.34 21 4.99 3.94 4.92 35 3.42 15 2.34 2.34

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170 Appendix E cont. CPA NTH2 NTH2(ave) NTtotal CEH CEH(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 0% 0.0280 0.1676 0.0280 0 0 -2.9% -2.9% -2.9% -2.2% -5.8% -5.2% 0.1% 0.0319 0.1700 0.0319 0 0 -2.8% -2.8% -2.8% -2.1% -5.5% -4.8% 0.2% 0.0366 0.1730 0.0366 0 0 -2.6% -2.6% -2.6% -1.9% -5.2% -4.5% 0.3% 0.0419 0.1761 0.0419 0 0 -2.4% -2.4% -2.4% -1.7% -4.8% -4.1% 0.4% 0.0479 0.1794 0.0479 0 0 -2.2% -2.3% -2.2% -1.5% -4.5% -3.8% 0.5% 0.0547 0.1829 0.0547 0 0 -2.1% -2.1% -2.1% -1.4% -4.1% -3.4% 0.6% 0.0625 0.1865 0.0625 0 0 -1.9% -1.9% -1.9% -1.2% -3.8% -3.1% 0.7% 0.0711 0.1903 0.0711 0 0 -1.7% -1.7% -1.7% -1.0% -3.5% -2.8% 0.8% 0.0808 0.1942 0.0808 0 0 -1.6% -1.6% -1.6% -0.8% -3.1% -2.4% 0.9% 0.0916 0.1982 0.0916 0 0 -1.4% -1.4% -1.4% -0.6% -2.8% -2.1% 1% 0.1037 0.2023 0.1037 0 0 -1.2% -1.2% -1.2% -0.5% -2.4% -1.7% 1.1% 0.1170 0.2064 0.1170 0 0 -1.0% -1.1% -1.0% -0.3% -2.1% -1.4% 1.2% 0.1316 0.2106 0.1316 0 0 -0.9% -0.9% -0.9% -0.1% -1.7% -1.0% 1.3% 0.1476 0.2148 0.1476 0 0 -0.7% -0.7% -0.7% 0.1% -1.4% -0.7% 1.4% 0.1651 0.2188 0.1651 0 0 -0.5% -0.6% -0.5% 0.2% -1.1% -0.3% 1.5% 0.1897 0.2235 0.1897 0 0 -0.3% -0.3% -0.3% 0.5% -0.6% 0.1% 1.6% 0.2179 0.2277 0.2179 0 0 -0.1% -0.1% -0.1% 0.7% -0.1% 0.6% 1.7% 0.2476 0.2308 0.2476 0 0 0. 2% 0.1% 0.2% 1.0% 0.3% 1.1% 1.8% 0.2780 0.2321 0.2780 0 0 0. 4% 0.4% 0.4% 1.2% 0.8% 1.6% 1.9% 0.3072 0.2310 0.3072 0 0 0. 6% 0.6% 0.6% 1.4% 1.3% 2.0% 2% 0.3327 0.2264 0.3327 0 0 0. 9% 0.8% 0.9% 1.7% 1.8% 2.5% 2.1% 0.3505 0.2170 0.3505 0 0 1. 1% 1.1% 1.1% 1.9% 2.2% 3.0% 2.2% 0.3554 0.2011 0.3554 0 0 1. 4% 1.3% 1.4% 2.1% 2.7% 3.5% 2.3% 0.3395 0.1767 0.3395 0 0 1. 6% 1.5% 1.6% 2.4% 3.2% 3.9% 2.4% 0.2916 0.1406 0.2916 0 0 1. 8% 1.8% 1.8% 2.6% 3.7% 4.4% 2.5% 0.1972 0.0896 0.1972 0 0 2. 1% 2.0% 2.1% 2.9% 4.1% 4.9% 2.6% 0.1347 0.0602 0.1347 0 0 2. 2% 2.1% 2.2% 3.0% 4.4% 5.1% 2.7% 0.1318 0.0583 0.1318 0 0.0015 2.2% 2.1% 2.2% 2.9% 4.4% 5.1%

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171 Appendix E cont. CPA NTH2 NTH2(ave) NTtotal CEH CEH(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 2.8% 0.1288 0.0565 0.1288 0 0.0064 2.2% 2.1% 2.2% 2.9% 4.4% 5.0% 2.9% 0.1259 0.0548 0.1259 0 0.0138 2.2% 2.1% 2.2% 2.9% 4.4% 5.0% 3% 0.1234 0.0532 0.1234 0 0.0232 2.2% 2.2% 2.2% 2.9% 4.4% 5.0% 3.1% 0.1221 0.0517 0.1221 0 0.0347 2.2% 2.2% 2.2% 2.8% 4.4% 5.0% 3.2% 0.1256 0.0502 0.1256 0 0.0482 2.2% 2.2% 2.2% 2.8% 4.4% 5.0% 3.3% 0.1433 0.0488 0.1433 0 0.0636 2.2% 2.2% 1.9% 2.8% 4.1% 5.0% 3.4% 0.1702 0.0472 0.1702 0 0.0806 2.2% 2.2% 0.9% 2.7% 3.1% 4.9% 3.5% 0.1315 0.0451 0.1315 0 0.0992 2.3% 2.2% 0.0% 2.7% 2.3% 4.9% 3.6% 0.1907 0.0447 0.1907 0 0.0980 2.3% 2.2% 0.0% 2.7% 2.3% 4.9% 3.7% 0.2205 0.0442 0.2205 0 0.0959 2.2% 2.2% 0.4% 2.6% 2.6% 4.8% 3.8% 0.2247 0.0439 0.2247 0 0.0942 2.1% 2.2% 1.5% 2.6% 3.7% 4.8% 3.9% 0.2035 0.0434 0.2035 0 0.0904 2.1% 2.2% 2.8% 2.6% 4.9% 4.8% 4% 0.1519 0.0426 0.1519 0 0.0881 2.1% 2.2% 3.9% 2.6% 6.0% 4.8% 4.1% 0.0409 0.0412 0.0409 0 0.0838 2.1% 2.2% 5.1% 2.5% 7.3% 4.8% 4.2% 0.0052 0.0400 0.0052 0 0.0821 2.2% 2.2% 5.2% 2.5% 7.4% 4.8% 4.3% 0 0.0387 0 0.5048 0.0821 2. 3% 2.2% 4.3% 2.5% 6.6% 4.7% 4.4% 0 0.0376 0 0.5032 0.0824 2. 4% 2.2% 3.1% 2.5% 5.4% 4.7% 4.5% 0.0207 0.0363 0.0207 0 0.0784 2.4% 2.2% 0.0% 2.4% 2.4% 4.7% 4.6% 0.0501 0.0357 0.0501 0 0.0793 2.4% 2.2% 0.0% 2.4% 2.4% 4.7% 4.7% 0.1195 0.0353 0.1195 0 0.0773 2.3% 2.2% 0.0% 2.4% 2.3% 4.6% 4.8% 0.1710 0.0353 0.1710 0 0.0790 2.3% 2.3% 0.0% 2.3% 2.3% 4.6% 4.9% 0.2277 0.0355 0.2277 0 0.0797 2.2% 2.3% 0.1% 2.3% 2.3% 4.6% 5% 0.2064 0.0360 0.2064 0 0.0801 2.1% 2.3% 2.7% 2.3% 4.8% 4.5% 5.1% 0.1273 0.0296 0.1584 0.2048 0.0 294 2.3% 2.3% 1.0% 2.3% 3.2% 4.5% 5.2% 0.0298 0.0119 0.0865 0.3739 0.1 497 2.3% 2.3% 2.3% 2.3% 4.6% 4.6% 5.3% 0 0 0.0888 1.09 0.4299 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 5.4% 0 0 0.0888 1.75 0.6930 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 5.5% 0 0 0.0888 2.41 0.9550 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 5.6% 0 0 0.0888 3.07 1.22 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 5.7% 0 0 0.0888 3.74 1.48 2.3% 2.3% 2.3% 2.3% 4.7% 4.7%

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172 Appendix E cont. CPA NTH2 NTH2(ave) NTtotal CEH CEH(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 5.8% 0 0 0.0888 4.40 1.74 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 5.9% 0 0 0.0888 5.06 2.00 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6% 0 0 0.0888 5.72 2.27 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.1% 0 0 0.0888 6.39 2.53 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.2% 0 0 0.0888 7.05 2.79 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.3% 0 0 0.0888 7.71 3.05 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.4% 0 0 0.0888 8.37 3.72 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.5% 0 0 0.0888 9.03 4.38 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.6% 0 0 0.0888 9.69 5.04 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.7% 0 0 0.0888 10 5.70 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.8% 0 0 0.0888 11 6.36 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 6.9% 0 0 0.0888 12 7.02 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 7% 0 0 0.0888 12 7.68 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 7.1% 0 0 0.0888 13 8.35 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 7.2% 0 0 0.0888 14 9.01 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 7.3% 0 0 0.0888 14 9.67 2.3% 2.3% 2.3% 2.3% 4.7% 4.7% 7.4% 0 0 0.0888 15 10 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 7.5% 0 0 0.0888 16 11 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 7.6% 0 0 0.0888 16 12 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 7.7% 0 0 0.0888 17 12 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 7.8% 0 0 0.0888 18 13 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 7.9% 0 0 0.0888 18 14 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 8% 0 0 0.0888 19 14 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 8.1% 0 0 0.0888 20 15 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 8.2% 0 0 0.0888 20 16 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 8.3% 0 0 0.0888 21 16 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 8.4% 0 0 0.0888 22 17 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7% 8.5% 0 0 0.0888 22 18 2.3% 2. 3% 2.3% 2.3% 4.7% 4.7%

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173 Appendix F. Final values of the 100-iteration peri od with the increase in nitrogen uptake rate (NIA) for the shallow-adapted coral. NIA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 0% 25 25 17 1.20 0 0 1.27 1.27 15 0.0252 0.0000 0.0395 0.1% 26 26 17 1.25 0 0 2.25 2.25 26 0.0446 0.0265 0.0265 0.2% 26 26 17 1.25 0 0 2.53 2.53 29 0.0495 0.0530 0.0530 0.3% 27 27 17 1.25 0 0 2.56 2.56 29 0.0496 0.0796 0.0796 0.4% 27 27 17 1.25 0 0 2.59 2.59 29 0.0497 0.1063 0.1063 0.5% 27 27 17 1.26 0 0 2.62 2.62 29 0.0497 0.1330 0.1330 0.6% 27 27 17 1.26 0 0 2.64 2.64 29 0.0497 0.1596 0.1596 0.7% 27 27 17 1.26 0 0 2.67 2.67 29 0.0497 0.1861 0.1861 0.8% 27 27 17 1.25 0 0 2.70 2.70 29 0.0497 0.2127 0.2127 0.9% 27 27 17 1.25 0 0 2.72 2.72 29 0.0497 0.2392 0.2392 1% 27 27 17 1.25 0 0 2.75 2.75 29 0.0497 0.2658 0.2658 1.1% 27 27 17 1.25 0 0 2.77 2.77 29 0.0497 0.2923 0.2923 1.2% 27 27 17 1.25 0 0 2.80 2.80 29 0.0497 0.3188 0.3188 1.3% 27 27 17 1.25 0 0 2.82 2.82 29 0.0497 0.3454 0.3454 1.4% 27 27 17 1.25 0 0 2.85 2.85 29 0.0496 0.3719 0.3719 1.5% 27 27 17 1.25 0 0 2.88 2.88 29 0.0496 0.3984 0.3984 1.6% 27 27 17 1.25 0 0 2.90 2.90 29 0.0496 0.4249 0.4249 1.7% 27 27 17 1.25 0 0 2.93 2.93 29 0.0496 0.4513 0.4513 1.8% 27 27 17 1.25 0 0 2.95 2.95 29 0.0496 0.4778 0.4778 1.9% 27 27 17 1.25 0 0 2.98 2.98 29 0.0496 0.5043 0.5043 2% 27 27 17 1.25 0 0 3.01 3.01 29 0.0496 0.5307 0.5307 2.1% 27 27 17 1.25 0 0 3.03 3.03 29 0.0496 0.5572 0.5572 2.2% 27 27 17 1.25 0 0 3.06 3.06 29 0.0496 0.5836 0.5836 2.3% 27 27 17 1.25 0 0 3.08 3.08 29 0.0496 0.6101 0.6101 2.4% 27 27 17 1.25 0 0 3.11 3.11 29 0.0496 0.6365 0.6365 2.5% 27 27 17 1.25 0 0 3.13 3.13 29 0.0496 0.6629 0.6629 2.6% 27 27 17 1.25 0 0 3.16 3.16 29 0.0496 0.6893 0.6893 2.7% 27 27 17 1.25 0 0 3.19 3.19 29 0.0495 0.7157 0.7157

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174 Appendix F cont. NIA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 2.8% 27 27 17 1.25 0 0 3.21 3.21 29 0.0495 0.7421 0.7421 2.9% 27 27 17 1.25 0 0 3.24 3.24 29 0.0495 0.7685 0.7685 3% 26 26 17 1.25 0 0 3.26 3.26 29 0.0495 0.7949 0.7949 3.1% 26 26 17 1.25 0 0 3.29 3.29 29 0.0495 0.8213 0.8213 3.2% 26 26 17 1.25 0 0 3.32 3.32 29 0.0495 0.8477 0.8477 3.3% 26 26 17 1.25 0 0 3.34 3.34 29 0.0495 0.8740 0.8740 3.4% 26 26 17 1.25 0 0 3.37 3.37 29 0.0495 0.9004 0.9004 3.5% 26 26 17 1.25 0 0 3.39 3.39 29 0.0495 0.9267 0.9267 3.6% 26 26 17 1.25 0 0 3.42 3.42 29 0.0495 0.9530 0.9530 3.7% 26 26 17 1.25 0 0 3.44 3.44 29 0.0495 0.9794 0.9794 3.8% 26 26 17 1.25 0 0 3.47 3.47 29 0.0495 1.01 1.01 3.9% 26 26 17 1.25 0 0 3.49 3.49 29 0.0495 1.03 1.03 4% 26 26 17 1.25 0 0 3.52 3.52 29 0.0495 1.06 1.06 4.1% 26 26 17 1.25 0 0 3.55 3.55 29 0.0494 1.08 1.08 4.2% 26 26 17 1.25 0 0 3.57 3.57 29 0.0494 1.11 1.11 4.3% 26 26 17 1.25 0 0 3.60 3.60 29 0.0494 1.14 1.14 4.4% 26 26 17 1.25 0 0 3.62 3.62 29 0.0494 1.16 1.16 4.5% 26 26 17 1.25 0 0 3.65 3.65 29 0.0494 1.19 1.19 4.6% 26 26 17 1.25 0 0 3.67 3.67 29 0.0494 1.22 1.22 4.7% 26 26 17 1.25 0 0 3.70 3.70 29 0.0494 1.24 1.24 4.8% 26 26 17 1.25 0 0 3.73 3.73 29 0.0494 1.27 1.27 4.9% 26 26 17 1.25 0 0 3.75 3.75 29 0.0494 1.29 1.29 5% 26 26 17 1.25 0 0 3.78 3.78 29 0.0494 1.32 1.32 5.1% 26 26 17 1.25 0 0 3.80 3.80 29 0.0494 1.35 1.35 5.2% 26 26 17 1.25 0 0 3.83 3.83 29 0.0494 1.37 1.37 5.3% 26 26 17 1.25 0 0 3.85 3.85 29 0.0494 1.40 1.40 5.4% 26 26 17 1.25 0 0 3.88 3.88 29 0.0493 1.43 1.43 5.5% 26 26 17 1.25 0 0 3.90 3.90 29 0.0493 1.45 1.45 5.6% 26 26 17 1.25 0 0 3.93 3.93 29 0.0493 1.48 1.48 5.7% 26 26 17 1.25 0 0 3.96 3.96 29 0.0493 1.50 1.50

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175 Appendix F cont. NIA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 5.8% 26 26 17 1.25 0 0 3.98 3.98 29 0.0493 1.53 1.53 5.9% 26 26 17 1.25 0 0 4.01 4.01 29 0.0493 1.56 1.56 6% 26 26 17 1.24 0 0 4.03 4.03 29 0.0493 1.58 1.58 6.1% 26 26 17 1.24 0 0 4.06 4.06 29 0.0493 1.61 1.61 6.2% 26 26 17 1.24 0 0 4.08 4.08 29 0.0493 1.63 1.63 6.3% 26 26 17 1.24 0 0 4.11 4.11 29 0.0493 1.66 1.66 6.4% 26 26 17 1.24 0 0 4.13 4.13 29 0.0493 1.69 1.69 6.5% 26 26 17 1.24 0 0 4.16 4.16 29 0.0493 1.71 1.71 6.6% 26 26 17 1.24 0 0 4.19 4.19 29 0.0493 1.74 1.74 6.7% 26 26 17 1.24 0 0 4.21 4.21 29 0.0492 1.77 1.77 6.8% 26 26 17 1.24 0 0 4.24 4.24 29 0.0492 1.79 1.79 6.9% 26 26 17 1.24 0 0 4.26 4.26 29 0.0492 1.82 1.82 7% 26 26 17 1.24 0 0 4.29 4.29 29 0.0492 1.84 1.84 7.1% 26 26 17 1.24 0 0 4.31 4.31 29 0.0492 1.87 1.87 7.2% 26 26 17 1.24 0 0 4.34 4.34 29 0.0492 1.90 1.90 7.3% 26 26 17 1.24 0 0 4.36 4.36 29 0.0492 1.92 1.92 7.4% 26 26 17 1.24 0 0 4.39 4.39 29 0.0492 1.95 1.95 7.5% 26 26 17 1.24 0 0 4.41 4.41 29 0.0492 1.97 1.97 7.6% 26 26 17 1.24 0 0 4.44 4.44 29 0.0492 2.00 2.00 7.7% 26 26 17 1.24 0 0 4.46 4.46 29 0.0492 2.03 2.03 7.8% 26 26 17 1.24 0 0 4.49 4.49 29 0.0492 2.05 2.05 7.9% 26 26 17 1.24 0 0 4.52 4.52 29 0.0492 2.08 2.08 8% 26 26 17 1.24 0 0 4.54 4.54 29 0.0492 2.10 2.10 8.1% 26 26 17 1.24 0 0 4.57 4.57 29 0.0491 2.13 2.13 8.2% 26 26 17 1.24 0 0 4.59 4.59 29 0.0491 2.16 2.16 8.3% 26 26 17 1.24 0 0 4.62 4.62 29 0.0491 2.18 2.18 8.4% 26 26 17 1.24 0 0 4.64 4.64 29 0.0491 2.21 2.21 8.5% 26 26 17 1.24 0 0 4.67 4.67 29 0.0491 2.23 2.23

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176 Appendix F cont. NIA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 0% 15 2.24 0.0395 0.0395 2.40 1.27 0.8487 27 15 9.87 0 0 0.1% 26 3.97 0.0265 0.0265 2.50 2.25 1.29 29 26 15 0 0 0.2% 29 4.41 0.0530 0.0530 2.50 2.50 1.54 29 29 18 0.0277 0.0141 0.3% 29 4.42 0.0796 0.0796 2.51 2.51 1.57 29 29 18 0.0540 0.0308 0.4% 29 4.43 0.1063 0.1063 2.51 2.51 1.58 29 29 18 0.0804 0.0475 0.5% 29 4.43 0.1330 0.1330 2.51 2.51 1.59 29 29 18 0.1068 0.0643 0.6% 29 4.43 0.1596 0.1596 2.51 2.51 1.59 29 29 18 0.1331 0.0811 0.7% 29 4.43 0.1861 0.1861 2.51 2.51 1.59 29 29 18 0.1594 0.0979 0.8% 29 4.43 0.2127 0.2127 2.51 2.51 1.59 29 29 18 0.1857 0.1148 0.9% 29 4.43 0.2392 0.2392 2.51 2.51 1.60 29 29 18 0.2120 0.1316 1% 29 4.43 0.2658 0.2658 2.51 2.51 1.60 29 29 18 0.2383 0.1484 1.1% 29 4.43 0.2923 0.2923 2.51 2.51 1.60 29 29 18 0.2646 0.1652 1.2% 29 4.42 0.3188 0.3188 2.51 2.51 1.60 29 29 18 0.2908 0.1820 1.3% 29 4.42 0.3454 0.3454 2.51 2.51 1.60 29 29 18 0.3171 0.1988 1.4% 29 4.42 0.3719 0.3719 2.51 2.51 1.60 29 29 18 0.3434 0.2156 1.5% 29 4.42 0.3984 0.3984 2.51 2.51 1.60 29 29 18 0.3696 0.2324 1.6% 29 4.42 0.4249 0.4249 2.51 2.51 1.60 29 29 18 0.3958 0.2492 1.7% 29 4.42 0.4513 0.4513 2.51 2.51 1.60 29 29 18 0.4221 0.2660 1.8% 29 4.42 0.4778 0.4778 2.51 2.51 1.60 29 29 18 0.4483 0.2828 1.9% 29 4.42 0.5043 0.5043 2.51 2.51 1.60 29 29 18 0.4745 0.2996 2% 29 4.42 0.5307 0.5307 2.51 2.51 1.60 29 29 18 0.5007 0.3163 2.1% 29 4.42 0.5572 0.5572 2.50 2.50 1.60 29 29 18 0.5269 0.3331 2.2% 29 4.42 0.5836 0.5836 2.50 2.50 1.60 29 29 18 0.5531 0.3498 2.3% 29 4.42 0.6101 0.6101 2.50 2.50 1.60 29 29 18 0.5792 0.3666 2.4% 29 4.42 0.6365 0.6365 2.50 2.50 1.60 29 29 18 0.6054 0.3833 2.5% 29 4.42 0.6629 0.6629 2.50 2.50 1.60 29 28 18 0.6316 0.4001 2.6% 29 4.42 0.6893 0.6893 2.50 2.50 1.60 29 28 18 0.6577 0.4168 2.7% 29 4.41 0.7157 0.7157 2.50 2.50 1.60 29 28 18 0.6839 0.4336

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177 Appendix F cont. NIA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 2.8% 29 4.41 0.7421 0.7421 2.50 2.50 1.60 29 28 18 0.7100 0.4503 2.9% 29 4.41 0.7685 0.7685 2.50 2.50 1.60 29 28 18 0.7362 0.4670 3% 29 4.41 0.7949 0.7949 2.50 2.50 1.60 29 28 18 0.7623 0.4837 3.1% 29 4.41 0.8213 0.8213 2.50 2.50 1.60 29 28 18 0.7884 0.5004 3.2% 29 4.41 0.8477 0.8477 2.50 2.50 1.60 29 28 18 0.8145 0.5172 3.3% 29 4.41 0.8740 0.8740 2.50 2.50 1.60 29 28 18 0.8406 0.5339 3.4% 29 4.41 0.9004 0.9004 2.50 2.50 1.60 29 28 18 0.8667 0.5506 3.5% 29 4.41 0.9267 0.9267 2.50 2.50 1.60 29 28 18 0.8928 0.5672 3.6% 29 4.41 0.9530 0.9530 2.50 2.50 1.60 29 28 18 0.9189 0.5839 3.7% 29 4.41 0.9794 0.9794 2.50 2.50 1.60 29 28 18 0.9449 0.6006 3.8% 29 4.41 1.01 1.01 2.50 2.50 1.60 29 28 18 0.9710 0.6173 3.9% 29 4.41 1.03 1.03 2.50 2.50 1.60 29 28 18 0.9970 0.6340 4% 29 4.41 1.06 1.06 2.50 2.50 1.60 29 28 18 1.02 0.6506 4.1% 29 4.41 1.08 1.08 2.50 2.50 1.60 29 28 18 1.05 0.6673 4.2% 29 4.40 1.11 1.11 2.50 2.50 1.60 29 28 18 1.08 0.6839 4.3% 29 4.40 1.14 1.14 2.50 2.50 1.60 29 28 18 1.10 0.7006 4.4% 29 4.40 1.16 1.16 2.50 2.50 1.60 29 28 18 1.13 0.7172 4.5% 29 4.40 1.19 1.19 2.50 2.50 1.60 29 28 18 1.15 0.7339 4.6% 29 4.40 1.22 1.22 2.50 2.50 1.60 29 28 18 1.18 0.7505 4.7% 29 4.40 1.24 1.24 2.49 2.49 1.59 29 28 18 1.21 0.7672 4.8% 29 4.40 1.27 1.27 2.49 2.49 1.59 29 28 18 1.23 0.7838 4.9% 29 4.40 1.29 1.29 2.49 2.49 1.59 29 28 18 1.26 0.8004 5% 29 4.40 1.32 1.32 2.49 2.49 1.59 29 28 18 1.28 0.8170 5.1% 29 4.40 1.35 1.35 2.49 2.49 1.59 29 28 18 1.31 0.8336 5.2% 29 4.40 1.37 1.37 2.49 2.49 1.59 29 28 18 1.33 0.8502 5.3% 29 4.40 1.40 1.40 2.49 2.49 1.59 29 28 18 1.36 0.8668 5.4% 29 4.40 1.43 1.43 2.49 2.49 1.59 29 28 18 1.39 0.8834 5.5% 29 4.40 1.45 1.45 2.49 2.49 1.59 29 28 18 1.41 0.9000 5.6% 29 4.40 1.48 1.48 2.49 2.49 1.59 29 28 18 1.44 0.9166 5.7% 29 4.39 1.50 1.50 2.49 2.49 1.59 29 27 18 1.46 0.9332

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178 Appendix F cont. NIA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 5.8% 29 4.39 1.53 1.53 2.49 2.49 1.59 29 27 18 1.49 0.9498 5.9% 29 4.39 1.56 1.56 2.49 2.49 1.59 29 27 18 1.52 0.9663 6% 29 4.39 1.58 1.58 2.49 2.49 1.59 29 27 18 1.54 0.9829 6.1% 29 4.39 1.61 1.61 2.49 2.49 1.59 29 27 17 1.57 0.9995 6.2% 29 4.39 1.63 1.63 2.49 2.49 1.59 29 27 17 1.59 1.02 6.3% 29 4.39 1.66 1.66 2.49 2.49 1.59 29 27 17 1.62 1.03 6.4% 29 4.39 1.69 1.69 2.49 2.49 1.59 29 27 17 1.65 1.05 6.5% 29 4.39 1.71 1.71 2.49 2.49 1.59 29 27 17 1.67 1.07 6.6% 29 4.39 1.74 1.74 2.49 2.49 1.59 29 27 17 1.70 1.08 6.7% 29 4.39 1.77 1.77 2.49 2.49 1.59 29 27 17 1.72 1.10 6.8% 29 4.39 1.79 1.79 2.49 2.49 1.59 29 27 17 1.75 1.12 6.9% 29 4.39 1.82 1.82 2.49 2.49 1.59 29 27 17 1.77 1.13 7% 29 4.39 1.84 1.84 2.49 2.49 1.59 29 27 17 1.80 1.15 7.1% 29 4.39 1.87 1.87 2.49 2.49 1.59 29 27 17 1.83 1.16 7.2% 29 4.38 1.90 1.90 2.49 2.49 1.59 29 27 17 1.85 1.18 7.3% 29 4.38 1.92 1.92 2.49 2.49 1.59 29 27 17 1.88 1.20 7.4% 29 4.38 1.95 1.95 2.48 2.48 1.59 29 27 17 1.90 1.21 7.5% 29 4.38 1.97 1.97 2.48 2.48 1.59 29 27 17 1.93 1.23 7.6% 29 4.38 2.00 2.00 2.48 2.48 1.59 29 27 17 1.96 1.25 7.7% 29 4.38 2.03 2.03 2.48 2.48 1.59 29 27 17 1.98 1.26 7.8% 29 4.38 2.05 2.05 2.48 2.48 1.59 29 27 17 2.01 1.28 7.9% 29 4.38 2.08 2.08 2.48 2.48 1.59 29 27 17 2.03 1.30 8% 29 4.38 2.10 2.10 2.48 2.48 1.59 29 27 17 2.06 1.31 8.1% 29 4.38 2.13 2.13 2.48 2.48 1.59 29 27 17 2.08 1.33 8.2% 29 4.38 2.16 2.16 2.48 2.48 1.59 29 27 17 2.11 1.35 8.3% 29 4.38 2.18 2.18 2.48 2.48 1.59 29 27 17 2.14 1.36 8.4% 29 4.38 2.21 2.21 2.48 2.48 1.59 29 27 17 2.16 1.38 8.5% 29 4.38 2.23 2.23 2.48 2.48 1.59 29 27 17 2.19 1.40

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179 Appendix F cont. NIA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 0% 0.2541 1.68 0.2541 11 0.7379 2.10 1.26 15 0.2206 1.68 0.2541 0.2206 0.1% 0.2646 1.75 0.2646 11 0.7684 2.18 1.31 16 1.87 1.75 0.2646 0.2646 0.2% 0.2650 1.75 0.2650 11 0.7695 2.19 1.31 16 2.30 1.75 0.2650 0.2650 0.3% 0.2654 1.75 0.2654 11 0.7706 2.19 1.31 16 2.30 1.75 0.2654 0.2654 0.4% 0.2658 1.75 0.2658 11 0.7717 2.19 1.32 16 2.30 1.75 0.2658 0.2658 0.5% 0.2660 1.76 0.2660 11 0.7724 2.19 1.32 16 2.30 1.76 0.2660 0.2660 0.6% 0.2659 1.76 0.2659 11 0.7723 2.19 1.32 16 2.29 1.76 0.2659 0.2659 0.7% 0.2659 1.75 0.2659 11 0.7722 2.19 1.32 16 2.29 1.75 0.2659 0.2659 0.8% 0.2659 1.75 0.2659 11 0.7720 2.19 1.32 16 2.28 1.75 0.2659 0.2659 0.9% 0.2658 1.75 0.2658 11 0.7719 2.19 1.32 16 2.28 1.75 0.2658 0.2658 1% 0.2658 1.75 0.2658 11 0.7718 2.19 1.32 16 2.28 1.75 0.2658 0.2658 1.1% 0.2657 1.75 0.2657 11 0.7717 2.19 1.32 16 2.27 1.75 0.2657 0.2657 1.2% 0.2657 1.75 0.2657 11 0.7716 2.19 1.32 16 2.27 1.75 0.2657 0.2657 1.3% 0.2657 1.75 0.2657 11 0.7715 2.19 1.31 16 2.26 1.75 0.2657 0.2657 1.4% 0.2656 1.75 0.2656 11 0.7713 2.19 1.31 16 2.26 1.75 0.2656 0.2656 1.5% 0.2656 1.75 0.2656 11 0.7712 2.19 1.31 16 2.25 1.75 0.2656 0.2656 1.6% 0.2655 1.75 0.2655 11 0.7711 2.19 1.31 16 2.25 1.75 0.2655 0.2655 1.7% 0.2655 1.75 0.2655 11 0.7710 2.19 1.31 16 2.24 1.75 0.2655 0.2655 1.8% 0.2655 1.75 0.2655 11 0.7709 2.19 1.31 16 2.24 1.75 0.2655 0.2655 1.9% 0.2654 1.75 0.2654 11 0.7708 2.19 1.31 16 2.24 1.75 0.2654 0.2654 2% 0.2654 1.75 0.2654 11 0.7706 2.19 1.31 16 2.23 1.75 0.2654 0.2654 2.1% 0.2653 1.75 0.2653 11 0.7705 2.19 1.31 16 2.23 1.75 0.2653 0.2653 2.2% 0.2653 1.75 0.2653 11 0.7704 2.19 1.31 16 2.22 1.75 0.2653 0.2653 2.3% 0.2653 1.75 0.2653 11 0.7703 2.19 1.31 16 2.22 1.75 0.2653 0.2653 2.4% 0.2652 1.75 0.2652 11 0.7702 2.19 1.31 16 2.21 1.75 0.2652 0.2652 2.5% 0.2652 1.75 0.2652 11 0.7701 2.19 1.31 16 2.21 1.75 0.2652 0.2652 2.6% 0.2651 1.75 0.2651 11 0.7699 2.19 1.31 16 2.21 1.75 0.2651 0.2651 2.7% 0.2651 1.75 0.2651 11 0.7698 2.19 1.31 16 2.20 1.75 0.2651 0.2651

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180 Appendix F cont. NIA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 2.8% 0.2651 1.75 0.2651 11 0.7697 2.19 1.31 16 2.20 1.75 0.2651 0.2651 2.9% 0.2650 1.75 0.2650 11 0.7696 2.19 1.31 16 2.19 1.75 0.2650 0.2650 3% 0.2650 1.75 0.2650 11 0.7695 2.19 1.31 16 2.19 1.75 0.2650 0.2650 3.1% 0.2649 1.75 0.2649 11 0.7694 2.19 1.31 16 2.18 1.75 0.2649 0.2649 3.2% 0.2649 1.75 0.2649 11 0.7692 2.19 1.31 16 2.18 1.75 0.2649 0.2649 3.3% 0.2649 1.75 0.2649 11 0.7691 2.19 1.31 16 2.18 1.75 0.2649 0.2649 3.4% 0.2648 1.75 0.2648 11 0.7690 2.18 1.31 16 2.17 1.75 0.2648 0.2648 3.5% 0.2648 1.75 0.2648 11 0.7689 2.18 1.31 16 2.17 1.75 0.2648 0.2648 3.6% 0.2647 1.75 0.2647 11 0.7688 2.18 1.31 16 2.16 1.75 0.2647 0.2647 3.7% 0.2647 1.75 0.2647 11 0.7687 2.18 1.31 16 2.16 1.75 0.2647 0.2647 3.8% 0.2647 1.75 0.2647 11 0.7685 2.18 1.31 16 2.15 1.75 0.2647 0.2647 3.9% 0.2646 1.75 0.2646 11 0.7684 2.18 1.31 16 2.15 1.75 0.2646 0.2646 4% 0.2646 1.75 0.2646 11 0.7683 2.18 1.31 16 2.14 1.75 0.2646 0.2646 4.1% 0.2645 1.75 0.2645 11 0.7682 2.18 1.31 16 2.14 1.75 0.2645 0.2645 4.2% 0.2645 1.75 0.2645 11 0.7681 2.18 1.31 16 2.14 1.75 0.2645 0.2645 4.3% 0.2644 1.75 0.2644 11 0.7680 2.18 1.31 16 2.13 1.75 0.2644 0.2644 4.4% 0.2644 1.75 0.2644 11 0.7678 2.18 1.31 16 2.13 1.75 0.2644 0.2644 4.5% 0.2644 1.74 0.2644 11 0.7677 2.18 1.31 16 2.12 1.74 0.2644 0.2644 4.6% 0.2643 1.74 0.2643 11 0.7676 2.18 1.31 16 2.12 1.74 0.2643 0.2643 4.7% 0.2643 1.74 0.2643 11 0.7675 2.18 1.31 16 2.11 1.74 0.2643 0.2643 4.8% 0.2642 1.74 0.2642 11 0.7674 2.18 1.31 16 2.11 1.74 0.2642 0.2642 4.9% 0.2642 1.74 0.2642 11 0.7673 2.18 1.31 16 2.11 1.74 0.2642 0.2642 5% 0.2642 1.74 0.2642 11 0.7671 2.18 1.31 16 2.10 1.74 0.2642 0.2642 5.1% 0.2641 1.74 0.2641 11 0.7670 2.18 1.31 16 2.10 1.74 0.2641 0.2641 5.2% 0.2641 1.74 0.2641 11 0.7669 2.18 1.31 16 2.09 1.74 0.2641 0.2641 5.3% 0.2640 1.74 0.2640 11 0.7668 2.18 1.31 16 2.09 1.74 0.2640 0.2640 5.4% 0.2640 1.74 0.2640 11 0.7667 2.18 1.31 16 2.08 1.74 0.2640 0.2640 5.5% 0.2640 1.74 0.2640 11 0.7666 2.18 1.31 16 2.08 1.74 0.2640 0.2640 5.6% 0.2639 1.74 0.2639 11 0.7664 2.18 1.31 16 2.08 1.74 0.2639 0.2639 5.7% 0.2639 1.74 0.2639 11 0.7663 2.18 1.31 16 2.07 1.74 0.2639 0.2639

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181 Appendix F cont. NIA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH BGH 5.8% 0.2638 1.74 0.2638 11 0.7662 2.18 1.31 16 2.07 1.74 0.2638 0.2638 5.9% 0.2638 1.74 0.2638 11 0.7661 2.18 1.31 16 2.06 1.74 0.2638 0.2638 6% 0.2638 1.74 0.2638 11 0.7660 2.18 1.31 16 2.06 1.74 0.2638 0.2638 6.1% 0.2637 1.74 0.2637 11 0.7659 2.18 1.31 16 2.05 1.74 0.2637 0.2637 6.2% 0.2637 1.74 0.2637 11 0.7657 2.18 1.31 16 2.05 1.74 0.2637 0.2637 6.3% 0.2636 1.74 0.2636 11 0.7656 2.18 1.31 16 2.05 1.74 0.2636 0.2636 6.4% 0.2636 1.74 0.2636 11 0.7655 2.17 1.30 16 2.04 1.74 0.2636 0.2636 6.5% 0.2636 1.74 0.2636 11 0.7654 2.17 1.30 16 2.04 1.74 0.2636 0.2636 6.6% 0.2635 1.74 0.2635 11 0.7653 2.17 1.30 16 2.03 1.74 0.2635 0.2635 6.7% 0.2635 1.74 0.2635 11 0.7652 2.17 1.30 16 2.03 1.74 0.2635 0.2635 6.8% 0.2634 1.74 0.2634 11 0.7650 2.17 1.30 16 2.02 1.74 0.2634 0.2634 6.9% 0.2634 1.74 0.2634 11 0.7649 2.17 1.30 16 2.02 1.74 0.2634 0.2634 7% 0.2634 1.74 0.2634 11 0.7648 2.17 1.30 16 2.02 1.74 0.2634 0.2634 7.1% 0.2633 1.74 0.2633 11 0.7647 2.17 1.30 16 2.01 1.74 0.2633 0.2633 7.2% 0.2633 1.74 0.2633 11 0.7646 2.17 1.30 16 2.01 1.74 0.2633 0.2633 7.3% 0.2632 1.74 0.2632 11 0.7645 2.17 1.30 16 2.00 1.74 0.2632 0.2632 7.4% 0.2632 1.74 0.2632 11 0.7643 2.17 1.30 16 2.00 1.74 0.2632 0.2632 7.5% 0.2632 1.74 0.2632 11 0.7642 2.17 1.30 16 1.99 1.74 0.2632 0.2632 7.6% 0.2631 1.74 0.2631 11 0.7641 2.17 1.30 16 1.99 1.74 0.2631 0.2631 7.7% 0.2631 1.74 0.2631 11 0.7640 2.17 1.30 16 1.99 1.74 0.2631 0.2631 7.8% 0.2630 1.74 0.2630 11 0.7639 2.17 1.30 16 1.98 1.74 0.2630 0.2630 7.9% 0.2630 1.74 0.2630 11 0.7638 2.17 1.30 16 1.98 1.74 0.2630 0.2630 8% 0.2630 1.74 0.2630 11 0.7636 2.17 1.30 16 1.97 1.74 0.2630 0.2630 8.1% 0.2629 1.74 0.2629 11 0.7635 2.17 1.30 16 1.97 1.74 0.2629 0.2629 8.2% 0.2629 1.74 0.2629 11 0.7634 2.17 1.30 16 1.96 1.74 0.2629 0.2629 8.3% 0.2628 1.73 0.2628 11 0.7633 2.17 1.30 16 1.96 1.73 0.2628 0.2628 8.4% 0.2628 1.73 0.2628 11 0.7633 2.17 1.30 16 1.96 1.73 0.2628 0.2628 8.5% 0.2628 1.73 0.2628 11 0.7633 2.17 1.30 16 1.95 1.73 0.2628 0.2628

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182 Appendix F cont. NIA NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 0% 0.0335 0.0082 0.0335 0 0.1502 0.8% 0.9% 1.3% 1.0% 2.1% 2.0% 0.1% 0 0.0006 0 11 5.08 1.0% 1.0% 1.2% 1.6% 2.2% 2.6% 0.2% 0 0.0004 0 13 7.95 1.0% 1.0% 1.0% 1.7% 2.0% 2.7% 0.3% 0 0.0003 0 13 8.22 1.0% 1.0% 1.0% 1.7% 2.0% 2.7% 0.4% 0 0.0001 0 13 8.31 1.0% 1.0% 1.0% 1.7% 2.0% 2.7% 0.5% 0 0 0 13 8.36 1.0% 1.0% 1.0% 1.7% 2.0% 2.7% 0.6% 0 0 0 13 8.39 1.0% 1.0% 1.0% 1.7% 2.0% 2.7% 0.7% 0 0 0 13 8.40 1.0% 1.0% 1.0% 1.7% 2.0% 2.7% 0.8% 0 0 0 13 8.40 1.0% 1.0% 1.0% 1.8% 2.0% 2.7% 0.9% 0 0 0 13 8.40 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1% 0 0 0 13 8.39 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.1% 0 0 0 13 8.39 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.2% 0 0 0 13 8.37 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.3% 0 0 0 13 8.36 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.4% 0 0 0 13 8.35 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.5% 0 0 0 13 8.34 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.6% 0 0 0 13 8.32 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.7% 0 0 0 13 8.31 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.8% 0 0 0 13 8.29 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 1.9% 0 0 0 13 8.28 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2% 0 0 0 13 8.26 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.1% 0 0 0 13 8.25 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.2% 0 0 0 13 8.23 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.3% 0 0 0 13 8.21 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.4% 0 0 0 13 8.20 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.5% 0 0 0 13 8.18 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.6% 0 0 0 13 8.16 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.7% 0 0 0 13 8.14 1.0% 1.0% 1.0% 1.8% 2.0% 2.8%

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183 Appendix F cont. NIA NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 2.8% 0 0 0 13 8.13 1.0% 1.0% 1.0% 1.8% 2.0% 2.8% 2.9% 0 0 0 13 8.11 1.0% 1.0% 1.0% 1.9% 2.0% 2.8% 3% 0 0 0 13 8.09 1.0% 1.0% 1.0% 1.9% 2.0% 2.8% 3.1% 0 0 0 13 8.08 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.2% 0 0 0 13 8.06 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.3% 0 0 0 13 8.04 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.4% 0 0 0 13 8.03 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.5% 0 0 0 13 8.01 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.6% 0 0 0 13 7.99 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.7% 0 0 0 12 7.97 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.8% 0 0 0 12 7.96 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 3.9% 0 0 0 12 7.94 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 4% 0 0 0 12 7.92 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 4.1% 0 0 0 12 7.91 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 4.2% 0 0 0 12 7.89 1.0% 1.0% 1.0% 1.9% 2.0% 2.9% 4.3% 0 0 0 12 7.87 1.0% 1.0% 1.0% 2.0% 2.0% 2.9% 4.4% 0 0 0 12 7.86 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 4.5% 0 0 0 12 7.84 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 4.6% 0 0 0 12 7.82 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 4.7% 0 0 0 12 7.81 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 4.8% 0 0 0 12 7.79 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 4.9% 0 0 0 12 7.77 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5% 0 0 0 12 7.75 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.1% 0 0 0 12 7.73 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.2% 0 0 0 12 7.71 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.3% 0 0 0 12 7.70 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.4% 0 0 0 12 7.68 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.5% 0 0 0 12 7.66 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.6% 0 0 0 12 7.64 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.7% 0 0 0 12 7.62 1.0% 1.0% 1.0% 2.0% 2.0% 3.0%

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184 Appendix F cont. NIA NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 5.8% 0 0 0 12 7.61 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 5.9% 0 0 0 12 7.59 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6% 0 0 0 12 7.57 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.1% 0 0 0 12 7.55 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.2% 0 0 0 12 7.53 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.3% 0 0 0 12 7.52 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.4% 0 0 0 12 7.50 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.5% 0 0 0 12 7.48 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.6% 0 0 0 12 7.46 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.7% 0 0 0 12 7.44 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.8% 0 0 0 12 7.43 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 6.9% 0 0 0 12 7.41 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7% 0 0 0 12 7.39 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.1% 0 0 0 12 7.37 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.2% 0 0 0 12 7.35 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.3% 0 0 0 11 7.34 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.4% 0 0 0 11 7.32 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.5% 0 0 0 11 7.30 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.6% 0 0 0 11 7.28 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.7% 0 0 0 11 7.26 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.8% 0 0 0 11 7.25 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 7.9% 0 0 0 11 7.23 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 8% 0 0 0 11 7.21 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 8.1% 0 0 0 11 7.19 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 8.2% 0 0 0 11 7.17 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 8.3% 0 0 0 11 7.16 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 8.4% 0 0 0 11 7.14 1.0% 1.0% 1.0% 2.0% 2.0% 3.0% 8.5% 0 0 0 11 7.12 1.0% 1.0% 1.0% 2.0% 2.0% 3.0%

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185 Appendix G. Final values of th e 100-iteration period with the incr ease in nitrogen uptake rate (NIA) for the deep-adapted coral. NIA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 0% 9.01 9.01 9.32 0.3506 0 0 0.9198 0.9198 1.92 0.0051 0.0000 0.2180 0.1% 8.87 8.87 9.25 0.3449 0 0 0.9156 0.9156 1.89 0.0050 0.0089 0.2250 0.2% 8.72 8.72 9.18 0.3394 0 0 0.9113 0.9113 1.86 0.0049 0.0174 0.2317 0.3% 8.58 8.58 9.12 0.3339 0 0 0.9069 0.9069 1.83 0.0048 0.0257 0.2381 0.4% 8.44 8.44 9.05 0.3285 0 0 0.9024 0.9024 1.80 0.0048 0.0338 0.2442 0.5% 8.31 8.31 8.98 0.3231 0 0 0.8978 0.8978 1.77 0.0047 0.0415 0.2501 0.6% 8.17 8.17 8.92 0.3179 0 0 0.8931 0.8931 1.74 0.0046 0.0490 0.2557 0.7% 8.07 8.07 8.87 0.3140 0 0 0.8897 0.8897 1.72 0.0046 0.0565 0.2618 0.8% 8.08 8.08 8.88 0.3143 0 0 0.8903 0.8903 1.72 0.0046 0.0646 0.2701 0.9% 8.08 8.08 8.88 0.3145 0 0 0.8909 0.8909 1.72 0.0046 0.0728 0.2784 1% 8.09 8.09 8.89 0.3147 0 0 0.8916 0.8916 1.72 0.0046 0.0809 0.2867 1.1% 8.10 8.10 8.89 0.3149 0 0 0.8922 0.8922 1.72 0.0046 0.0891 0.2950 1.2% 8.10 8.10 8.90 0.3152 0 0 0.8928 0.8928 1.73 0.0046 0.0972 0.3033 1.3% 8.11 8.11 8.91 0.3154 0 0 0.8935 0.8935 1.73 0.0046 0.1054 0.3116 1.4% 8.11 8.11 8.91 0.3156 0 0 0.8941 0.8941 1.73 0.0046 0.1136 0.3199 1.5% 8.12 8.12 8.92 0.3158 0 0 0.8946 0.8946 1.73 0.0046 0.1218 0.3282 1.6% 8.12 8.12 8.92 0.3159 0 0 0.8948 0.8948 1.73 0.0046 0.1299 0.3364 1.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1380 0.3446 1.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1462 0.3527 1.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1543 0.3608 2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1624 0.3689 2.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1705 0.3770 2.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1786 0.3852 2.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1868 0.3933 2.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.1949 0.4014 2.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2030 0.4095 2.6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2111 0.4176 2.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2192 0.4258

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186 Appendix G cont. NIA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 2.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2274 0.4339 2.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2355 0.4420 3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2436 0.4501 3.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2517 0.4582 3.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2598 0.4664 3.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2680 0.4745 3.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2761 0.4826 3.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2842 0.4907 3.6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.2923 0.4988 3.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3004 0.5070 3.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3086 0.5151 3.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3167 0.5232 4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3248 0.5313 4.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3329 0.5394 4.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3410 0.5476 4.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3492 0.5557 4.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3573 0.5638 4.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3654 0.5719 4.6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3735 0.5800 4.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3816 0.5882 4.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3898 0.5963 4.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.3979 0.6044 5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4060 0.6125 5.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4141 0.6206 5.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4222 0.6288 5.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4304 0.6369 5.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4385 0.6450 5.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4466 0.6531 5.6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4547 0.6612 5.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4628 0.6694

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187 Appendix G cont. NIA BHmax BHfinal BHfinal(ave) BAmin NTH1 NTH1(ave) BA1 BA2 CPA CRA DIN NIA 5.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4710 0.6775 5.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4791 0.6856 6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4872 0.6937 6.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.4953 0.7018 6.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5034 0.7100 6.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5116 0.7181 6.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5197 0.7262 6.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5278 0.7343 6.6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5359 0.7424 6.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5440 0.7506 6.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5522 0.7587 6.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5603 0.7668 7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5684 0.7749 7.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5765 0.7830 7.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5846 0.7912 7.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.5928 0.7993 7.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6009 0.8074 7.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6090 0.8155 7.6% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6171 0.8236 7.7% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6252 0.8318 7.8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6334 0.8399 7.9% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6415 0.8480 8% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6496 0.8561 8.1% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6577 0.8642 8.2% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6658 0.8724 8.3% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6740 0.8805 8.4% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6821 0.8886 8.5% 8.12 8.12 8.92 0.3159 0 0 0.8949 0.8949 1.73 0.0046 0.6902 0.8967

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188 Appendix G cont. NIA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 0% 1.92 0.2902 0.2180 0.2180 0.7012 0.7012 0.7192 9.71 1.70 1.74 0.2186 0.2239 0.1% 1.88 0.2855 0.2250 0.2250 0.6899 0.6899 0.7140 9.56 1.66 1.72 0.2257 0.2331 0.2% 1.85 0.2809 0.2317 0.2317 0.6787 0.6787 0.7090 9.40 1.62 1.69 0.2326 0.2423 0.3% 1.82 0.2763 0.2381 0.2381 0.6677 0.6677 0.7040 9.25 1.59 1.67 0.2392 0.2513 0.4% 1.79 0.2718 0.2442 0.2442 0.6569 0.6569 0.6990 9.10 1.55 1.65 0.2455 0.2602 0.5% 1.77 0.2674 0.2501 0.2501 0.6463 0.6463 0.6941 8.95 1.51 1.63 0.2515 0.2689 0.6% 1.74 0.2631 0.2557 0.2557 0.6358 0.6358 0.6893 8.81 1.48 1.61 0.2573 0.2775 0.7% 1.72 0.2599 0.2618 0.2599 0.6281 0.6281 0.6858 8.70 1.46 1.59 0.2635 0.2861 0.8% 1.72 0.2601 0.2701 0.2601 0.6285 0.6285 0.6866 8.71 1.46 1.59 0.2718 0.2952 0.9% 1.72 0.2603 0.2784 0.2603 0.6290 0.6290 0.6873 8.71 1.46 1.59 0.2800 0.3043 1% 1.72 0.2605 0.2867 0.2605 0.6294 0.6294 0.6880 8.72 1.46 1.59 0.2883 0.3134 1.1% 1.72 0.2606 0.2950 0.2606 0.6299 0.6299 0.6887 8.73 1.46 1.60 0.2966 0.3226 1.2% 1.72 0.2608 0.3033 0.2608 0.6303 0.6303 0.6895 8.73 1.46 1.60 0.3050 0.3317 1.3% 1.72 0.2610 0.3116 0.2610 0.6308 0.6308 0.6902 8.74 1.46 1.60 0.3133 0.3409 1.4% 1.72 0.2612 0.3199 0.2612 0.6312 0.6312 0.6909 8.74 1.46 1.60 0.3216 0.3501 1.5% 1.72 0.2614 0.3282 0.2614 0.6316 0.6316 0.6915 8.75 1.46 1.60 0.3299 0.3592 1.6% 1.73 0.2614 0.3364 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3381 0.3683 1.7% 1.73 0.2614 0.3446 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3462 0.3772 1.8% 1.73 0.2614 0.3527 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3544 0.3861 1.9% 1.73 0.2614 0.3608 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3625 0.3951 2% 1.73 0.2614 0.3689 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3706 0.4040 2.1% 1.73 0.2614 0.3770 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3787 0.4129 2.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3868 0.4218 2.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.3950 0.4299 2.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4031 0.4381 2.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4112 0.4462 2.6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4193 0.4543 2.7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4274 0.4624

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189 Appendix G cont. NIA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 2.8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4356 0.4705 2.9% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4437 0.4787 3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4518 0.4868 3.1% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4599 0.4949 3.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4680 0.5030 3.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4762 0.5111 3.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4843 0.5193 3.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.4924 0.5274 3.6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5005 0.5355 3.7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5086 0.5436 3.8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5168 0.5517 3.9% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5249 0.5599 4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5330 0.5680 4.1% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5411 0.5761 4.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5492 0.5842 4.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5574 0.5923 4.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5655 0.6005 4.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5736 0.6086 4.6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5817 0.6167 4.7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5898 0.6248 4.8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.5980 0.6329 4.9% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6061 0.6411 5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6142 0.6492 5.1% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6223 0.6573 5.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6304 0.6654 5.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6386 0.6735 5.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6467 0.6817 5.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6548 0.6898 5.6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6629 0.6979 5.7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6710 0.7060

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190 Appendix G cont. NIA CFA CGA NGA BGA BAmax BA3 BA3(ave) BHo CTA CTA(ave) NEA NEA(ave) 5.8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6792 0.7141 5.9% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6873 0.7223 6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.6954 0.7304 6.1% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7035 0.7385 6.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7116 0.7466 6.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7198 0.7547 6.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7279 0.7629 6.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7360 0.7710 6.6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7441 0.7791 6.7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7522 0.7872 6.8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7604 0.7953 6.9% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7685 0.8035 7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7766 0.8116 7.1% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7847 0.8197 7.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.7928 0.8278 7.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8010 0.8359 7.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8091 0.8441 7.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8172 0.8522 7.6% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8253 0.8603 7.7% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8334 0.8684 7.8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8416 0.8765 7.9% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8497 0.8847 8% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8578 0.8928 8.1% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8659 0.9009 8.2% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8740 0.9090 8.3% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8822 0.9171 8.4% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8903 0.9253 8.5% 1.73 0.2614 0.3852 0.2614 0.6317 0.6317 0.6918 8.75 1.46 1.60 0.8984 0.9334

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191 Appendix G cont. NIA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH 0% 0.2118 1.40 0.2118 1.88 0.4521 0.3569 0.4461 3.13 -0.0060 1.40 0.2118 0.1% 0.2084 1.38 0.2084 1.85 0.4448 0.3511 0.4389 3.08 -0.0075 1.38 0.2084 0.2% 0.2050 1.35 0.2050 1.82 0.4376 0.3455 0.4318 3.03 -0.0090 1.35 0.2050 0.3% 0.2017 1.33 0.2017 1.79 0.4305 0.3399 0.4248 2.99 -0.0104 1.33 0.2017 0.4% 0.1984 1.31 0.1984 1.76 0.4235 0.3344 0.4180 2.94 -0.0117 1.31 0.1984 0.5% 0.1952 1.29 0.1952 1.73 0.4167 0.3290 0.4112 2.89 -0.0130 1.29 0.1952 0.6% 0.1921 1.27 0.1921 1.70 0.4099 0.3236 0.4045 2.84 -0.0143 1.27 0.1921 0.7% 0.1897 1.25 0.1897 1.68 0.4049 0.3197 0.3996 2.81 -0.0152 1.25 0.1897 0.8% 0.1899 1.25 0.1899 1.68 0.4052 0.3199 0.3999 2.81 -0.0152 1.25 0.1899 0.9% 0.1900 1.25 0.1900 1.69 0.4055 0.3202 0.4002 2.81 -0.0152 1.25 0.1900 1% 0.1901 1.25 0.1901 1.69 0.4058 0.3204 0.4005 2.81 -0.0152 1.25 0.1901 1.1% 0.1903 1.26 0.1903 1.69 0.4061 0.3206 0.4008 2.82 -0.0153 1.26 0.1903 1.2% 0.1904 1.26 0.1904 1.69 0.4064 0.3208 0.4010 2.82 -0.0153 1.26 0.1904 1.3% 0.1905 1.26 0.1905 1.69 0.4067 0.3211 0.4013 2.82 -0.0153 1.26 0.1905 1.4% 0.1907 1.26 0.1907 1.69 0.4070 0.3213 0.4016 2.82 -0.0153 1.26 0.1907 1.5% 0.1908 1.26 0.1908 1.69 0.4072 0.3215 0.4019 2.82 -0.0153 1.26 0.1908 1.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 1.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 1.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 1.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908

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192 Appendix G cont. NIA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH 2.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 2.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 3.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 4.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908

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193 Appendix G cont. NIA BIH CIH NIH CRH CMH CSH CLH CUH CGH/6.6 CGHmax NGH 5.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 5.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 6.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.6% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.7% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 7.9% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 8% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 8.1% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 8.2% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 8.3% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 8.4% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908 8.5% 0.1908 1.26 0.1908 1.69 0.4073 0.3216 0.4019 2.82 -0.0153 1.26 0.1908

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194 Appendix G cont. NIA BGH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 0% -0.0060 0.2179 0.2277 0.2179 0 0 -0.07% -0.10% -0.07% 0.72% -0.13% 0.61% 0.1% -0.0075 0.2159 0.2276 0.2159 0 0 -0.09% -0.12% -0.09% 0.69% -0.17% 0.57% 0.2% -0.0090 0.2140 0.2274 0.2140 0 0 -0.10% -0.14% -0.10% 0.67% -0.21% 0.53% 0.3% -0.0104 0.2121 0.2273 0.2121 0 0 -0.12% -0.15% -0.12% 0.65% -0.24% 0.49% 0.4% -0.0117 0.2102 0.2271 0.2102 0 0 -0.14% -0.17% -0.14% 0.63% -0.28% 0.46% 0.5% -0.0130 0.2082 0.2269 0.2082 0 0 -0.16% -0.19% -0.16% 0.61% -0.31% 0.42% 0.6% -0.0143 0.2063 0.2267 0.2063 0 0 -0.17% -0.20% -0.17% 0.59% -0.35% 0.39% 0.7% -0.0152 0.2049 0.2266 0.2049 0 0 -0.19% -0.22% -0.19% 0.58% -0.38% 0.36% 0.8% -0.0152 0.2051 0.2267 0.2051 0 0 -0.19% -0.22% -0.19% 0.58% -0.38% 0.37% 0.9% -0.0152 0.2052 0.2268 0.2052 0 0 -0.19% -0.21% -0.19% 0.58% -0.38% 0.37% 1% -0.0152 0.2054 0.2268 0.2054 0 0 -0.19% -0.21% -0.19% 0.59% -0.38% 0.37% 1.1% -0.0153 0.2055 0.2269 0.2055 0 0 -0.19% -0.21% -0.19% 0.59% -0.38% 0.38% 1.2% -0.0153 0.2057 0.2270 0.2057 0 0 -0.19% -0.21% -0.19% 0.60% -0.38% 0.38% 1.3% -0.0153 0.2058 0.2271 0.2058 0 0 -0.19% -0.21% -0.19% 0.60% -0.38% 0.39% 1.4% -0.0153 0.2060 0.2271 0.2060 0 0 -0.19% -0.21% -0.19% 0.61% -0.38% 0.40% 1.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 1.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 1.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 1.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 1.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41%

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195 Appendix G cont. NIA BGH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 2.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 2.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 3.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 4.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41%

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196 Appendix G cont. NIA BGH NTH2 NTH2(ave) NTtotal CME CME(ave) %BH %BH(ave) %BA %BA(ave) %BHol %BHol(ave) 5.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 5.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 6.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.6% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.7% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 7.9% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 8% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 8.1% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 8.2% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 8.3% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 8.4% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41% 8.5% -0.0153 0.2061 0.2272 0.2061 0 0 -0.19% -0.21% -0.19% 0.62% -0.38% 0.41%