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The role of abiotic and biotic factors in suspension feeding mechanics of Xenopus tadpoles

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Title:
The role of abiotic and biotic factors in suspension feeding mechanics of Xenopus tadpoles
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Ryerson, William G
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Ontogeny
Scaling
Viscosity
Biomechanics
Morphology
Dissertations, Academic -- Biology -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

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ABSTRACT: As a comparison to the suction feeding mechanics in aquatic environments, I investigated buccal pumping in an ontogenetic series of suspension feeding Xenopus laevis tadpoles (4-18 mm snout-vent length) by examining the morphology, kinematics, fluid flow, pressure generated in the buccal cavity, and effects of viscosity manipulation. Investigation of the dimensions of the feeding apparatus of Xenopus revealed that the feeding muscles exhibited strong negative allometry, indicating that larger tadpoles had relatively smaller muscles, while the mechanical advantage of those muscles did not change across the size range examined. Buccal volume and head width also exhibited negative allometry: smaller tadpoles had relatively wider heads and larger volumes. Tadpoles were imaged during buccal pumping to obtain kinematics of jaw and hyoid movements as well as fluid velocity.Scaling patterns were inconsistent with models of geometric growth, which predict that durations of movements are proportional to body length. Only scaling of maximum hyoid distance, duration of mouth closing, and duration of hyoid elevation could not be distinguished from isometry. The only negatively allometric variable was maximum gape distance. No effect of size was found for duration of mouth opening, duration of hyoid depression, and velocity of hyoid elevation. Velocity of mouth opening, velocity of mouth closing, and velocity of hyoid depression decreased with increasing size. Fluid velocity increased with size, and is best predicted by a piston model that includes head width and hyoid depression velocity. Reynolds number increased with size and spanned two flow regimes (laminar and intermediate) ranging from 2 to over 100. Pressure was found to be greatest in the smallest tadpoles and decreased as size increased, ranging from 2 kPa to 80 kPa.The viscosity of the water was altered to explore changes in body size, independent of development (higher viscosity mimicked smaller tadpole size). Viscosity manipulations had a significant effect on the kinematics. Xenopus initially increased velocity and distance of movements as viscosity increased, but these values declined as viscosity increased further. These results suggest that abiotic factors such as fluid viscosity may set a lower size limit on suspension feeding.
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Thesis (M.S.)--University of South Florida, 2008.
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by William G. Ryerson.
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The Role of Abiotic And Biotic Factors In Suspension Feeding Mechanics Of Xenopus Tadpoles by William G. Ryerson A thesis submitted in partial fulfillment Of the requirements for the degree of Master of Science Department of Biology College of Arts and Sciences University of South Florida Major Professor: Stephen M. Deban, Ph.D. Phillip J. Motta, Ph.D. Henry R. Mushinsky, Ph.D. Date of Approval: November 13, 2008 Keywords: ontogeny, scaling, viscosity, biomechanics, morphology Copyright 2008, William Ryerson

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Acknowledgments I would first like to my parents, William and LeeAnn Ryerson, for allowing me to choose my own path in life. Without thei r unwavering support, I would not have been able to continue my edu cation and development. I thank the members of my thesis committee: Stephen Deban, Phil Motta, and Henry Mushinsky. Thank you so much for your time and guidance. I am also grateful for the advice and help from Wendy Olson. He r knowledge of the pipid frogs and their biology were invaluable throughout my work. I cannot thank enough my fellow graduate students from the Department of Biology, Integrative Biology Division, during my time here. My friends here were without a doubt an integral part of my success, and without them I dont know what I would have done. I would also like to tha nk the members of the Deban lab: Lance Bastian, Chris Anderson, and Maranda Holley. They were able to provide a learning environment that was both intellectually ri gorous and unadulterated fun, all in the confines of the lab. I would be hard pr essed to ask for a better group of labmates. Finally, I would like to extend my greates t thanks to my advisor, Dr. Stephen Deban. Steve took an undergraduate with little research experience and with patience and some good-natured ribbing turned him into a motivated, ambitious lifelong student of science. I dont know what more a student could ask for from an advisor. Thank you again.

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i Table of Contents List of Figures ii List of Tables iii Abstract v Chapter 1: Introduction 1 Chapter 2: Scaling of the feeding morphology in tadpoles of Xenopus laevis 6 Chapter 3: Reynolds number, ontogeny, viscosity and Xenopus : the role of biotic and abiotic factors in the suspension feeding tadpoles of Xenopus laevis 28 Chapter 4: Conclusion 57 References 61 Appendix 67

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ii List of Figures Figure 2.1. Ventral view of cleared and stained tadpole 12 Figure 2.2. Illustration of the buccal pumping mechanism of Xenopus laevis 13 Figure 2.3. Scaling of head width and buccal volume 15 Figure 2.4. Scaling patterns of IH and OH wet mass 17 Figure 2.5. Ratio of the cross-sectional areas of the IH/OH 19 Figure 2.6. Scaling patterns of the CSA, LAR, and force for the IH and OH 20 Figure 3.1. Representative lateral image of a tadpo le 35 Figure 3.2. Image sequence of tadpole feeding 40 Figure 3.3. Scaling patterns of fluid velocity with the piston model 42 Figure 3.4. Scaling patterns of Reynolds number 42 Figure 3.5. Velocity of mouth closing with increasing viscosity 44 Figure 3.6. Cleared and stained tadpoles illustrating the filtering mechanism and pipe model 45 Figure 3.7. Scaling patterns of pressure gene rated during feeding 46 Figure 3.8. Kinematic profiles of hyoid movement during feeding in water and in increased viscosity. 52

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iii List of Tables Table 2.1. Scaling of morphological variables. 16 Table 3.1. Results of the viscosity treatments. 44 Table A.1. Head Width 68 Table A.2. Buccal Volume 69 Table A.3. Filter Morphology 70 Table A.4. IH Mass 72 Table A.5. OH Mass 73 Table A.6. OH Length 74 Table A.7. IH C.S.A. 76 Table A.8. OH C.S.A. 77 Table A.9. IH/OH Ratio 78 Table A.10. OH L.A.R. 79 Table A.11. IH L.A.R. 79 Table A.12. Force 82 Table A.13. OH Resolved Force 85 Table A.14. IH Resolved Force 85 Table A.15. Fluid Velocity 88 Table A.16. Reynolds Number 90 Table A.17. Piston Model 91

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i v Table A.18. Pressure Calculations 92 Table A.19. Viscosity Pressure Calculations 95 Table A.20. Viscosity Data 107

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v The Role Of Abiotic And Biotic Factors In Suspension Feeding Mechanics Of Xenopus Tadpoles William G. Ryerson ABSTRACT As a comparison to the suction feeding mechanics in aquatic environments, I investigated buccal pumping in an ontogenetic series of suspension feeding Xenopus laevis tadpoles (4-18 mm snout-vent length) by examining the morphology, kinematics, fluid flow, pressure generated in the buccal cavity, and effects of viscosity manipulation. Investigation of the dimensions of the feeding apparatus of Xenopus revealed that the feeding muscles exhibited str ong negative allometry, indicatin g that larger tadpoles had relatively smaller muscles, while the mechanical advantage of those muscles did not change across the size range examined. Buccal volume and head width also exhibited negative allometry: sm aller tadpoles had relatively wi der heads and larger volumes. Tadpoles were imaged during buccal pumping to obtain kinematic s of jaw and hyoid movements as well as fluid velocity. Scaling patterns were inconsistent with models of geometric growth, which predict that dura tions of movements are proportional to body length. Only scaling of maximum hyoid distance, duration of mouth closing, and duration of hyoid elevation could not be distinguish ed from isometry. The only negatively allometric variable wa s maximum gape distance. No effect of size was found for duration

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vi of mouth opening, duration of hyoid depression, and velocity of hyoid elevation. Velocity of mouth opening, velocity of mouth closing, and velocity of hyoid depression decreased with increasing size. Fluid velocity increased with size, and is best predicted by a piston model that includes head width and hyoi d depression velocity. Reynolds number increased with size and spanned two flow regimes (laminar and intermediate) ranging from 2 to over 100. Pressure was found to be greatest in the smallest tadpoles and decreased as size increased, ranging from 2 kPa to 80 kPa. The viscosity of the water was altered to explore changes in body size, inde pendent of development (higher viscosity mimicked smaller tadpole size). Viscosity mani pulations had a significant effect on the kinematics. Xenopus initially increased velocity and distance of movements as viscosity increased, but these values declined as viscos ity increased further. These results suggest that abiotic factors such as fluid viscosity may set a lower size limit on suspension feeding.

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Chapter 1: Introduction Effects of changing body size on mor phology and movement mechanics are ubiquitous among animals (Hill, 1950; Schmidt-Nielsen, 1984; Koehl, 2000; Alexander, 2005; Biewener, 2005). Locomotion has been the focal point of many studies in scaling (Rand and Rand, 1966; Biewener, 1983, 1989; Wilson and Franklin, 2000; Wilson et al., 2000; Toro et al., 2003; McHenry and Lauder, 2005; Noren et al., 2006; Jayne and Riley, 2007). In contrast, data on the scaling of feeding mechanisms is less common (Richard and Wainwright, 1995; Wainwright and Shaw, 1999; Hernandez, 2000; Robinson and Motta, 2002, Deban and OReilly, 2005; Herrel et al., 2005; Vincent et al., 2007). In the aquatic environment, scaling of the feeding mechanism has been primarily restricted to suction feeding fish (Richard and Wainw right, 1995; Wainwright and Shaw, 1999; Hernandez, 2000; Robinson and Motta, 2002; Herr el et al., 2005) with few examples of other taxa (e.g. amphibians, Deban and OReilly, 2005), and no examples of other feeding strategies, such as suspension feeding. In addition to being focused entirely on suction feeding in the aquatic environment, the examined taxa all exhibit geometrically similar growth in morphology, in which proportions of the feeding system remain constant. Tw o models have been proposed that predict the scaling pattern of movement in geometrically scaling systems. First, Hills (1950) geometric similarity model predicts the scaling coefficients for aspects of both kinematics and morphology, acco rding to dimensional analysis of the variables. According to the model, proportions of elements of morphology and absolute

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velocities do not change despite changes in size. In aquatic suction feeding, the diversity of studies has yet to demonstrate geomet rically similarity in movement, with the exception of the hellbender salamander, Cryptobranchus alleganiensis (Deban and OReilly, 2005). The second model, devel oped from Richard and Wainwrights (1995) work on largemouth bass, Micropterus salmoides describes different predictions for movements as size increases. In this model, velocities and excursions increase isometrically with body length. Move ments exhibited by the nurse shark, Ginglymostoma cirratum (Robinson and Motta, 2002) supported this model, but the model failed to predict the kinematic patterns exhibited the hellbender salamander, Cryptobranchus alleganiensis (Deban and OReilly, 2005). Instead, scaling coefficients of Cryptobranchus matched the predictions of Hills (1950) original geometrically similar model. Cryptobranchus also exhibited scaling patterns similar to toad feeding, which led Deban and OReilly ( 2005) to suggest that scaling patterns of amphibians were best predicted by phylogenetic relatedness, rather than by biomechanical similarity. Another factor contributing to scaling patte rns is the effect of abiotic factors on organisms of different sizes. In water, smaller body sizes or reduced speeds of fluid flow increase the effect of viscosity (the fluids resistance to flow) relative to inertial effects (i.e. momentum) of the behavior of the fluid (Vogel, 1994). Reynolds number (Re) is a dimensionless number that represents the relative importance of inertial versus viscous forces, and is used to compare the flow type (laminar or turbulent) of a fluid around or through an object by examining four variables: fluid speed, object size, fluid density, and fluid viscosity (Denny, 1993; Vogel, 1994).

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Reynolds number can be used to compare flow regimes experienced by two organisms of different size in the same envir onment. For biological systems, three flow regimes are used for comparison. A low Re ynolds regime, Re<75, indicates that viscous forces are more important in determining the behavior of the fluid than inertial forces, and flow is generally laminar. High Reynolds number regimes, Re>200, indicate that inertial forces are relatively more important, and flow is turbulent. Between these two values is the intermediate Reynolds numbe r regime, 75
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flow regime (Deban and Olson, 2002). Both of these studies focused on organisms that use suction feeding to capture prey, but l ittle research has focused on the effects of Reynolds number on suspension feeding organisms (Koehl, 1995; Koehl and Strickler, 1981) and none on vertebrate suspension feeders. Among suspension feeding organisms, tadpol es employ a large and diverse array of feeding strategies, such as scraping the substrate, skimming the surface, and midwater suspension feeding. Of the 5000 species of anurans, most have tadpoles (e.g. genus Rana) that use keratinized mouth parts to scrape algae or other detritus from a surface, creating a suspension that the tadpole pumps into its buccal cavity (Seale et al., 1982; Seale and Wassersug, 1979). In contrast, most tadpoles of the family Pipidae are obligate suspension feeders. Pipid tadpoles lack keratinized mouth parts, therefore are constrained to extract suspended particles from the water, relying only on their mucus secreting organs and on the branchial basket to trap food, without the ability to scrape food from the substrate to generate a concentrated suspension (Cannatella, 1999; Gradwell, 1971). Xenopus laevis a member of the Pipidae, is an obligate midwater suspension feeder as tadpoles. Without the ability to scrape algae and detritus, Xenopus instead relies on particles are already in the water column. Xenopus tadpoles pump water into the buccal cavity similar to suction feeders, but do not rely on one explosive movement to capture prey. Instead, they continuously pump water through their branchial basket to remove particles suspended in the water. The buccal pumping appartus of tadpoles has been well described (Gradwell, 1968; Kenny, 1969; Wassersug and Hoff, 1979) and is formed by paired ceratohyal cartilages that lie on the floor of the buccal cavity. Rotation of the ceratohyals is the

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result of two muscles. Contraction of the orbithyoideus muscle flexes the apparatus ventrally, expanding the cavity, drawing water in Contraction of the interhyoideus results in dorsally flexing of the apparatus compressing the cavity, pushing water through the branchial apparatus and out the spiracles. The goal of this work is to investigate ontogeny of suspension feeding mechanics and the role of abiotic and biotic factors in suspension feeding tadpoles of Xenopus laevis I examine the scaling of the feeding morphology of these tadpoles, specifically the dimensions of the head, buccal pump, filter ba sket, hyoid muscles, and lever arm ratios. Using the cross-sectional areas of the muscles and the corresponding lever arms, I estimate force generated during hyoid depression and elevation. I examine the scaling of kinematics and the effects of viscosity on the kinematics of suspension feeding and compare the scaling of the kinematics with the Hill (1950) and Richard and Wainwright (1995) models. In addition, I calculate Re ynolds number and pressure generated during suspension feeding to determine the flow regimes and potential constraints on suspension feeding.

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Chapter 2: Scaling of the feeding morphology in tadpoles of Xenopus laevis Introduction The scaling of morphology and physiology is important in the natural history of an organism. Changes in the muscular and skeletal morphology in turn affect the behavior of an organism, including kinema tics (Deban and OReilly, 2005; Holzman et al., 2008; Robinson and Motta, 2002) and ecology (Vincent et al., 2007). Work on the scaling of feeding behaviors and morphology has been primarily restricted to fishes (Adriaens and Verraes, 1997; Hernandez, 2000; Richard and Wainwright, 1995; Robinson and Motta, 2002; Van Wassenbergh et al., 2007), while work on amphibians and reptiles has focused on locomotor performance: jumping (Wilson et al., 2000), snake locomotion (Jayne and Riley, 2007) and sw imming (Wilson and Franklin, 2000), with the exception of few studies on feeding (Deban and OReilly, 2005; Reilly, 1995). Work on the scaling of morphology has also been show n to affect kinematic s: changes in skull shape predict peak fluid speed (Holzman et al., 2008), changes in musculature predict suction generation (Herrel et al., 2005), costs of generating force in muscles predict cost of transport (Rome, 1992). Suction feeding has been the primary feeding mode examined in scaling studies of fish (Herrel et al., 2005; Hernandez, 2000; Holzman et al., 2008; Richard and Wainwright, 1995; Robinson and Motta, 2002) and aquatic amphibians (Deban and OReilly, 2005). Patterns of movement vary from organism to organism, even among

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closely related taxa. Largemouth bass, Micropterus salmoides did not match predicted patterns for geometrically scaling systems, which predict that durations of movements should be proportional to length, and Richard and Wainwright (1995) instead proposed a new model for the scaling of suction feeding in water. The feeding mechanism in the hellbender salamander Cryptobranchus alleganiensis shows scaling coefficients that match predictions by Hill (1950) for geometrically scaling systems, and it was concluded that the scaling pattern is phylogenetically conserved in amphibians rather than being determined by biomechanical constraints (D eban and OReilly, 2005). The nurse shark, Ginglymostoma cirratum exhibited patterns that matc hed the Richard and Wainwright (1995) model (Robinson and Motta, 2002). With su ch variety among taxa that employ the same mode of feeding, it makes sense to ask how other feeding modes scale comparatively. Tadpoles of Xenopus laevis the African clawed frog, feed by removing particles suspended in the water. Lacking the keratinized mouthparts common among other tadpoles (Seale et al., 1982), Xenopus are unable to scrape algae and detritus from the substrate and instead rely entirely on particles already suspended in the water column. The buccal pumping mechanism utilized by feeding Xenopus tadpoles is superficially similar to suction feeding: opening of mouth and depression of the hyoid results in water entering the buccal cavity. Subsequent closi ng of the mouth and elevation of the hyoid pushes water through the brancial apparatus, which traps suspended particles and water travels out through paired spiracles. Unlike suction feeding, which relies on a single explosive event to capture individual prey items, suspension feeding is rhythmic in nature

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and it is during the water expulsion phase that particles are entrapped in the branchial apparatus. Here I examine the scaling of the feeding mechanism of tadpoles of the African clawed frog, Xenopus laevis (Anura: Pipidae) to examine the scaling patterns in the morphology of a suspension feeding organism. The feeding morphology and behavior of the tadpoles of Xenopus have been well documented (G radwell, 1969; Gradwell, 1971; Satel and Wassersug, 1981; Seale et al., 1982; Seale and Wassersug, 1979; Wassersug and Hoff, 1979), and tadpoles are readily available. The buccal pumping apparatus is relatively simple, with only two antagonistic muscles responsible for the movements of the hyoid, and the ease of identifying and removing these muscles for analysis makes Xenopus an ideal organism for this approach. In tadpoles, the orbitohyoideus muscle (OH) is the primary muscle responsible for depressing the floor of the buccal cavity and generating sucti on (Cannatella, 1999; Larson and Reilly, 2003). It is paired, originating on the muscular process of the palatoquadrate and inserting on the lateral e dge of the ceratohyals. Upon contraction, the OH rotates the lateral end of the ceratohyal dor sally. Each ceratohyal forms a lever with its fulcrum with the palatoquadrate located ne ar its lateral end. Thus, rotation of the ceratohyals depresses the floor of the buccal cavity, drawing water in. The water is then pushed out the back of the buccal cavity and out the spiracles through the action of the interhyoideus muscle (IH), which spans the width of the head, along the ventral surface of the ceratohyals, and inserts at the lateral edge of the ceratohyal. Contraction of the IH rotates the lateral ends of the ceratohyals ventrally and the medial portions dorsally, thus

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elevating the floor of the buccal cavity. This compression of the buccal cavity forces water out through the branchial appa ratus, removing particles. The ratio of cross-sectional areas of the IH to OH is correlated with feeding mode, low values with macrophagy, and high values with microphagous suspension feeding (Satel and Wassersug, 1981). The lowest ratios are associated with tadpoles whose primary mode of feeding is macrophagous carnivory, with Hymenochirus having a value of 0.07, the second lowest value recorded. Xenopus lies at the opposite extreme, with an IH/OH ratio of 1.67, the highest value recorded. It is interesting to note that these are the only pipids measured, but the closest relative of the pipids, Rhinophrynus was found to have a similar to value as Xenopus at 1.22 (Satel and Wassersug, 1981). Similarly, Wassersug and Hoff (1979) created a model to describe how buccal volume changed with size, and in doing so investigated the ceratohyal lever arm ratio (i.e., the length of the in-lever divided by the length of the out-lever). The ratios were compared to the feeding mode of each taxon, and the two pipids investigated lie at opposite extremes of the spectrum. Hymenochirus has the highest lever arm ratio, 0.50, comparable to other macrophagous carnivores, while Xenopus registers a value of 0.14, lowest in the study, similar to other midwater suspension feeders. The goals of this study are to: (1) investigate the scaling patterns of the feeding morphology in tadpoles of Xenopus laevis and (2) compare the morphology of a suspension feeding organism to previously examined suction feeding organisms. I examined the dimensions of the head and made eleven measurements related to the suspension feeding mechanism of tadpoles: (1) head width, (2) buccal volume, (3) length of the filter basket, (4) length of the ceratohyal, (5) IH wet mass, (6) IH cross-sectional

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area, (7) OH wet mass, (8) OH cross-sectional area, (9) OH length, (10) OH lever arm ratio, (11) IH lever arm ratio. I also estimated force output of both the IH and OH muscles, based on muscle cross-sectional areas and ceratohyal lever arm ratios. I hypothesize that in smaller organisms suspensi on feeding will be affected by the viscous properties of the medium, and as a result have developed a more robust feeding morphology to compensate for this. Methods To examine the scaling of the morphology of Xenopus laevis tadpoles, tadpoles were euthanized by submersion in aqueous, buffered MS 222 (300mg/L), and preserved in 10% phosphate-buffered formalin. Sixteen tadpoles (SVL 4.3-18.3 mm) were utilized for morphological measurements and dissection. Head width at the eyes was measured using digital calipers (Mitutoyo Corp., Japan). Buccal volume was measured by first sealing the spiracles with silicone aquarium sealant, and then filling the buccal cavity with water using a micropipette. The buccal cavity was kept open using a #14 fishing hook and a small piece of string, under the dissecting microscope (Wild M5-101796 dissecting microscope, Heerbrugg, Switzerland). Po ints of insertion and origin of the IH and OH muscles on the palatoquadrate and ceratohya l were identified. Using fine forceps, the IH muscle was peeled from the ventral portion of the buccal cavity, and the OH was removed from both sides of the head. Muscles were stored in 10 % formalin until analysis. IH length was not independently measured, because the muscle extends the width of the head, so only OH length was measured. Wet mass of the muscles was obtained using a Sartorius CP225D balance; each OH muscle was measured separately,

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and averaged for one value per individual. The muscles were then placed in paraffin wax, and sectioned by razor blade. The IH muscle was bisected, the OH was sectioned 2/3 of the total length of the muscle from the origin, near the center of mass for that muscle. The circumference of the muscle cross sections were drawn using a Wild M5101796 dissecting microscope with camera lucida attachment, and analyzed using ImageJ software. Analysis of isometric growth was conducted via students t-test using SigmaStat v3.1 software, and regressi ons plotted in SigmaPlot v8. In order to examine the scaling of the sk eletal elements tadpoles were cleared and stained for cartilage with alcian blue usi ng a modification of published methods (Hanken and Wassersug, 1981; Deban, 1997). Staine d specimens where imaged using a Leica MZ75 dissecting microscope and Leica DFC290 digital camera. Ventral images were used to measure the length of the ceratohyals, length of the filter basket (Fig. 2.1), and the ceratohyal lever arm ratios. Lateral images were used to measure the thickness of the ceratohyal, which was used as the in-lever for the IH. For the OH muscle, the in-lever is the length of the ceratohyal that extends laterally beyond its articulation with the palatoquadrate, while the out-lever extends from that same articulation towards the midline, where it abuts the median copula (Fig. 2.2). Two lengths were measured: 1) total length of the ceratohyal, and 2) length of the ceratohyal from its articulation with the palatoquadrate to the median copula. The ra tio is calculated by subtracting length 2 from length 1 then dividing by length 1 (Wassersug and Hoff, 1979). For the IH muscle, the out-lever is the same. The force generated by each muscle was calculated by multiplying the crosssectional area of the muscle by the specific tension of amphibian muscle, 22 N/cm2

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Figure 2.1: Ventral view of a cleared and stained tadpole illustrating morphological measurements. The solid black line corresponds to ceratohyal width (CH width), the dashed line corresponds to head width (HW), and the dotted line corresponds to the filter basket length (FB length).

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A B OH OH IH IH Figure 2.2: Illustration of the the buccal pumping mechanism of Xenopus laevis. Image A is a ventral view of a cleared and stained Xenopus tadpole illustrating the ceratohyal and the lengths used to determine the lever arm ratios for the OH muscle (the in-lever is the length of the shorter dashed line subtracted from the other). B is the lateral view of the same tadpole, illustrating the lever arms for the IH muscle (the out lever is the shorter dashed line from A, the in lever is the dashed line in B). Scale is 1 mm. Images C and D are schematic diagrams of the same buccal pumping mechanism, as viewed from the front of the tadpole. These images illustrate the actions of the OH and IH muscles expanding and compressing the buccal cavity. Arrows indicate direction of muscle contraction. The shorter dashed line indicates the in-lever for the acting muscle, the longer dashed line indicates the out-lever, the point represents the fulcrum upon which the ceratohyal rotates. Redrawn from Gradwell (1968). C D

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(Regnier and Herrera, 1993). This force multiplied by the in-lever is proportional to the final force output multiplied by the out-lever. This allows me to calculate the resolved force of hyoid depression and hyoid elevation at the median copula. Results Head width was negatively allometric with SVL (slope = 0.360.03), smaller tadpoles having relatively wider heads than larger tadpoles. Buccal volume also was negatively allometric with a slope of 1.220.13, compared to a slope of 3 for geometric similarity (Fig. 2.3). Width of the ceratohyal scaled isometrically with SVL (slope = 0.810.21), as did the length of the filter basket (slope = 0.910.15). OH length also increased isometrically with SVL (slope = 1.000.18). IH length corresponds to head width, so it was not independently assessed (Table 2.1). The relationship of muscle cross-sectional area and wet mass to body size were assessed independently of each other and lever arm ratios. The slopes of the regressions were compared to the expected values for each variable according to geometric scaling models (Hill, 1950; Richard and Wainwright, 1995). According to this model, when regressed against body length, wet muscle mass should scale with a slope of three, crosssectional area with a slope of two, and lever arm ratio with a slope of zero (i.e. it is constant at all body lengths). The ratio of the interhyoideus (IH) to orbitohyoideus (OH) cross sectional areas should scale with a slope of zero for isometry. Wet mass of the IH and OH muscles displa yed two different scaling patterns. The IH exhibited isometric growth with a slope of 2.770.53, while the OH showed negatively allometric growth with a slope of 1.610.43 (Fig. 2.4 ) These values were

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Figure 2.3: Scaling of head width and buccal volume to snout-vent length (SVL) in Xenopus tadpoles, illustrating the allometric relationship among the variables. Dashed lines indicate 95% confidence intervals, the grey lines represent isometric slopes: head width, 1; buccal volume, 3.

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Morphological CharacterSlopeExpected SlopeLower 95%Upper 95% FP IH/OH Ratio 0.35 0 0.270.420.8999.46<0.001 OH LAR 0.16 0 -0.490.81<0.0010.290.60 IH LAR 0.25 0 -0.300.810.151.090.33 Head Width 0.36 1 0.330.390.97391.27<0.001 CH Width 0.81 1 0.601.020.8569.96<0.001 Filter Basket Length 0.91 1 0.761.060.93165.51<0.001 OH Length 1.00 1 0.821.180.95164.55<0.001 OH CSA 0.44 2 0.260.610.6929.13<0.001 IH CSA 0.78 2 0.561.000.8258.32<0.001 OH Resolved Force 0.67 2 0.031.320.305.200.04 IH Resolved Force 1.20 2 0.641.750.7524.450.001 Buccal Volume 1.22 3 1.091.350.98479.71<0.001 OH Mass 1.61 3 1.182.030.8567.55<0.001 IH Mass 2.77 3 2.213.280.92125.96<0.001 r2* * * * *Table 2.1: Table describing the regression statistics for the 14 variables tested against size. The r2, F, and p values describe the significance of the regression. Asterisks indicate variables with slopes that differed significantly from the expected value.

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OH Mass (mg) 0.02 0.05 0.20 0.50 0.10 1.00 OH Mass = 1.61 SVL 5.25 r 2 = 0.85 SVL (mm) 34 68101418 25 IH Mass (mg) 0.01 0.05 0.15 0.50 2.00 5.00 10.00 IH Mass = 2.77 SVL 6.03 r 2 = 0.92Figure 2.4: Scaling patterns of the wet mass of both the IH and OH muscles, illustrating the allometric growth of the OH muscle and isometric growth of the IH muscle thorugh ontogeny. The grey line indicates an isometric slope of 3.0. Dashed lines are 95% confidence intervals.

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confirmed by calculating the volume of the muscle using the width of the head (IH length) and the cross-sectional area. IH volume scaled with a slope of 2.680.34, and OH volume scaled with a slope of 1.580.41. Muscle cross-sectional area, lever arm ratio, and force output were integrated to examine the relative contributions of each factor to buccal pumping in Xenopus (Fig. 2.6). The cross-sectional areas of both the orbitohyoideus (slope = 0.440.17) and interhyoideus (slope = 0.780.22) exhibited ne gatively allometric growth (Table 2.1). A comparison of the two slopes found significant differences, with the orbitohyoideus exhibiting stronger negative allo metry than the interhyoideus (F = 4.55, p < 0.05). The ratio of the IH to the OH cross-sectional area was also found to increase with increasing body size (F = 101.20, p < 0.001; Fig. 2.5). Smaller tadpoles had a lower IH/OH ratio than larger tadpoles, indicating that the IH is relatively smaller th an the OH in smaller tadpoles. OH lever arm ratio had no relationship with body length (F = 0.01, p > 0.05; Fig. 2.6). Similarly, the IH lever arm ratio had no relationship with body size (F = 1.41, p > 0.05). Cross-sectional area and force generate d by the OH muscle increased with size (F = 29.13, p < 0.001), as did that of the IH muscle (F = 58.32, p < 0.001). Resolved force generated by both muscles also increased with size (OH: F = 5.20, p < 0.05; IH: F = 24.45, p < 0.005), although the correlation was not as strong as absolute force output by each muscle (Fig. 2.6).

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SVL (mm) 2468101214161820 IH CSA/OH CSA 0.8 1.0 1.2 1.4 1.6 1.8 2.0 IH/OH = 0.05 SVL + 0.82 r 2 = 0.89Figure 2.5: Figure describing the ratio of the cross-sectional area of the IH muscle to the OH muscle, illustrating the changes in the relative size of the two muscles through ontogeny.

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IH CSA (m m2) 005 007 010 020 030 015 CSA = 078 SVL 175 r 2 = 082 SVL (mm) 10141825 IH Resolved Force (N ) 0001 0003 0005 0015 0025 0010 IH Force = 120 SVL 333 r 2 = 07534 8 6 OH CSA (m m2) 005 007 010 020 015 CSA = 044 SVL 151 r 2 = 069 SVL (mm) OH Resolved Force (N) 00005 00010 00025 00050 00100 OH Force = 067 SVL 321 r 2 = 03010141825 34 8 6 OH LAR 004 006 020 040 010 014 030 LAR = 522e-4 SVL + 017 r 2 = 117e-3 IH LAR 010 030 050 020 014 080 100 IH LAR = 968e-3 SVL + 022 r 2 = 015Figure 2.6: Figure illustrating the scaling patterns of the muscle crosssectional area (CSA), lever arm ratio (LAR) and resulting force. Force was calculated using both the lever arms and the CSA of the muscle. Grey lines represent lines of isometric slope: CSA, 2; LAR, 0; Force, 2.

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Discussion The effects of ontogeny on the natural history of an organism are often underappreciated, especially in morphology and biomechanics. Most research has been focused on the behavioral aspect of scaling in feeding (Deban and OReilly, 2005; Reilly, 1995; Richard and Wainwright, 1995) with few works examine the scaling of musculature of the head region (Adriaens a nd Verraes, 1997; Emerson, 1990). The lack of research on the scaling of musculature prevents many authors from drawing complete conclusions regarding how the behavior of an organism can change during growth, or why it does so. Most of even those few studies did not integrate their results with the behavioral consequences, while those who did we re able to show changes in behavior (if any) as the individual grew (Altringham et al., 1996; Herrel et al., 2005; Vincent et al., 2007). Here, I examined the scaling of the morphology of tadpoles of Xenopus laevis associated with suspension feeding. Of the 5000+ species of anurans, the majority of taxa have tadpoles that feed on detritus or algae. Most tadpoles accomplish this through a two-step process involving two separate mechanisms. The first of these involves the use of keratinized mouthparts, which scrape algae and other material from the substrate. This action suspends these particles in the water column. The second step involves depression of the hyoid to generate negative pressure in the buccal cavity, which in turn draws water into the buccal cavity through the mouth. Food is removed from the water by an elaborate branchial basket (Cannatella, 1999; Wasse rsug, 1972; Wassersug and Hoff, 1979). In tadpoles of Xenopus laevis this feeding mechanism differs from most other anuran taxa. These tadpoles lack the keratinized mouthparts that allow other tadpoles to scrape food off of a

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substrate. As a result, Xenopus tadpoles must suspension feed on particles that are already suspended in the water column. This highlights the importance of the buccal pumping mechanism, as it the only means by which these tadpoles ingest food. While similar to suction feeding mechanically, suspension feedings cyclical nature and lack of explosive movements allow for an interesting comparison. Our understanding of the scaling of suction feeding is currently limited to organisms that grow with geometric similarity, or nearly so (Deban and OReilly, 2005; Herrel et al., 2005; Reilly, 1995; Richard and Wainwright, 1995). My initial examination of head width and buccal volume of Xenopus revealed negative allometry through ontogeny (Fig. 2.3). Direct measurements of buccal volume confirmed indirect methods of estimating the volume based on pumping rates (Seale, 1982). Primarily then, the smaller tadpoles have heads that are wider and volumes that are larger than their larger counterparts. This may lead to ch anges in the feeding morphology, which would then affect the feeding behavior of these ta dpoles. Smaller tadpoles, with their relatively larger muscles should have higher velocities of mouth and hyoid movements than larger tadpoles, and generate higher Re ynolds numbers bringing food into the mouth. Elements of the morphology associated with the length of the body exhibited isometry with respect to SVL, including rostro-caudal length of the ceratohyal and length of the branchial basket. This indicates that while the head is getting relatively narrower as the tadpole grows, these elements continue to grow in proportion with body length. The interhyoideus muscle (IH) is primarily responsible for elevating the hyoid apparatus, compressing the buccal cavity, which pushes the water through the branchial apparatus and out the paired spiracles. The IH originates on one side of the ceratohyals,

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and inserts on the other side. Contraction of the IH results in rotation of the ceratohyals upward, compressing the buccal cavity. Suspension feeding tadpoles, including Xenopus remove material as the buccal cavity is compressed. Water is being pushed through the branchial apparatus, where particles are remove d, and then exits through paired spiracles. Examination of the wet mass of the IH muscle showed that growth of this muscle is isometric (Table 2.1). The IH extends the entire width of the head, and as Xenopus tadpoles grow, it was found that the width of the head exhibited negative allometry compared with the growth of the body. This tr anslates to smaller tadpoles have larger IH muscles, and are therefore able to generate relatively more force to push water out of the buccal cavity. The orbitohyoideus muscle (OH) is responsible for depression of the hyoid apparatus, expanding the buccal cavity. The mu scle originates on the palatoquadrate and inserts on the ceratohyal. The OH is antagonistic to the IH, such that the two muscles are responsible for the functioning of the buccal pumping mechanism. Contraction of the OH results in rotation of the ceratohyals downward, expanding the buccal cavity. In Xenopus tadpoles, both wet mass and cross-secti onal area of the OH exhibited negative allometric growth. Sm aller tadpoles have rela tively larger OH than larger tadpoles and therefore generate larger forces for their size. It is possible that the larger OH allows smaller tadpoles to be less impacted by the rela tive increase in the viscosity of water as a result of their smaller size. The larger OH allows the tadpoles to better compensate for changes in viscosity that would co me as a result of being smaller. Examination of the OH ceratohyal lever arm ratio confirmed values given for larger tadpoles in previous research with a ratio of 0.18-0.22 and is similar for other

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microphagous suspension feeding tadpoles (Wa ssersug and Hoff, 1979). Examination of the IH lever arm ratio has not been undertaken previously. There is no relationship between body size and lever arm ratio in Xenopus (Fig. 2.6). There was no significant change in either lever arm ratio as size increased, and the high variance suggests that intraspecific variation negated any relationship. As the tadpoles grow, I had expected that the lever arm ratio would decrease. Smaller tadpoles require more force to expel water through their branchial apparatus (due to increased viscous forces, a result of smaller size), and a larger in-lever to out-lever ratio would provide higher force outputs. Larger tadpoles, conversely, would be limited by how fast they could clear their branchial apparatus. The lack of a relationship betw een lever arm ratio and body length indicates that the lever arm is not responsible for changing the force output from the OH and IH muscles as the tadpole grows. Rather, it means that the scaling of cross-sectional area determines the scaling of force. Integrating the results from all aspects of these morphological characters allows for examination of the repercussions of sca ling in an evolutionary context. Lever arm ratios were not found to differ across the range of sizes examined here, as a result the only variable that is affecting the force output of this feeding mechanism is the crosssectional area of the muscles. For wet mass, the OH muscle was shown to be negatively allometric, while the IH muscle was found to be isometric. Analysis of the crosssectional area showed that both the OH and IH muscles were negatively allometric. Further analysis examining the ratio of the cross-sectional area of the IH to the OH allowed me to observe the growth relationship of one muscle to the other. This ratio was previously examined to investigate a link between muscle cross-sectional area and

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feeding mode in a wide range of anuran species (Satel and Wassersug, 1981). For small individuals, this ratio was less than one, indicating that the OH muscle is larger than the IH, while in larger tadpoles the ratio approached values closer to two. The slope of this line was greater than zero, indicating that the IH was growing in cross-sectional area relative to the OH. Cross-sectional area is a suitable surrogate for maximum force (Schmidt-Nielsen, 1997), therefore smaller tadpoles are generating relatively more force depressing the buccal floor than elevating it, and as body length increased, the relationship reversed. Larger tadpoles began to generate more force elevating the buccal floor than depressing it. The trend I observed has some potentially important interpretations. This demonstrates that smaller tadpoles, with the relatively larger OH muscles, are more adept at overcoming the physical properties of water pulling it into the buccal cavity. Instead, smaller tadpoles are more challenged pushing the water through the branchial apparatus. As water is forced through the branchial apparatus and out of the buccal cavity, algae and other material are removed. Further decreases in size may make suspension feeding difficult, if not impossible. Tadpoles that began to feed at smaller sizes would have to adapt to the increased ro le of viscosity. With a smaller IH/OH ratio than their larger counterparts, a viable a lternative to suspension feeding for smaller tadpoles would be suction feeding. Rather than pump water continuously to remove algae particles in the water, tadpoles may i ndividually target prey items and consume them, such as in the pipid frog, Hymenochirus boettgeri Hymenochirus boettgeri larvae are macrophagous suction feeding carnivores, starting to feed at less than 1 mm SVL (Deban and Olson, 2002). The small size of Hymenochirus larvae may be related to its method of feeding, using suction feeding rather than suspension feeding. From my

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examination of the scaling of the musculature of Xenopus it is possible that smaller tadpoles, with relatively larger OH muscles (allowing them to more effectively draw water into the buccal cavity) faced selective pr essures that favored tadpoles able to draw in larger prey items individually. In this scenario, larger OH muscles would be favored, as the drawing in prey items would be considerably more important than attempting to push out the remainder of the water. However, even in the smallest Xenopus the IH/OH ratio did not approach values previously recorded for Hymenochirus (IH/OH = 0.07, Satel and Wassersug, 1981). It remains to be seen how the musculature associated with Hymenochirus scales, and this data in turn may provide an opportunity to investigate why suction feeding evolved in the family Pipidae. In summary, I found that many of structures associated with suspension feeding in Xenopus laevis tadpoles scale with negative allometr y to body length. Head width and buccal volume are negatively allometric, while lengths of the filter basket and ceratohyals scaled isometrically. I found that the feeding musculature of Xenopus laevis tadpoles is also negatively allometric with body length, indicating th at smaller tadpoles have relatively larger muscles than larger tadpoles. The OH muscle initially has a larger crosssectional area than the IH muscle, however this ratio changes through ontogeny, resulting in the IH muscle having a larger cross-sectional area than the OH muscle. This shift indicates that early on in development, more force is required to pull water into the mouth than push that water through the branchial appa ratus. As the tadpole grows larger, there is a shift towards a larger IH muscle, generating more force to push the water through the branchial apparatus. I found no relations hip between lever arm ratio and body length, indicating that muscle cross-sectional area is the primary indicator of force generated

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during feeding.

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Chapter 3: Reynolds number, ontogeny, viscosity and Xenopus : the role of biotic and abiotic factors in the suspension feeding tadpoles of Xenopus laevis Introduction The effects of body size on the kinematics of movement in animals have been the focus of many studies, especially studies of locomotion (see Alexander, 2005 and Biewener, 2005 for reviews). Several vari ables associated with locomotion and locomotor performance correlate with changes in some measures of size, either limb length or body mass, for example, stride length increases in proportion to limb length (Rand and Rand, 1966; Biewener, 1983; Wilson et al., 2000; Toro et al., 2003). Research on the effects of body size on feeding kinematics is less complete. Literature on the comparative behavior of feeding is prolific (Lauder, 1985; Lauder and Shaffer, 1993; Motta and Wilga, 2001; Schwenk, 2000; Wainwright et al., 1989). The scaling of feeding behavior has been far le ss explored, with only a small number of fish, amphibians, and reptiles examined (Deban and OReilly, 2005; Hernandez, 2000; Holzman et al., 2008; Meyers et al., 2002; Reilly, 1995; Richard and Wainwright, 1995; Robinson and Motta, 2002; Vincent et al., 2007; Van Wassenbergh et al., 2005; Wainwright and Shaw, 1999). Examination of aquatic feeding and its scaling has been limited among vertebrates to primarily suction feeding organisms such as teleost fish, sharks, and amphibians

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(Deban and OReilly, 2005; Hernandez, 2000; Richard and Wainwright, 1995; Robinson and Motta, 2002; Van Wassenbergh et al., 2005; Wainwright and Shaw, 1999). One of the limits of these studies is the inconsistent results obtained. Hill (1950) proposed the original scaling coefficients for movement and morphology. Richard and Wainwright (1995) developed a different model to accu rately predict the movements of the largemouth bass, Micropterus Robinson and Motta (2002) reported scaling coefficients for the nurse shark, Ginglystoma that matched both Hills and Richard and Wainwrights respective models, while Deban and OReillys (2005) work on Cryptobranchus closely matched the predictions made originally by Hill. The large variation among results prevents adequate prediction of the behavior of suction feeding organisms as they grow. Compared to suction feeders, suspension feeders have received far less attention. Scaling of suspension feeding has been investig ated previously, in invertebrates, in terms of how size affects the fluid flow as the organism feeds, and the scaling of the suspension feeding mechanism (Koehl, 2000). The aforementioned studies also utilized species that grow either geometrically or nearly geometrically (Deban and OReilly, 2005; Reilly, 1995). The relative dimensions of the head and feeding apparatus remain th e same. Allometric growth of any of the morphology of the head has the potential to alter the mechanics of suspension feeding, therefore changes in feeding kinematics may not be solely attributable to changes in size; changes in the shape of the organism may al so be responsible for the deviations in kinematics. Very recently work has investigated the aspect of changing shape and its effects on feeding (Holzman et al., 2008; Vincent et al., 2007). Allometric growth of the skull in bluegills predicted peak fluid velocities (Holzman et al., 2008), and in the case of

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water snakes allometric growth of the skull allowed the snakes to move from feeding on fish to larger, more robust prey such as frogs (Vincent et al., 2007). Compared to air, water is much more viscous and presents different challenges. Viscosity can change how the fluid flows around an organism, as well as the organisms performance and behavior in the fluid (McHenry and Lauder, 2005). Changing the viscosity allows examination of the effects of abiotic factors on the biomechanics of suspension feeding. The effects of changes in viscosity as a result of temperature have been well studied, from invertebrate locomo tion (McHenry et al., 2003; Van Duren and Videler, 2003) to reproductive physiology (Brokaw, 1966), all of which showed that lower temperatures resulted in higher viscosity, which turn reduced velocity of movement. Reynolds number, Re, is used to describe the flow of a medium in relation to an object with higher values indicating flow th at is dominated by the inertial properties of the medium and which tends to be more turbul ent, and lower values of Re indicating flow that is dominated by viscous properties and wh ich tends to be laminar (Vogel, 1994). In biological systems where fluid density and vi scosity are the same for organisms in the same environment, size and speed are importa nt factors in determining Re and flow regime; larger, faster organisms experience larger Re, and the opposite is true for smaller, slower organisms. Previous research on the feeding mechanisms of organisms in low Re (Koehl and Strickler, 1981; Koehl, 2000), and the effects of Re on vertebrate locomotion (Fuiman and Webb, 1988; Hunt von Herbing and Keating, 2003; Johnson et al 1998; Muller et al, 2008; Videler et al, 2002; Wilson and Franklin, 2000) which showed that Re has an sizeable impact on an organisms performance. Organisms with a lower Re move slower (Hunt von Herbing and Keating, 2003; Wilson and Franklin, 2000) and a lower Re

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can change a sieving mechanism into a paddl e in copepod feeding (Koehl and Strickler, 1981). The only studies examining the effects of Re through ontogeny have focused on zebrafish ( Danio) and revealed that increasing size and the resulting increase in Re have strong effects on both feeding and locomotor performance (Hernandez, 2000; McHenry and Lauder, 2005). Small Danio move slower and do not turn as sharply as larger Danio (McHenry and Lauder, 2005). Most tadpoles (e.g. genus Rana) of the over 5000 species of frogs are omnivorous planktivores that use keratinized mouth parts to scrape algae or other detritus from submerged surfaces, creating a suspension of particles. The tadpole pumps this suspension into its buccal cavity and through its pharyngeal filter basket by rhythmic dorsoventral movements of its hyobranchial apparatus coupled w ith jaw movements (Seale et al., 1982; Seale and Wassersug, 1979). Particles are removed from suspension by mucus entrapment and ingested, and wate r exits posteriorly through a single or double spiracle. Tadpoles of the family Pipidae are unusual among tadpoles in that most are obligate suspension feeders (Feder et al., 1984; Gradwell, 1971; Seale, 1982; Seale et al., 1982). Pipid tadpoles lack keratinized mouth parts and the ability to scrape detritus from the substrate, therefore must trap particle s already in suspension in the water column (Cannatella, 1999; Gradwell, 1971). Feeding in an obligate suspension feeder such as Xenopus laevis occurs utilizing both the mouth and hyoid. The mouth opens and shortly afterwards, the hyoid begins to depress, lowering the floor of the buccal cavity, generating negative pressure pulling water into the cavity. The mouth then closes, followed by elevation of the hyoid. Water is pushed through the branchial baskets at the

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back of the cavity, and out paired sp iracles (Seale et al, 1982; Wassersug 1996; Wassersug and Hoff 1979). I chose tadpoles of Xenopus for their unique manner of feeding among anurans and the opportunity to examine the effects of abiotic and biotic factors on suspension feeding. During buccal pumping events, the entirety of the mouth and hyoid is visible, allowing me to examine the kinematics of both apparatus during feeding. In other tadpoles, dark pigmentation of ten makes it difficult to observe the hyoid moving during feeding. The mechanics of suspension feeding in Xenopus is very similar to that of suction feeders, however the temporal pattern of movement differs. There are two main differences between suspension feeding in Xenopus and suction feeding taxa. Suspension feeding in the tadpoles is cyclic whereas suction feeding consists of one explosive event, while Xenopus may repeat the buccal pumping mechanism many times in a short period of time. In addition, only the inhalation phase of suction feeding is of interest, the drawing of prey items into the mouth. In suspension feeding, both the inhalation and exhalation phases are of importance. Water is drawn into the mouth with food in it, but the mechanism by which food is removed and the remaining water pushed out is also of importance. Xenopus tadpoles are also a good system in which to examine the effects of body size. Previous work has determined that the buccal volume of Xenopus exhibits negative allometry, and this relatively reduced volume may alter the kinematics of feeding (Seale, 1982). This allometry allows to me examine the scaling of kinematics in an organism that does not grow geometrically. Previously, I had investigated the scaling of the feeding

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morphology in tadpoles of Xenopus The dimensions of the head and hyoid muscles exhibit negative allometry thr ough ontogeny. Smaller tadpoles have larger muscles and larger heads than larger tadpoles, and generate relatively more force. As a result, I would predict that smaller tadpoles, w ith relatively larger muscles, would show higher velocities and shorter durations than larger tadpoles. The goals of this research are to investigate the effects of ontogenetic and abiotic factors on the kinematics of suspension feeding in Xenopus tadpoles via three approaches. First, I examine the scaling patterns of buccal pumping kinematics during feeding in water and with the viscosity of the medium altered. I hope to examine the effects of this abiotic factor on the buccal pumping ability of Xenopus This also may allow me to tease apart the effects of changes in shape from size. Increasing viscosity effectively decreases the size of the organism in terms of Reynolds numbers. I can thus examine kinematic patterns for differently shap ed tadpoles, all of which feed in the same manner. Second, I calculate the Re of an ontogenetic series of buccal pumping tadpoles. Re is calculated for each individual at the point where water enters the buccal cavity through the mouth. Smaller tadpoles (SVL < 8 mm) operate under a viscous regime (Re<75) while larger tadpoles (SVL > 10 mm) operate under an intermediate and potentially inertial regime (75
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resulting pressure change as water is pushed through the branchial apparatus. With this data I can describe the flow regime of feeding tadpoles, modeling both Re and the pressures generated during suspension feeding. Methods Buccal Pumping Kinematics Seventy-five tadpoles of Xenopus laevis (4-16 mm SVL) were imaged at 125 frames/sec using a Photron PCI-1024 FastCam camera. Only images with the entire tadpole body in the frame and presenting a latera l profile were used for digitizing. X, y coordinates of four landmarks on each frame were chosen (Fig. 3.1): (1) Upper jaw tip, (2) lower jaw tip, (3) head directly dorsal to the eye, and (4) hyoid apparatus directly ventral to the eye. These coordinate data were used to generate ten kinematic variables: (1) Maximum gape (distance between points 1 and 2) and (2) hyoid depression distance (distance between points 3 and 4), durations of (3) mouth opening, (4) mouth closing, (5) hyoid depression and (6) hyoid elevation and ve locities of (7) mouth opening, (8) mouth closing, (9) hyoid depression and (10) hyoid el evation. Ten buccal pumping cycles were recorded per tadpole and kinematic variab les were averaged for each individual. To examine differences in kinematics as a result of food in the water, a subset of fifteen tadpoles were first imaged without food particles suspended in water, then imaged again once food had been introduced. Food consisted of ground up commercial algae flakes (Hagen Nutrafin Spirulina Algae Flake Food). For tadpoles that were imaged with food in the water; frames were used only if particles were observed moving into the mouth.

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Figure 3.1: Representative lateral image of a Xenopus laevis tadpole during maximum gape and hyoid depression showing landmarks and distances used for kinematic analysis. Scale is 3 mm.

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Reynolds Number Calculation Re of water flowing into the mouth was calculated using the equation: Re = U l / v (Eq. 1) Where U is the velocity of the object moving through the water, l is the characteristic length of the object, and v is th e kinematic viscosity of the fluid (v) (Vogel 1994). For my experiments, one Re was calculate d for water entering the buccal cavity through the mouth. In this case head width was used as the characteristic length (l). Fluid velocity (U) was calculated as the average velocity of three food particles measured over the time they started moving until they entered the mouth. Only particles directly in front of the mouth were used for these calculations. Viscosity Manipulations To examine the effects of increasing viscosity on buccal pumping rates and kinematics, a methylcellulose solution (MP Biomedicals, #155496) was used, chosen for its non-toxic properties as well as its dige stibility (Hunt von Herbing and Keating, 2003). Five separate solutions where chosen by calculations of Re experienced by small Xenopus laevis tadpoles. Kinematic viscosities were measured with a Cole-Palmer Viscometer at 1.0, 3.5, 6.9, 10.3, 14.6, 23.5 cSt. Tadpoles were placed individually in the e xperimental fluid and then imaged as above to record ten buccal pumping even ts. Each tadpole was exposed to only one experimental fluid. Kinematic variables for the ten pumps were averaged, yielding one value per variable for each tadpole.

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Morphology Following imaging, each tadpole was euthanized by overdose of a 1 % solution of MS-222 and fixed in 10% neutral buffered form alin for generating scaling relationships and calculating pressure (discussed below). Sixteen tadpoles (SVL 4.3-18.3 mm) were utilized for morphological measurements and dissection. From these, two external morphological measurements were made with a digital caliper (Mitutoyo Corp., Japan): snout-vent length (SVL), and head width at the mouth. Buccal volume was measured by maximally depressing the hyoid with forceps, sealing the spiracles with silicone, and measuring the volume of water needed to fill the buccal cavity with a micropipette. Fifteen tadpoles ranging in size from 4-16 mm were cleared and stained (Hanken and Wassersug, 1981), and the branchial basket of each was imaged ventrally, dorsally, and laterally using a Leica MZ75 dissecting mic roscope and Leica DFC290 digital camera. Pressure Model To determine the pressure required to push water through the branchial apparatus during suspension feeding, I generated a model based on morphological and kinematic measurements. Pressure (p) is calculated using a variation of Ohms Law (Vogel, 1994) where flow rate (F) is equal to the change in pressure ( p) divided by the resistance (R) (Eq. 2): F = p / R Eq. 2 For my model, flow rate was calculated as buccal volume divided by duration of hyoid elevation (i.e., the time it took to empty the known buccal volume of water). Pipe resistance (R) was determined using the dimensions of the branchial apparatus and the viscosity of the fluid. In Xenopus tadpoles, water is forced via compression of the buccal

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cavity through the branchial apparatus, which is bilaterally symmetrical. Each side of the apparatus has three channels through which wa ter passes before exiting the spiracle. The channels were treated as pipes in parallel, which allows the resistance (R) through the branchial apparatus to be calculated us ing the dynamic viscosity of the fluid ( ), the length of the pipe (l) and the hydraulic diamet er of the pipe (d) (Eq. 3, Vogel, 1994): R = (128 l) / ( d4) Eq. 3 The resistance calculated from Eq. 3 was then used in conjunction with the calculated flow rate to determine the average positive pressure, using Eq. 2, of the buccal cavity necessary to push water through the branchial apparatus. The cone shape of each chamber was represented as a series of three pipes with progressively smaller diameters. During examination of the branchial apparatus, openings on each end of the chambers were discovered to be non-circular. To calcu late resistance using non-circular pipes, the hydraulic diameter of the pipe was used (W hite, 1991). The hydraulic diameter (h) is calculated using the cross-sectional area of the pipe (a) and the perimeter ( ): h = 4 (a/ ) Eq. 4 For circular pipes, the hydraulic diameter is equal to the measured diameter (White, 1991). The hydraulic diameter re placed diameter in Eq. 3 an d resistance was calculated. Resistance was calculated for each pipe in series, and then all the channels in parallel. The resulting resistance was treated as one half of the branchial apparatus, in parallel with the same resistance for the other half. The total calculated resistance was multiplied by the flow rate of fluid leaving the buccal cavity to determine the pressure change (Eq. 2).

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Statistical Analyses To examine the effects of body size, viscosity, and presence of food particles on buccal pumping, kinematic variables were log transformed, and regressed against log SVL; residuals were then tested in a one-way ANOVA. Morphological variables were also log transformed and regressed against l og SVL to examine scaling relationships. To examine trends of movement through increasing viscosity, size classes were implemented. Each size class consisted of a ll the tadpoles with a 2 mm SVL range (e.g., 4-6 mm SVL is one size class). Data were analyzed using SigmaStat v3.1 (Systat Software Inc., California, USA), and regressions graphed using SigmaPlot v8 (Systat Software Inc., California, USA). Results Morphology and Kinematics In Xenopus laevis tadpoles, a buccal pumping event consists of the tadpole opening its mouth, and depressing the hyoid to draw water into the buccal cavity, then closing the mouth and elevating the hyoid to expel water through the branchial apparatus and out the paired spiracles. A single buccal pump typically lasts less than one second (Fig. 3.2). Head width scaled with negative allometry relative to SVL (slope=0.36), smaller tadpoles having relatively wider heads than larger tadpoles. Buccal volume also scaled with negative allometry with a slope of 1.2, compared with an isometric slope of 3 (Fig. 2.3).

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0 0.25 0.34 0.40 0.55 0.94Figure 3.2: Image sequence of tadpole feeding to illustrate the four step buccal pumping mechanism. Time during sequence represented in the bottom left corner of each image, in seconds. Scale is 3 mm.

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Results of the ANOVA revealed that none of the ten kinematic variables were different between feeding and non-feeding trials (F=0.07-2.82, p=0.10-0.79). Tadpole pumping rate, however, was significantly greater in feeding trials (F=13.286, p=0.003). Kinematic variables of buccal pumping events in water plotted against SVL did not exhibit consistent patterns as a func tion of body length. Only maximum hyoid distance (scaling coefficient 95% CI, 0.60 0.74), duration of mouth closing (0.74 0.51), duration of hyoid elevation (0.69 0.55) increased isometrically with SVL. The only negatively allometric vari able (slope between 0 and 1) was maximum gape distance (0.52 0.37). Duration of mouth opening (-0.05 0.60), duration of hyoid depression (0.40 0.51), and velocity of hyoid elevation (-0.31 0.39) showed no effect of increasing SVL (slope not different from 0.00 given confidence intervals). Kinematic variables scaling between 0 and -1 included velocity of mouth opening (-0.72 0.20), velocity of mouth closing (-0.50 0.35), and velocity of hyoid depression (-0.65 0.16). Reynolds Number Tadpoles imaged in water with food partic les were used to calculate Re during feeding. Fluid velocity was best predicted using a piston model using the buccal floor area (square of the head width) multiplied by the hyoid depression velocity to describe changes in fluid velocity observed (Fig. 3. 3). The minimum fluid velocity observed was 0.6 mm/s and the maximum 13.2 mm/s. Fluid velo city along with the viscosity of water and width of the tadpoles head were used to calculate the Re for feeding. Calculated Re ranged from 2 for the smallest tadpole (4.3 mm SVL) to 106 for the largest in this study (16.5 mm SVL). Re scaled to SVL with a factor of approximately 8 (Fig. 3.4).

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Figure 3.4: Scaling of Reynolds Number to snout-vent length. SVL (mm) 4681012141618 Re -20 0 20 40 60 80 100 120 140 Re = 8.09 SVL 27.79 r 2 = 0.82 Hyoid Depression Velocity Head Width 2 (mm 3 / s) 50 75100 200 300 150 Fluid Velocity (mm/s) 0.3 1 4 10 20 FV = 2.92 HDV HW 2 5.27 r 2 = 0.70Figure 3.3: Relationship of fluid velocity entering the mouth with our piston model. Here the piston is represented by buccal floor area (square of head width) and hyoid depression velocity.

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Effects of Viscosity All ten kinematic variables were significantly affected by the viscosity treatments, with similar patterns of significance (Table 3.1). For individual size classes, velocities exhibited a non-linear pattern. Velocity of mouth closing increased until the 10.3 cSt treatment, then decreased for the remainder of the trials (Fig. 3.5). Hyoid and gape distances increased until the 10.3 cSt treatment, then remained unchanged for all further treatments for all sizes. Durations showed no obvious trend for any size class or viscosity treatment. Pressure Model Images of the branchial apparatus indicate that there are three chambers on either side of the buccal cavity, confirming previous work (reviewed in Cannatella, 1999). Each chamber is cone-shaped, with a larger opening towards the dorsal surface that narrows ventrally (Fig. 3.6). The interior wall of each chamber is lined with channels and mucus secreting cells that act to trap food pa rticles as they travel through each channel (Wassersug and Rosenberg, 1979). To calculate pressure generated during evacuation of the buccal cavity, I developed a model to represent water flow in the branchial apparatus (Fig. 3.6). In water (1.01 cSt), the maximum calculated theoretical pressure was 81.2 kPa (4.3 mm SVL) and the minimum was 1.6 kP a (14.6 mm SVL), pressure generated was inversely proportional to SVL (Fig. 3.7). The maximum pressure generated during a viscosity trial was 577.7 kPa (5.1 mm SVL, 10.3 cSt). Pressure was significantly affected by body size and viscosity (Table 3.1). Increasing viscosity resulted in an increase in pressure.

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Figure 3.5: Velocity of mouth closing as viscosity increases for one size class of tadpoles (SVL 10-12 mm). Kinematic Variable DF SS MS F P Duration of Mouth Opening 5 23.7464.749 7.066<0.001 Duration of Mouth Closing 5 11.6592.332 2.581 0.036 Duration of Hyoid Depression 5 31.8 6.36 12.196<0.001 Duration of Hyoid Elevation 5 31.9266.38512.297<0.001 Maximum Gape Distance 5 19.19 3.838 5.108<0.001 Maximum Hyoid Distance 5 24.8934.979 7.745<0.001 Velocity of Mouth Opening 5 46.3859.27737.041<0.001 Velocity of Mouth Closing 5 34.2256.84514.361<0.001 Velocity of Hyoid Depression 5 48.7329.74647.053<0.001 Velocity of Hyoid Elevation 5 42.9658.59327.459<0.001 Pressure 5 56.13411.227151.742<0.001 Viscosity (cSt) 0 5 10 15 20 25 VMC (mm/s) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 VMC = 2.17 + 0.29 Viscosity + -0.01 Viscosity 2 r 2 =0.63Table 3.1: Results of the ANCOVA on viscosity treatment. All variables were found to be significantly affected by viscosity (df=5, p<0.05).

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Buccal Cavity Pipe 1a Pipe 1b Pipe 1c Pipe 2a Pipe 2c Pipe 2b Pipe 3c Pipe 3b Pipe 3aFilter Apparatus Spiracle Figure 3.6: Cleared and stained Xenopus tadpoles illustrating branchial apparatus from the ventral view. One half of the filter apparatus is highlighted. The inset illustrates the schematic diagram of the pipe model used to calculate pressure in the buccal cavity (one half of cavity shown). Arrows indicate direction of water flow. Scale is 2 mm.

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Figure 3.7: Scaling pressure vs. snout-vent length illustrating the decrease in pressure generated as size of the tadpole (SVL) increases. SVL (mm) 34 681013162025 Pressure (kPa) 1 5 10 30 2 60 100 17 Pressure = -2.40 SVL + 3.34 r 2 = 0.84

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Micropterus salmoides Maximum gape distance was significantly less than 1.0, but more than zero. This is likely the result of the change in head shape as the tadpoles grow. A relatively smaller head for larger tadpoles would translate into a smaller mouth. The lack of congruence with these results to any one of the previous works suggests two possibilities. The first, suspension feeding is intrinsically different from suction feeding, despite the similar mechanics. This could be the result of the different food items or in the cyclical nature of suspension feeding, which may impose different requirements on the muscles and skeleton, and may thus present different constraints than suction feeding. The second is that the allometry of the feeding morphology prevents the Xenopus from behaving similarly to either the Richard a nd Wainwright (1995) or Hill (1950) model, both of which assume geometric similarity. Reynolds Number Calculation The scaling of Reynolds number in aqua tic systems varies greatly between organisms. The definition of a low Re regime, where viscous forces dominate differs by over an order of magnitude, as low as 10 (Weihs, 1980) to over 300 (McHenry and Lauder, 2005). Here, I use the scale employed by Fuiman and Webb (1988), commonly used by other authors in studies of fish lo comotion (Mller et al, 2008; Videler et al, 2002). This scale has low Reynolds number regimes with an upper limit of 75 and an intermediate regime between 75 and 270 (Fuiman and Webb 1988). Xenopus laevis tadpoles suspension feeding in water obtained Reynolds numbers ranging from 2 to 106. These data point to a shift from low Re regime into an intermediate Re regime when the tadpoles reach approximately 10 mm SVL. These values are the lowest measured in vertebrates; previously larvae of the zebrafish Danio were shown to feed at Re as low as

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5 (Hernandez, 2000). Functional shifts are known to occur at very low Re, especially in invertebrates (Koehl, 2001). This also contrasts with Reynolds numbers calculated for feeding Hymenochirus boettgeri which generated Reynolds numbers up to 300 (Deban and Olson, 2002), placing them in the high Re regime. Hymenochirus is a suction feeding carnivorous tadpole in the family Pipidae with Xenopus Hymenochirus is much smaller at first feeding (< 1 mm, Deban and Olson, 2002) than Xenopus (4 mm, see results), as a result the differences in Re were solely the result of increased fluid velocity. These closely related taxa present a unique relationship where one member of the family is a suspension feeder (by a method uncommon to other members of its Order) and the other is a suction feeder that is four times smaller. It is possible that Re could be a factor in the evolution of suction feeding in Hymenochirus and this link is discussed later. Kinematics and Reynolds Number The results of experimental manipulations of Re, feeding kinematics, and scaling of the buccal volume present a conundrum. Fluid velocity increased with body size, as did Re. Buccal volume showed negative allo metry, and kinematic velocities (i.e., movements of the feeding apparatus of the tadpole) were lower in larger tadpoles. How are the Xenopus able to increase fluid velocity while moving these feeding elements slower and possessing relatively smaller volumes? Mouth diamet er was negatively allometric compared to the buccal volume and kinematic velocities, but buccal floor area was isometric relative to body size. To appr oach this dilemma the buccal movement is modeled as a piston. Modeling the floor of the buccal cavity with the velocity of hyoid depression proved to be a good pr edictor of fluid velocity (r2 = 0.7) entering the mouth. In smaller tadpoles, the buccal floor area is relatively large compared to the size of the

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body. While smaller tadpoles are moving fast er, the area through which the water moves is larger, slowing the velocity of the water. This leads to the increase in fluid velocity in proportion to body length that I observed. Effects of viscosity Increased viscosity has an effect on the buccal pumping kinematics of Xenopus laevis The strongest effects were seen in the movement velocities. Examining the results of the two-way ANOVA, all four velocities were significantly affected by viscosity treatment. After an initial decrease in velocity when comparing water to the first viscosity treatment (3.5 cSt), I observed an increase in the velocity as I further increased the viscosity. The increasing trend continues as the viscosity is further increased until the treatment reached 10.3 cSt. After this point, increased viscosity was correlated with a decrease in velocity. This trend was observed in all size classes and for all kinematic variables. Surprisingly, for tadpoles in the smallest size class (4-6 mm SVL), velocities of the kinematic variables were always lower in the viscosity treatments than in water. For larger tadpoles (SVL >10mm), velocities in creased in viscosity treatments beyond the values found in water. Examination of kine matic variables with respect to body size showed that velocities decreased as body size increased. The slopes of these lines were found to be significantly different from 0.0 but not different from -1.0. For different viscosity treatments, the slopes of the lines varied (from -1.4 to 0.8). Increasing viscosity treatments was correlated with an increase in the slope of the regression. The two highest viscosity treatments (14.6 cSt and 23.5 cSt) had positive slopes, but these were not significantly different from zero. Plotting velocity of movement against viscosity for single size classes allows for a clearer illustration of this trend (Fig. 3.5). As the viscosity

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increases, velocity increases until approximately 10.268 cSt. Increasing the viscosity further beyond this point was correlated w ith a decrease in velocity of movement. Evidence of this peak and subsequent decline in velocity point toward the compensatory behavior discussed earlier. The peak in ve locity may be the upper limit of performance, and beyond this point Xenopus are unable to adapt to the increasing viscosity. Unable to exert any more effort, the tadpoles are constrained by the viscosity of the fluid. The viscosity also significantly affected duration of hyoid depression and elevation. Increasing viscosity did not affect the relationship between duration of these variables and body size. One distance, hyoid depression distance, was significantly affected by viscosity. Isolating a single size class, as the viscosity increases the displacement of the hyoid increases sharply, then asymptotes around 10.3 cSt. These results show maximal performance by tadpoles at this viscosity treatment. Beyond this point, as was the case with the durations, Xenopus are unable to increase the distance further, instead performing at this maximum at higher viscosity. Unexpectedly, the viscosity treatments did not have an effect on the pumping rate of tadpoles. Evidence for Xenopus laevis altering pumping rates is prolific in the literature (Seale, 1982; Seale et al, 1982; Seale and Wassersug, 1979; Wassersug and Hoff, 1979). My results with the viscosity trials indicate that while tadpoles are able to sense the amount of food in the water by adju sting the rate of buccal pumping events, the methylcellulose did not provoke a similar response. Kinematic profiles for Xenopus were compared for water and viscosity treatments. Profiles for hyoid m ovement were nearly symmetrical in water, however, an increase in viscosity increased the duration of hyoid depression at a lower rate than

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duration of hyoid elevation. The resulting kinematic profile showed a relatively shorter duration in hyoid depression than hyoid eleva tion (Fig. 3.8). Profiles of hyoid movement in suction feeding were found to demonstr ate a similar pattern (Richard and Wainwright, 1995). There is a short duration while the hyoid depresses, then a longer duration while the hyoid elevates. This pattern is very similar to the kinematic profiles of suction feeding fish (Richard and Wainwright, 1995), sala manders (Deban and OReilly, 2005), and tadpoles (Deban and Olson, 2002). There is a rapid depression of the hyoid as food is pulled into the mouth, and a much slower movement during the recovery phase as the hyoid is elevated, pushing the water out of the buccal cavity. This similarity between kinematic profiles of Xenopus in higher viscosity and suction feeding vertebrates suggests again that the evolution of suction feeding in Hymenochirus may be linked to small size and the resulting impacts of viscous forces. Pipe Model In an attempt to better unde rstand the effects of viscosity of the buccal pumping of Xenopus I developed the pipe model to calcula te the pressure generated by the tadpole as it pushes water through the branchial appa ratus. Morphological examinations of the branchial apparatus (results not presented here) confirmed previous work on the number of channels and the general structure (C annatella, 1999; Gradwell, 1971; Seale et al. 1982; Weisz, 1945). In water smaller tadpoles ge nerated more positive pressure than the larger individuals. The smallest tadpole generated the largest pressure, 81.2 kPa. This is similar to values from larger vertebrates: water jetting from the mouth of seals during foraging (Marshall et al. 2008), and whales during water expulsion (Werth, 2006), supporting the model. Larger tadpoles did not generate larger pressures in response to

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Figure 3.8: Kinematic profile for hyoid movement during one feeding event, illustrating the increased time of hyoid elevation during feeding in higher viscosity. Time (s) 0.00.20.40.60.81.0 Hyoid Depression Distance (mm) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.0 cSt 10.0 cSt

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Discussion Scaling of morphology and kinematics The scaling of the morphology of Xenopus laevis tadpoles across ontogeny shows several examples of negatively allometric growth. Both head width and buccal volume exhibited negative allo metry through ontogeny. Smaller tadpoles have relatively larger mouths and can ingest relatively larger amounts of water than their larger counterparts. The allometric growth of this taxon suggest s that the normal rules of scaling, the patterns generated by previous work on aquatic suction feeders (Deban and OReilly, 2005; Hill, 1950; Richard and Wainwright, 1995; Robinson and Motta, 2002), may not apply to Xenopus tadpoles. Four of the ten kinematic va riables did not fit any previous pattern: velocity of mouth opening, velocity of mouth closing, velocity of hyoid depression, and maximum gape distance. Velocities of mouth opening, mouth closing, and hyoid depression all had slopes between 0 and -1. While all were significantly different from -1, the pattern does suggest that these velocities are different to those reported for the largemouth bass, Micropterus salmoides, (Richard and Wainwright, 1995) which reported increasing velocities of movement with body length. The remaining velocity, hyoid elevation, had a slope of 0. No previous study has measured th is variable, but it matches the velocities of other movements in the hellbender, Cryptobranchus alleganiensis (Deban and OReilly, 2005) and the model developed by Hill (1950) for geometric scaling. Maximum hyoid depression distance, duration of mouth closing, and duration of hyoid elevation were also found to be similar to Cryptobranchus with a slope of 1.0. The other two durations: mouth opening and hyoid depression, were found to be in line with similar results from

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increased viscosity, but smaller tadpoles in hi gher viscosity generated increased pressure. The increase in pressure, even with the decrease in flow rate, suggests that if the smaller tadpoles attempted to maintain the flow rate that was achieved in water in higher viscosity, then pressures would rise above what the musculature could possible generate. The effects of biotic and abiotic factors on suspension feeding From my results, I found that both biotic and abiotic factors play an integral role in the mechanics of suspension feeding for tadpoles of Xenopus laevis The changes in the kinematics as a whole through ontogeny did not exhibit similar sca ling patterns as any of the previous models, but individual variab les were consistent with patterns of both largemouth bass (Richard and Wainwright, 1995) and hellbenders (Deban and OReilly, 1995). Any similarity between the results pr esented here and the previous work on aquatic suction feeding is likely due to the similarity in the mechanics. The movements and timing are very similar, with the exception that the depression of the hyoid elements is much slower in suspension feeding. In suction feeding, one explosive movement is used to generate negative pressure and draw the prey item into the mouth. The major discrepancy I found was that Xenopus lacked a consistent pattern with regards to the other taxa. As was reported, some of th e kinematics matched one taxon(durations of movement in Micropterus salmoides Richard and Wainwright, 1995), and the other variables matched others (d istances of movement in Cryptobranchus allegiansensis Deban and OReilly, 2005), with even a few variables not matching any previous work. The source of this discrepancy may be the a llometric scaling of the morphology. As the tadpoles grow, both the head width and buccal volume were not growing as rapidly. With a relatively narrower head and smaller buccal volume in larger animals, it seems

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obvious that the mechanics of feeding and their scaling patterns w ill be altered. However, this does not imply that I cannot predict the kinematics and resulting fluid behavior because the shape of the animal is changing as it grows. I found that despite being larger and moving slower, larger tadpoles were able to intake water at a faster velocity than their smaller counterparts. By modeling the system as a piston, I observed that a combination of morphology and kinematic s were best suited to accurately predict the velocity of algae moving into the mouth. I found strong effects of viscosity on the buccal pumping mechanism of Xenopus particularly at the transition between intermediate and viscous flow regimes. Initial increases in viscosity results in increased velocities and distances, peaking at the aforementioned transition (~10 cSt). Increasi ng viscosity further resulted in decreased performance of all kinematic variables, indicating the tadpole was no longer able to compensate for the additional resistance to flow. The kinematic profile of hyoid movement during buccal pumping illustrates th is (Fig. 3.8). In water, hyoid depression and elevation are nearly symmetrical in duration and velocity. My representative profile at 10.3 cSt shows no symmetry during hyoid movement. Hyoid depression is similar to a buccal pumping event in water. Hyoid eleva tion lasts much longer for the viscosity treatment than in water, and resembles that of suction feeding vertebrates (Deban and Olson, 2002; Deban and OReilly, 2005; Richard and Wainwright, 1995). This may have some important implications. Hyoid elevation, and with it the ability to push water through the branchial apparatus, appear to be the constraining factors for suspension feeding in Xenopus Increasing viscosity, as a result of smaller body size, cannot be eliminated as a factor. Sokol (1977) argues that Hymenochirus is likely derived from a

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suspension-feeding tadpole, with its predatory habit rooted in its small size. Ecologically, a reduction in size and feeding may allow Hymenochirus to exploit a new niche. It may also be possible that suspension feeding at such a small size is no longer energetically profitable, and that suction feeding (targeti ng individual prey items) is a more profitable feeding mode (Sokol, 1977). This is consistent with my findings using Xenopus tadpoles in higher viscosity solutions. Further re ducing the size of the tadpole may make suspension feeding energetically unfavorable. If this is the case, then selection for suction feeding as a result of reduced body size is feasible. These results are a good example of the importance that abiotic factors play in the physiology of an organism.

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Chapter 4: Conclusions Results indicate that both abiotic and biotic factors play integral roles in the suspension feeding of tadpoles of Xenopus laevis In understanding the scaling patterns of behavior, it is vital that the underlying m echanics of the behavior be fully explored prior to making any conclusions. Here, by examining the morphology, kinematics, and abiotic effects, I have attempted to quantify these effects on the resulting suspension feeding behavior in tadpoles. Examining the scaling of the feeding morphology found that tadpoles of Xenopus laevis exhibit allometric growth. Width of the head and buccal volume exhibited strong negative allometry, resulting in larger tadpoles that had relatively narrower heads and smaller volumes. These drastic changes in head shape influence the patterns of movement. Length of the filter basket a nd rostro-caudal length of the ceratohyals increased isometrically with length. Two muscles are responsible for depressing and elevating the hyoid, the orbitohyoideus and interhyoideus. Mass of the interhyoideus also exhibited isometric growth, but the mass of the orbitohyoideus exhibited negatively allometry. Cross-sectional areas of both mu scles exhibited negative allometry, indicating that as the tadpoles grew larger, they were capable of generating relatively less force. This could be explained by the changes in the relative importance of the physical properties of the water that resist flow (i.e., viscosity) as the tadpole increases in size. The viscous properties of the water are more important for smaller tadpoles, which face

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greater resistance to generating flow as a result of those properties. Comparison of the slopes of the cross-sectional areas revealed differing growth rates; the interhyoideus grew faster than the orbitohyoideus. The ratio of the cross-sectional area of the orbitohyoideus is larger than that of the interhyoideus in smaller tadpoles, but as the tadpoles grow, the interhyoideus becomes larger in cross section. Initially then, sma ller tadpoles generate more force pulling water into the buccal cavity while larger tadpoles generate the most force expelling water. Again, this is likely the result of the changing importance of the physical properties of the water. Drawing water into the buccal cavity requires more force in smaller tadpoles. Lever arm ratios, capable of altering the force generated by the muscles, were found to have no relationship with body size. The resulting force, causing rotation of the ceratohyals, is therefore best predicted by the dimensions of the muscles. I found that several key elements of the feeding morphology of Xenopus exhibit allometric growth. The changes in the morphol ogy of an organism play an important role for the changes in behavior. All current m odels for the scaling of kinematics apply to organisms that scale geometrically (Hill, 1950; Richard and Wainwright, 1995). Considering the variance among results for geometrically scaling organisms, it would appear unlikely that Xenopus with several allometric morphological characters, would match any previous models. Scaling coeffici ents that did match th e bass model (Richard and Wainwright, 1995) would confirm the hypothe sis that movement velocities increase with size. Coefficients similar to the Hill geometrically similar model (Hill, 1950) share similar results with both terrestrial and a quatic amphibians (Deban and OReilly, 2005). Scaling of the kinematics indicated dissimilarities from both of the standard scaling models. None of the durations were significantly different from the bass model

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(Richard and Wainwright, 1995), while th e durations of mouth opening and hyoid depression were both significantly less than th e Hill (1950) model. Both maximum gape distance and maximum hyoid depression were different from the bass model, while only hyoid depression was different from the geom etrically similar model. All of the velocities decreased with increasing size, different from both models. The varying scaling coefficients for these kinematic variables prevent me from attributing the patterns to either the Richard and Wainwright (1995) or Hill (1950) models, but instead conclude that the allometric growth of the feeding morphology drives variation. Fluid velocity increased as body length increased, but SVL length was a poor predictor of the velocity. Given that bot h mouth opening and hyoi d depression velocities decreased with SVL length, it was difficult to determine why fluid velocity entering the mouth would increase. Modeling the system as a piston, using morphology and kinematics, resulted in more predictive power. Kinematic velocities were decreasing, but both head width and buccal volume exhibited negatively allometric relationships with body length. Using head width and hyoid depression velocity, I was able to predict fluid velocity entering the mouth for a tadpole. The scaling coefficient of hyoid depression velocity was closer to isometry than head width, and this accounted for the resulting increase in fluid velocity as body length increased. Reynolds number increased as body length increased, as a function of length and fluid velocity. Values of Reynolds numbe r spanned two flow regimes in feeding Xenopus laminar and intermediate. In Xenopus the tadpoles are limited by the amount of water they can filter. For smaller tadpoles the ingestion of water moves against the forces resisting the waters flow. Larger tadpoles are not subject to the same magnitude

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of viscous forces. This also indicates that the abiotic properties of water play an important role in the mechanics of suspension feeding. Hyperambient pressure ge nerated in the buccal cavity during water expulsion was calculated using a pipe model. Pressure d ecreased with size, the smallest tadpoles generating the highest pressures in the buccal cavity. The highest pressures were similar to those generated by large mammals (Mar shall et al., 2008; Werth, 2006), but by organisms several thousands times smaller. Smaller orga nisms generating even higher pressures may be beyond what the hyoid muscle are capable of producing, which indicates that the physical properties play an important role in the scaling of suspension feeding. Viscosity manipulations exhibited strong effects on the kinematics of feeding. Initial increases in the viscosity elicited compensatory behavior from the tadpoles, velocities, and maximum displacements increased. As viscosity further increased, the behavior of large tadpoles changed. Highe r viscosities for larger tadpoles resulted in lower Reynolds numbers, transitioning from in termediate to laminar flow regimes. Velocities and displacements decreased, and dur ations increased. If the tadpoles were still attempting to compensate, it was no longe r detectable. These results indicate that abiotic factors are crucial in the understanding of aquatic feeding, especially in smaller organisms, and the physical properties of water may present a lower size limit on suspension feeding. Future research may be able this possibility directly by raising Xenopus tadpoles in high viscosity water and ex amining changes in the growth of the dimensions of the hyoid and associated muscles.

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References Adriaens, D. and Verraes, W. (1997). Ontogeny of the maxillary barbell muscles in Clarias gariepinus (Siluroidei: Clariidae), with some notes on the palatine-maxillary mechanism. J. Zool. Lond. 241, 117-133. Alexander, R.M. (2005). Models and the scaling energy costs for locomotion. J. Exp. Biol. 208, 1645-1652. Altringham, J.D., Morris, T., James, R.S. and Smith, C.I. (1996). Scaling effects in the swimming of the African clawed toad, Xenopus laevis I. Muscle function. Exp. Biol. Onl. 1.6 Biewener, A.A. (1983). Allometry of quadrapedal locomotion: the scaling of duty factor, bone curvature and limb orientation to body size. J. Exp. Biol. 105, 147-171. Biewener, A.A. (2005). Biomechanical consequences of scaling. J. Exp. Biol. 208, 16651676. Brokaw, C.J. (1966). Effects of increased viscosity on the movements of some invertebrate spermatozoa. J. Exp. Biol. 45, 113-139. Cannatella, D.C. (1999). Architecture: Cranial and Axial Musculoskeleton. In Tadpoles eds. R. W. McDiarmid and R. Altig), pp. 52-91. Chicago: University of Chicago Press. Deban, S.M. (1997). Development and evolution of feeding behavior and functional morphology in salamanders of the family Plethodontidae. Ph.D. dissertation, University of California, Berkeley. Deban, S.M. and OReilly, J.C. (2005). The ontogeny of feeding kinematics in a giant salamander Cryptobranchus alleganiensis : does current function or phylogenetic relatedness predict the scaling patterns of movement? Zool. 108, 155-167. Deban, S.M. and Olson, W.M. (2002). Suction feeding by a tiny predatory tadpole. Nature 420(6911) 41-42. Denny, M.W. (1993). Air and Water: The Biology and Physics of Life's Media. Princeton: Princeton University Press.

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Deuchar, E.M. (1975). Xenopus: The South African Clawed Frog. London: John Wiley & Sons. Emerson, S.B. (1990). Scaling of the epicoracoid horn muscle in arciferal frogs. J. Herp. 24, 84-87. Feder, M.E., Seale, D.B., Boraas, M.E., Wassersug, R.J. and Gibbs, A.G. (1984). Functional conflicts between feeding and gas exchange in suspension-feeding tadpoles, Xenopus laevis J. Exp. Biol. 110, 91-98. Fuiman, L. and Webb, P.W. (1988). Ontogeny of routine swimming activity and performance in zebra danios (Teleostei:Cyprinidae). Anim. Beh. 36 250-261. Gradwell, N. (1968). The jaw and hyoidean mechanism of the bullfrog tadpole during aqueous ventilation. Can. J. Zool. 46, 1041-1052. Gradwell, N. (1971). Xenopus tadpole: On the water pumping mechanism. Herpetologica 27, 107-123. Gradwell, N. (1972). Gill irrigation in Rana catesbiana. Part I. On the anatomical basis. Can. J. Zool. 50, 481-499. Hanken, J. and Wassersug, R.J. (1981). The visible skeleton. A new double-stain technique reveals the native of the hard tissues. Func. Photo. 16, 22-26. Hernandez, L.P. (2000). Intraspecific scaling of feeding mechanics in an ontrogenetic series of zebrafish, Danio rerio. J. Exp. Biol. 203, 3033-3043. Herrel, A., Van Wassenbergh, S., Wouters, S., Adriaens, D. and Aerts, P. (2005). A functional morphological approach to the scaling of the feeding system in the African catfish, Clarias gariepinus J. Exp. Biol. 208, 2091-2102. Hill, A.V. (1950). The dimensions of animals and their muscular dynamics. Sci. Prog., Lond. 38, 209-230. Holzman, R., Collar, D.C., Day, S.W., Bishop, K.L., and Wainwright, P.C. (2008). Scaling of suction-induced flows in bluegill: morphological and kinematic predictors for the ontogeny of feeding performance. J. Exp. Biol. 211, 2658-2668. Hunt von Herbing, I. and Keating, K. (2003). Temperature-induced changes in viscosity and its effects on swimming speed in larval haddock. In The Big Fish Bang. Proceedings of the 26th Annual Larval Fish Conference. 2003 (ed. Browman, H.I. and Skiftesvik, A.B.) Jayne, B.C. and Riley, M.A. (2007). Scaling of the axial morphology and gap-bridging ability of the brown tree snake, Boiga irregularis J. Exp. Biol. 210, 1148-1160.

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Appendix

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Tadpole IDSVLHWVel XenoF01 4.6 3.10.625 XenoF02 4.7 3.42.777778 XenoF03 5.1 3.93.472222 XenoF04 5.5 3.61.282051 XenoF05 6.4 4.33.947368 XenoF06 7.5 4.7 15 XenoF07 8.6 4.98.66720085 XenoF08 9.5 5.311. 111111 XenoF09 12.1 6.18.18903319 XenoF10 11.3 5.99.375 XenoF11 10.8 5.57.11805556 XenoF12 8.3 4.6 10 XenoF13 14.4 6.714.4230769 XenoF14 13.6 6.414.84375 XenoF15 6.7 4.77.14285714 XenoF16 16.5 8.113.2352941 SVL vs. HW SUMMARY OUTPUT Regression Statistics Multiple R 0.98257574 R Square 0.96545509 Adjusted R Square0.9629876 Standard Error0.25768246 Observations 16 ANOVA df SSMS FSignificance F Regression 125.980396525.9803965391.26954511.2488E-11 Residual 140.929603530.06640025 19.62 51 latoT CoefficientsStandard Erro r t StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0% Intercept 1.835904130.175967710.43318835.51066E-081.458490952.21331731.4584909522.2133173 X Variable 10.35594460.0179946919.78053451.24877E-110.317349830.394539370.3173498280.39453937 (mm)(mm) (mm/s)Table A.1: Head Width

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Log Transformed loV LVS )Lu( loV)mc( LVS )mm( LVS 58815696.02358815217.2 186224243.111699232.1 22 17.1 1. 71 19479568.71832345143.2 699920103.1780756891.1 02 85.1 8. 51 42882307.31768479597.1 389911402.1765027631.1 61 73.1 7. 31 87409678.01335445524.1 253349311.173587280.1 31 12.1 1. 21 447729901.9696169391.1 642181970.1586293140.1 21 1. 1 11 739714702.8813776570.1 1 933330710.1 01 40.1 4.01 31175367.5848283557.0 506327779.0154894439.0 5. 9 68.0 6.8 6039 71942.4432409655.0 789980309.068223368.0 8 37.0 3.7 409231077.2840850363.0 52151877.0499724367.0 6 85.0 8.5 937329997.1388009532.0 199950206.0238757266.0 4 64.0 6. 4 Log SVL vs. Log Vol SUMMARY OUTPUT Regression Statistics Multiple R 0.99176444 R Square 0.98359671 Adjusted R Square0.9815463 Standard Error 0.03127856 Observations 10 ANOV A df SS MS FSignificance F Regression 10.469320570.469320574479.70705981.99274E-08 843879000.097628700.08 la udiseR 63741774.09 latoT CoefficientsStandard Erro r t Stat P-valueLower 95%Upper 95%Lower 95.0%Upper 95.0% Intercept -0.185178510.05636451-3.2853739410.011098401-0.315155311-0.055201704-0.315155311-0.055201704 X Variable 11.223475540.0558608121.902215861.99274E-081.0946602761.3522907971.0946602761.352290797 Seale Model Table A.2: Buccal Volume

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37 614.1 1.62 4.931.149219110.209515010.69284692 368.116.3 2.32 6.661.21218760.365487980.82347423 392.7 4.3 0.92 1.830.63346846-0.036212170.26245109 409.217.3 2.58 7.751.23804610.411619710.8893017 417.915.8 2.3 5.451.198657090.361727840.7363965 424.4 7.9 1.33 3.420.897627090.123851640.53402611 435.710.8 1.56 4.171.033423760.19312460.62013605 449.216.8 2.7 7.511.225309280.431363760.87563994 457.714.6 2.09 7.011.164352860.320146290.84571802 465.9 9.3 1.65 4.550.968482950.217483940.6580114 477.112.4 2.07 5.621.093421690.315970350.74973632 504.5 8.7 1.24 3.160.939519250.093421690.49968708 493.7 7 0.75 3.180.84509804-0.124938740.50242712 512.7 4.1 0.81 2.130.61278386-0.091514980.3283796 ID HW (mm)SVL (mm) CH Width (mm) FB Length (mm)Log SVLLog CWLog FBTable A.3: Filter Morphology

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CW Regression Statistics Multiple R0.92389509 R Square0.85358213 Adjusted R Squar e 0.84138064 Standard Error0.07357821 Observations 14 ANOVA df SS MS FSignificance F Regression 10.37873110.37873110269.957210522.3772E-06 Residual 120.064965040.005413754 41696344.031 latoT CoefficientsStandard Erro r t Stat P-valueLower 95%Upper 95% Intercept -0.62718510.10075885-6.224615314.41972E-05-0.84671978-0.40765042 X Variable 10.814239120.097349958.3640427142.3772E-060.60213181.02634643 FB Regression Statistics Multiple R0.96560763 R Square0.93239809 Adjusted R Squar e 0.9267646 Standard Error0.05348324 Observations 14 ANOVA df SS MS FSignificance F Regression 10.473433580.473433577165.50977392.2184E-08 Residual 120.034325480.002860457 60957705.031 latoT CoefficientsStandard Erro r t Stat P-valueLower 95%Upper 95% Intercept -0.27996590.07324056-3.8225519610.002428198-0.43954334-0.12038838 X Variable 10.910365950.0707626712.86506022.2184E-080.756187351.06454455 Table A.3: Filter Morphology (continued)

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ssaM HI LVS 18.7 0.0019700000 9000.0 6.21 14.8 0.0014400000 16.9 0.0016900000 9.3 0.0006600000 5.5 0.0000500000 5.2 0.0001200000 4.1 0.0000300000 9.5 0.0004900000 7.3 0.0003300000 11.1 0.0008000000 16.4 0.0024700000 10 0.0009600000 8.9 0.0005400000 Log(SVL)Log(IHM)Log(SVL)^2Log(IHM)^2 1.271841607-2.705533771.6175810727.319913 1.100370545-3.161150911.2108153379.99287507 1.170261715-2.841637511.3695124838.07490373 1.227886705-2.77211331.5077057597.68461212 0.968482949-3.180456060.93795922210.1153008 0.740362689-4.301030.54813691218.498859 0.716003344-3.920818750.51266078815.3728197 0.612783857-4.522878750.37550405520.4564321 0.977723605-3.309803920.95594344810.954802 0.86332286-3.481486060.74532636112.1207452 1.045322979-3.096910011.092700139.59085163 1.214843848-2.607303051.4758455756.79802918 1-3.01772877 19.10668691 0.949390007-3.267606240.90134138510.6772505 IH Mass Regression Statistics Multiple R 0.9555199 R Square0.91301829 Adjusted R Squar e 0.90576981 Standard Error0.17845398 Observations 14 ANOVA df SS MS FSignificance F Regression 14.0113011954.01130119125.9600361.0156E-07 Residual 120.3821498950.03184582 980154393.431 latoT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept-6.016162460.246752708-24.38134321.3657E-11-6.55379043-5.4785345 X Variable 12.744853480.24456977211.22319191.0156E-072.211981723.27772524 Table A.4: IH Mass(mm) (g)

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SVL OH Mass Average 12.60.000415 1.7223E-07 4.13.5E-05 1.225E-09 5.29.5E-05 9.025E-09 16.40.00056 3.136E-07 9.50.000165 2.7225E-08 11.10.000175 3.0625E-08 9.30.000215 4.6225E-08 18.70.00037 1.369E-07 16.90.00046 2.116E-07 7.30.000125 1.5625E-08 8.90.000325 1.0563E-07 100.000265 7.0225E-08 14.80.00062 3.844E-07 5.59.5E-05 Log (SVL)Log (OHMA)Log(SVL)^2Log(OHMA)^2 1.100370545-3.3819519031.2108153411.4375987 0.612783857-4.4559319560.3755040619.8553296 0.716003344-4.0222763950.5126607916.1787074 1.214843848-3.2518119731.4758455810.5742811 0.977723605-3.7825160560.9559434514.3074277 1.045322979-3.7569619511.0927001314.1147631 0.968482949-3.667561540.9379592213.4510077 1.271841607-3.4317982761.6175810711.7772394 1.227886705-3.3372421681.5077057611.1371853 0.86332286-3.9030899870.7453263615.2341114 0.949390007-3.4881166390.9013413812.1669577 1-3.576754126 112.7931701 1.170261715-3.2076083111.3695124810.2887511 0.740362689-4.0222763950.5481369116.1787074 OH Mass Regression Statistics Multiple R 0.92149784 R Square 0.849158268 Adjusted R Square0.836588124 Standard Error0.142732743 41 snoitavresbO ANOVA df SS MS FSignificance F 60-E3848.25185355.7635442673.135442673.11 noissergeR 46273020.036174442.021 la udiseR 61617026.131 latoT CoefficientsStandard Erro r t StatP-valueLower 95%Upper 95% Intercept -5.2548110610.19736007-26.62550264.8329E-12-5.68482171-4.82480041 X Variable 1 1.6077715260.195614098.219098582.8483E-061.181565032.03397802 Average Squared Table A.5: OH Mass(mm) (g)

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16.3 8.12.41611.21218760.383114905 17.3 9.22.38771.23804610.377979759 14.6 7.71.91291.164352860.281692267 7 3.70.94950.84509804-0.022505031 9.3 5.91.25730.968482950.099438916 4.1 2.70.56780.61278386-0.245804612 10.8 5.71.24811.033423760.096249383 12.4 7.11.52151.093421690.182271957 15.8 7.92.34751.198657090.370605601 8.7 4.51.42820.939519250.154789029 Table A.6: OH LengthSVL (mm)HW (mm)OH L (mm) Log SVL Log OH Length

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Table A.6: OH Length (continued) Regression Statistics Multiple R 0.976542829 R Square 0.953635897 Adjusted R Square0.947840385 Standard Error0.0458096 Observations 10 ANOVA df SS MS FSignificance F 60-E76782.16482745.461376503543.0376503543.01 noissergeR 915890200.0551887610.08 laudiseR 828390263.09 la toT CoefficientsStandard Errort Stat P-valueLower 95%Upper 95% Intercept -0.8599528570.081418225-10.562166565.63445E-06-1.047703621-0.67220209 X Variable 10.9972237030.07774048312.827598551.28767E-060.8179538281.17649358

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Tadpole IDMuscleSVL CSA XenoDis01 IH 18.70.222 XenoDis02 IH 12.60.095 XenoDis03 IH 14.80.139 XenoDis04 IH 16.90.167 XenoDis05 IH 9.3 0.096 XenoDis06 IH 5.5 0.073 XenoDis07 IH 5.2 0.068 XenoDis08 IH 4.1 0.061 XenoDis09 IH 9.5 0.09 XenoDis10 IH 7.3 0.096 XenoDis11 IH 11.10.122 XenoDis12 IH 16.40.226 XenoDis13 IH 10 0.106 XenoDis14 IH 8.9 0.088 XenoDis15 IH 12.20.104 IH CSA SUMMARY OUTPUT Regression Statistics Multiple R 0.904285575 R Square 0.817732402 Adjusted R Square0.803711817 Standard Error 0.075363409 51 snoitavresbO ANOVA df SS MS FSignificance F 60-E10407.357207323.8538752133.038752133.01 noissergeR 346976500.0363538370.031 laudiseR 391390504.041 latoT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -1.7450905570.103914961-16.793448623.4016E-10-1.969585181-1.520595933 X Variable 1 0.7824313770.1024527727.6369956623.70401E-060.561095621.003767135 Table A.7: IH C.S.A.(mm) (mm2)

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Tadpole IDMuscleSVL CSA XenoDis01 OH 18.70.137 XenoDis02 OH 12.60.075 XenoDis03 OH 14.80.092 XenoDis04 OH 16.90.102 XenoDis05 OH 9.3 0.077 XenoDis06 OH 5.5 0.066 XenoDis07 OH 5.2 0.069 XenoDis08 OH 4.1 0.063 XenoDis09 OH 9.5 0.073 XenoDis10 OH 7.3 0.077 XenoDis11 OH 11.10.084 XenoDis12 OH 16.40.138 XenoDis13 OH 10 0.082 XenoDis14 OH 8.9 0.071 XenoDis15 OH 12.20.083 OH CSA SUMMARY OUTPUT Regression Statistics Multiple R 0.831507631 R Square 0.69140494 Adjusted R Square0.667666858 Standard Error 0.059378808 51 snoitavresbO ANOVA df SS MS FSignificance F 987121000.044304621.9221596201.021596201.01 noissergeR 348525300.0759538540.031 la udiseR 770135841.041 la toT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -1.5122839630.081874568-18.470741351.03375E-10-1.689163213-1.335404714 X Variable 1 0.4356503690.080722515.3968883110.0001217890.261259990.610040748 Table A.8: OH C.S.A.(mm) (mm2)

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Tadpole ID SVLIH/OH Ratio XenoDis01 18.71.620437956 XenoDis02 12.61.266666667 XenoDis03 14.81.510869565 XenoDis04 16.91.637254902 XenoDis05 9.31.246753247 XenoDis06 5.51.106060606 XenoDis07 5.20.985507246 XenoDis08 4.10.968253968 XenoDis09 9.51.232876712 XenoDis10 7.31.246753247 XenoDis11 11.11.452380952 XenoDis12 16.41.637681159 XenoDis13 101.292682927 XenoDis14 8.91.23943662 XenoDis15 12.21.253012048 IH/OH Ratio SUMMARY OUTPUT Regression Statistics Multiple R 0.940426173 R Square 0.884401388 Adjusted R Square0.875509187 Standard Error 0.025578322 51 snoitavresbO ANOVA df SS MS FSignificance F 70-E58658.144790854.99515070560.0515070560.01 noissergeR 152456000.0752505800.031 la udiseR 377575370.041 la toT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -0.2328065930.035268712-6.6009384031.71289E-05-0.309000012-0.156613174 X Variable 1 0.3467810080.0347724459.9728680651.85685E-070.2716597080.421902309 Table A.9: IH/OH Ratio(mm)

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SVL HW CH total lengthMedial CH lengthIn-LeverLever Arm RatioLog SVLLog LAR 14.1 6 2.129 1.99150.13750.0690434351.14921911-1.16087761 16.3 8.1 2.6722 2.45390.21830.088960431.2121876-1.05080312 4.3 2.7 1.163 0.9513 0.21170.222537580.63346846-0.65259664 17.3 9.2 3.3934 2.82660.56680.2005235971.2380461-0.69783451 15.8 7.9 3.1273 2.5510.57630.2259114071.19865709-0.64606184 7.9 4.4 1.8369 1.62770.20920.1285249120.89762709-0.89101268 10.8 5.7 2.0728 1.68810.38470.2278893431.03342376-0.64227598 16.8 9.2 3.4056 2.83310.57250.2020754651.22530928-0.69448641 14.6 7.7 2.821 2.30480.51620.2239673721.16435286-0.64981525 9.3 5.9 2.2096 1.82540.38420.2104744170.96848295-0.67680069 12.4 7.1 2.639 2.34610.29290.1248454881.09342169-0.90362715 7 3.7 1.4616 1.13890.32270.2833435770.84509804-0.54768663 8.7 4.5 1.8216 1.59920.22240.1390695350.93951925-0.856768 4.1 2.7 1.1334 1.07550.05790.0538354250.61278386-1.26893185 16.3 8.1 2.4539 1.29590.528098131.212187604-0.27728537 17.3 9.2 2.8266 1.05840.3744427931.238046103-0.42661452 14.6 7.7 2.3048 0.89870.3899253731.164352856-0.4090185 7 3.7 1.1389 0.53210.4672051980.84509804-0.33049233 9.3 5.9 1.8254 0.52050.2851429820.968482949-0.54493731 4.1 2.7 1.0755 0.25710.2390516040.612783857-0.62150834 10.8 5.7 1.6881 0.32630.1932942361.033423755-0.7137811 12.4 7.1 2.3461 0.52520.2238608751.093421685-0.6500218 15.8 7.9 2.551 0.80440.3153273231.198657087-0.5012384 8.7 4.5 1.5992 0.41790.2613181590.939519253-0.58283041 Table A.10: OH L.A.R.SVL (mm)(mm)HW (mm)(mm)CH med (mm) CH thick (mm)Lever Arm Ratio Log SVLLog LARTable A.11: IH L.A.R.

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Table A.10: OH LAR (continued) Regression Statistics Multiple R 0.152576344 R Square 0.023279541 Adjusted R Square-0.058113831 Standard Error0.225933817 Observations 14 ANOVA df SS MS FSignificance F 189555206.0437210682.0238995410.0238995410.01 noissergeR 90640150.0570355216.021 laudiseR 709251726.031 la toT CoefficientsStandard Errort Stat P-valueLower 95%Upper 95% Intercept -0.9722537150.309396368-3.142421230.008493635-1.64637049-0.29813694 X Variable 1 0.159867580.2989287710.5348015840.602555981-0.491442260.81117742

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Table A.11: IH LAR (continued) Regression Statistics Multiple R 0.345664619 R Square 0.119484029 Adjusted R Square0.009419532 Standard Error0.142123085 Observations 10 ANOVA df SS MS FSignificance F 227219723.0339185580.1836729120.0836729120.01 noissergeR 179891020.0177195161.08 laudiseR 904915381.09 la toT CoefficientsStandard Errort Stat P-valueLower 95%Upper 95% Intercept -0.7647584430.252597915-3.0275722660.016369761-1.347250279-0.18226661 X Variable 10.2512966310.2411878151.0419126320.327912722-0.3048834670.80747673

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Muscle SVLCSA (mm2)CSA (cm2)Force (N)Log SVLLog Force IH 18.70.222 0.002220.048841.271841607-1.311224345 IH 12.60.095 0.000950.02091.100370545-1.679853714 IH 14.80.139 0.001390.030581.170261715-1.514562519 IH 16.90.167 0.001670.036741.227886705-1.434860848 IH 9.3 0.096 0.000960.021120.968482949-1.675306086 IH 5.5 0.073 0.000730.016060.740362689-1.794254459 IH 5.2 0.068 0.000680.014960.716003344-1.825068406 IH 4.1 0.061 0.000610.013420.612783857-1.872247484 IH 9.5 0.09 0.00090.01980.977723605-1.70333481 IH 7.3 0.096 0.000960.021120.86332286-1.675306086 IH 11.10.122 0.001220.026841.045322979-1.571217489 IH 16.40.226 0.002260.049721.214843848-1.30346888 IH 10 0.106 0.001060.02332 1-1.632271454 IH 8.9 0.088 0.000880.019360.949390007-1.713094647 IH 12.20.104 0.001040.022881.086359831-1.64054398 OH 18.70.137 0.001370.030141.271841607-1.520856752 OH 12.60.075 0.000750.01651.100370545-1.782516056 OH 14.80.092 0.000920.020241.170261715-1.693789492 OH 16.90.102 0.001020.022441.227886705-1.648977147 OH 9.3 0.077 0.000770.016940.968482949-1.771086594 OH 5.5 0.066 0.000660.014520.740362689-1.838033384 OH 5.2 0.069 0.000690.015180.716003344-1.818728228 OH 4.1 0.063 0.000630.013860.612783857-1.85823677 OH 9.5 0.073 0.000730.016060.977723605-1.794254459 OH 7.3 0.077 0.000770.016940.86332286-1.771086594 OH 11.10.084 0.000840.018481.045322979-1.733298033 OH 16.40.138 0.001380.030361.214843848-1.517698233 OH 10 0.082 0.000820.01804 1-1.743763467 OH 8.9 0.071 0.000710.015620.949390007-1.80631897 OH 12.20.083 0.000830.018261.086359831-1.738499227 Specific Tension of Amphibian Muscle: 22 N/cm2 Table A.12: Force(mm)

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Regression Statistics Multiple R 0.904285575 R Square 0.817732402 Adjusted R Square0.803711817 Standard Error0.075363409 Observations 15 ANOVA df SS MS FSignificance F 60-E10407.357207323.8538752133.038752133.01 noissergeR 346976500.0363538370.031 laudiseR 391390504.041 latoT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -2.4026678760.103914961-23.121481786.04985E-12-2.6271625-2.178173252 X Variable 1 0.7824313770.1024527727.6369956623.70401E-060.561095621.003767135 Table A.12: IH Force (continued)

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Regression Statistics Multiple R 0.831507631 R Square 0.69140494 Adjusted R Square0.667666858 Standard Error0.059378808 Observations 15 ANOVA df SS MS FSignificance F 987121000.044304621.9221596201.021596201.01 noissergeR 348525300.0759538540.031 laudiseR 770135841.041 latoT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -2.1698612820.081874568-26.502262461.06232E-12-2.346740532-1.992982033 X Variable 1 0.4356503690.080722515.3968883110.0001217890.261259990.610040748 Table A.12: OH Force (continued)

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SVL ForceIn-LeverOut-LeverResolved ForceLog SVLLog RF 14.10.02230.013750.199150.0015396691.149219113-2.81257275 16.30.02450.021830.245390.0021795311.212187604-2.661637041 4.30.01250.021170.095130.002781720.633468456-2.555686626 17.30.02550.056680.282660.0051133521.238046103-2.291294333 15.8 0.0240.057630.25510.0054218741.198657087-2.265850597 7.90.01610.020920.162770.0020692510.897627091-2.684186807 10.8 0.0190.038470.168810.0043298981.033423755-2.363522383 16.8 0.0250.057250.283310.0050518871.225309282-2.296546404 14.60.02280.051620.230480.0051064561.164352856-2.291880398 9.30.01750.038420.182540.0036833020.968482949-2.433762637 12.40.02060.029290.234610.0025718171.093421685-2.589759927 70.01520.032270.113890.0043068220.84509804-2.36584304 8.70.01690.022240.159920.0023502750.939519253-2.628881294 4.10.01230.005790.107550.0006621760.612783857-3.17902674 SVL ForceIn-LeverOut-LeverResolved ForceLog SVLLog RF 16.30.038590.129590.245390.0203793071.212187604-1.690810592 17.30.040890.105840.282660.0153109661.238046103-1.814997413 14.60.034680.089870.230480.0135226121.164352856-1.868939415 70.01720.053210.113890.0080359290.84509804-2.094963887 9.30.022490.052050.182540.0064128660.968482949-2.192947857 4.10.010530.025710.107550.0025172130.612783857-2.599079967 10.80.025940.032630.168810.0050140521.033423755-2.299811124 12.40.029620.052520.234610.0066307591.093421685-2.178436748 15.80.037440.080440.25510.0118058551.198657087-1.927902557 8.70.021110.041790.159920.0055164260.939519253-2.258342177 Table A.13: OH Resolved Force(mm) (mm) (N) (N) (mm) (mm) (mm) (mm)Table A.14: IH Resolved Force

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Regression Statistics Multiple R 0.549839131 R Square 0.30232307 Adjusted R Square0.244183326 Standard Error 0.223356706 41 snoitavresbO ANOVA df SS MS FSignificance F 678256140.0390839991.5546514952.0546514952.01 noissergeR 812888940.0516856895.021 laudiseR 62470858.031 la toT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -3.2141004270.305867242-10.508155122.09094E-07-3.880527898-2.547672957 X Variable 1 0.6738830910.2955190442.2803372760.0416528760.0300024081.317763775 Table A.13: OH Resolved Force (continued)

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Regression Statistics Multiple R 0.868025838 R Square 0.753468856 Adjusted R Square0.722652463 Standard Error 0.142616321 01 snoitavresbO ANOVA df SS MS FSignificance F 643821100.061162054.42800403794.0800403794.01 noissergeR 514933020.023517261.08 laudiseR 823910066.09 latoT CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept -3.3259856290.253474552-13.121576131.08217E-06-3.910498993-2.741472265 X Variable 1 1.1967452590.2420248534.9447205340.0011283460.6386349481.75485557 Table A.14: IH Resolved Force (continued)

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XenoF01 4.6 3.1960 1000 0.20.320.625 87777777.2612.0 6.0 321 69 4. 3 7.4 20FoneX 22222274.3441.0 5.0 101 38 9. 3 1.5 30FoneX 82150282.1213.0 4.0 04 1 6. 3 5.5 40FoneX 24863749 .3251.0 6. 0 23 31 3.4 4. 6 50FoneX 51 40.0 6.0 21 7 7.4 5.7 60FoneX 329 67037.6401.0 7.0 82 51 9.4 6. 8 70FoneX 5739.01460.0 7.0 52 71 9.4 6. 8 70FoneX 33333333.8690.0 8.0 24 03 9.4 6. 8 70FoneX .11270.0 8.0 71 8 3.5 5.9 80FoneX 1111111 41758241.7650.0 4.0 12 41 1.6 1.21 90FoneX 5.21 650.0 7. 0 5 1 8 1.6 1.21 90FoneX 24242429.4462.0 3.1 46 13 1 .6 1.21 90FoneX 573.9 690.0 9. 0 62 41 9.5 3. 11 01FoneX 44444449.6270.0 5.0 43 52 5.5 8.01 11FoneX 76666192.7690.0 7.0 51 3 5.5 8.01 11FoneX 5.7 80.0 6.0 72 71 6.4 3. 8 21Fo neX 5.21 880.0 1.1 02 9 6.4 3.8 21FoneX 9670324.41401 0 5.1 22 9 7.6 4.41 31FoneX 57348.41821.0 9.1 15 53 4.6 6.31 41FoneX 41758241.7861.0 2.1 84 72 7.4 7. 6 51FoneX 1492532.31631.0 8.1 12 4 1. 8 5.61 61FoneX Averages XenoF01 4.6 3.1 0.625 0.662757832 -0.20411998 XenoF02 4.7 3.42.777778 0.6720978580.44369753 XenoF03 5.1 3.93.472222 0.7075701760.54060748 XenoF04 5.5 3.61.282051 0.7403626890.1079053 XenoF05 6.4 4.33.947368 0.8061799740.59630762 XenoF06 7.5 4.7 15 0.8750612631.17609126 XenoF07 8.6 4.98.66720085 0.9344984510.93787886 XenoF08 9.5 5.311. 111111 0.9777236051.04575749 XenoF09 12.1 6.1 8.18903319 1.08278537 0.91323263 XenoF10 11.3 5.99.375 1.0530784430.97197128 XenoF11 10.8 5.57.11805556 1.0334237550.85236137 XenoF12 8.3 4.6 10 0.919078092 1 XenoF13 14.4 6.714.4230769 1.1583624921.15905792 XenoF14 13.6 6.414.84375 1.1335389081.17154363 XenoF15 6.7 4.77.14285714 0.8260748030.85387196 XenoF16 16.5 8.113.2352941 1.2174839441.1217336 Table A.15: Fluid Velocity(mm) ID SVLHW (mm)Frame Start Log SVL Dist. (mm)Time (sec) Vel (mm/s) ID SVLHW (mm) (mm) Vel (mm/s) Log Vel Frame End

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Table A.15: Fluid Velocity (continued)Regression Statistics Multiple R 0.79334175 R Square 0.62939113 Adjusted R Square0.60291907 Standard Error0.25213957 Observations 16 ANOVA df SS MS F Significance F Regression 11.511523381.51152338 23.775674520.00024503 63475360.090140098.041 laudiseR 74465104.251 la toT CoefficientsStandard Erro r t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0% Intercept -0.848554090.34250699-2.47747962 0.026598065-1.58315853-0.11394966-1.58315853-0.113949657 X Variable 11.774636870.363951134.87603061 0.0002450280.994039322.555234410.994039322.555234412

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SVL (m) HW (m)Velocity (m/s) Reynolds Numb e Log SVLLog Re 0.00460.00310.000625 1.918316832-2.337242170.28292034 0.00470.00340.00277778 9.350935842-2.327902140.97085508 0.00510.00390.00347222 13.4075899-2.292429821.12735072 0.00550.00360.00128205 4.569686733-2.259637310.65988643 0.00640.00430.00394737 16.80562614-2.193820031.2254547Re = u*r/ 0.00750.00470.015 69.8019802-2.124938741.84386774 0.00860.00490.0086672 42.04879623-2.065501551.62375357 0.00950.00530.01 111111 58.30583-2.022276391.76571198Re = Reynolds Number 0.01210.00610.00818903 49.45851728-1.917214631.69424109 0.01130.00590.009375 54.76485149-1.946921561.73850191u = velocity 0.01080.00550.00711806 38.76168867-1.966576241.58840269r = characteristic length 0.00830.00460.01 45.54455446-2.080921911.65843646 = viscosity 0.01440.00670.01442308 95.67783701-1.841637511.98081135 0.01360.00640.01484375 94.05940594-1.866461091.97340223 0.00670.00470.00714286 33.23903819-2.17392521.52164845 0.01650.00810.01323529 106.144438-1.782516062.02589724 Log Re vs. Log SVL SUMMARY OUTPUT Regression Statistics Multiple R 0.86011789 R Square 0.73980278 Adjusted R Square0.72121727 Standard Error0.26361103 Observations 16 ANOVA df SSMS FSignificance F Regression 12.766103972.7661039739.805341181.9256E-05 Residual 140.972870840.06949077 8479837.351 latoT CoefficientsStandard Erro r t StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0% Intercept 6.461494130.792301238.155350371.09398E-064.762177018.160811264.7621770068.16081126 X Variable 12.400691280.380509626.309147421.92558E-051.584579323.216803251.5845793193.21680325 Table A.16: Reynolds Number

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SVL HWHDV (mm/s)Fluid Vel (mm/ s HW^2HDV*HW^2 Log Fluid VelLog HDV*HW^2 4.6 3.17.377081140.6259.6170.8937498 -0.204119981.850607948 4.7 3.47.272562352.77777811.5684.0708207 0.443697531.924645287 5.1 3.96.88892683.47222215.21104.780577 0.540607482.020280784 5.5 3.66.552299451.28205112.9684.9178009 0.10790531.928998739 6.4 4.35.92548593.94736818.49109.562234 0.596307622.03966088 7.5 4.75.33360972 1522.09117.819439 1.176091262.071216949 8.6 4.94.870624628.66720085524.01116.943697 0.937878862.06797682 9.5 5.34.5593692911.11111128.09128.072683 1.045757492.107456509 12.1 6.13.883258388.18903318937.21144.496044 0.913232632.159855959 11.3 5.94.063561489.37534.81141.452575 0.971971282.150610858 10.8 5.54.187431547.11805555630.25126.669804 0.852361372.102673099 137133320.21 952915.50161.1201 54237689.46.4 3.8 14.4 6.73.45979914.4230769244.89155.310377 1.159057922.191200474 13.6 6.43.5935303414.8437540.96147.191003 1.171543632.167881264 6.7 4.75.748092537.14285714322.09126.975364 0.853871962.103719466 16.5 8.13.1609948313.2352941265.61207.39287 1.12173362.316793823 Log Fluid Vel vs. Log HDV*HW^2 Regression Statistics Multiple R0.83723282 R Square 0.7009588 Adjusted R Squar e 0.67959871 Standard Error0.22648979 Observations 16 ANOVA df SS MS FSignificance F Regression 11.683397741.68339774532.81629135.2171E-05 Residual 140.718166720.051297623 74465104.251 latoT CoefficientsStandard Erro r t StatP-valueLower 95%Upper 95% Intercept-5.272032091.06024956-4.972444480.00020472-7.54604123-2.99802295 X Variable 12.920536690.509821235.7285505435.2171E-051.82707894.01399447 Table A.17: Piston Model(mm) (mm)

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Areas (mm2) SVL (mm)HW (mm)Pipe Length (m m Upper A Mid ALower AUpper BMid B Lower BUpper CMid C Lower C 16.38.1 1.264 8.78675.22741.66815.23963.298751.35795.2262.919050.6121 14.1 6 0.963 4.74882.963951.17913.68352.219550.75563.07361.84540.6172 4.32.7 0.373 0.61940.373150.12690.56360.335550.10750.36410.227950.0918 17.39.2 1.358 11.70816.68451.66097.07744.230851.38437.13274.32421.5157 15.87.9 1.283 8.73495.106351.47784.6523.01831.38463.69382.28090.868 10.85.7 0.964 4.1626 2.3541 0.54562.4862 1.5392 0.59221.5678 1.0049 0.442 16.89.2 1.462 12.8444 7.36015 1.87596.5327 3.93235 1.3324.2359 2.41195 0.588 14.67.7 1.185 9.457 5.57175 1.68655.1831 3.16025 1.13744.4593 2.78865 1.118 9.35.9 1.029 5.6806 3.3761 1.07163.3585 2.0618 0.76512.9888 1.7577 0.5266 12.47.1 1.254 7.5072 4.3732 1.23925.4231 3.431 1.43893.113 1.9254 0.7378 6.73.5 0.421 1.2774 0.7668 0.25621.039075388 0.628381004 0.217686620.70300767 0.439276005 0.17554434 7.94.4 0.568 2.2213 1.3223 0.42331.647244305 1.00148333 0.355722361.17019927 0.720742311 0.27128536 73.7 0.441 1.4611 0.87525 0.28941.162091226 0.703674453 0.245257680.79560687 0.495361128 0.19511538 8.74.5 0.58 2.3453 1.395 0.44471.723492696 1.048395394 0.373298091.23024625 0.756689642 0.28313303 4.12.7 0.34 0.6821 0.4135 0.14490.616193325 0.370461294 0.124729260.39445861 0.250806755 0.1071549 Perimeter (mm) Upper AMid ALower AUpper B Mid BLower BUpper CMid C Lower C 12.4497 9.53285 6.61611.6421 8.7951 5.948110.3257 7.33295 4.3402 9.1564 7.5844 6.0124 9.772 7.121 4.477.4073 5.96305 4.5188 3.4213 2.629 1.8367 3.6383 2.94475 2.25122.991 2.60655 2.2221 14.9291 10.86995 6.810813.8281 10.22535 6.622612.0768 9.25705 6.4373 12.5093 9.245 5.980710.5806 8.7418 6.9039.5051 7.21965 4.9342 8.50985.93953.3692 8.43016.34614.26216.47074.86373.2567 15.26 411.07875 6.8935 12.9298 9.657356.38498.88396.92324.9625 13.12559.48885.8521 12.04958.9775.90459.20627.151955.0977 10.11967.579555.0395 9.90817.204554.5017.86925.59763.326 11.36368.37145.3792 12.09238.939855.78748.25286.27674.3006 4.8264343.681963462.5374928215.1402600313.991184242.842108444.083589973.3268940372.5701981 6.3506534.800906543.2511602676.5168393385.009191523.501543715.1670105194.1139118643.06081321 5.1590523.926972712.694893445.4451431514.217483952.989824764.3237322423.5026545532.68157686 6.5241414.927699593.3312581016.6704785135.122255813.574033115.2878044554.2007906573.11377686 3.5355762.725678841.9157819923.92755273.08539932.24324593.1271471462.6177132392.10827933 Table A.18: Pressure Calculations

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Hydraulic Diameter (mm) SVL (mm)HW (mm)Pipe Length (m m Upper A Mid ALower AUpper BMid B Lower BUpper CMid C Lower C 16.38.1 1.2642.8231041712.193425891.008524791.8002250451.5002671940.913165552.024463231.5922923240.56412147 14.1 6 0.9632.0745271071.563182320.784445481.5077773231.2467630950.676152131.659768071.2378900060.54633974 4.32.7 0.3730.7241691750.567744390.276365220.6196300470.455794210.191009240.486927450.3498110530.16524909 17.39.2 1.3583.1369874942.459808920.975450752.0472516111.6550435930.836106672.362447011.8685002240.94182344 15.87.9 1.2832.7930899412.209345590.988379291.7586904331.3810885630.802317831.554449721.263717770.70366017 10.85.7 0.9641.9566147271.585385980.647750211.1796775840.9701706560.555782360.969168710.8264490.54288083 16.89.2 1.4623.3659329142.657393661.088503662.0209748021.6287490870.834468821.907225431.3935463370.47395466 14.67.7 1.1852.8820235422.348769081.152748591.7206025151.4081541720.770530951.937520371.5596585550.87725837 9.35.9 1.0292.2453851931.781688890.850560571.3558603571.1447210440.679937791.519239571.2560383020.63331329 12.47.1 1.2542.6425428562.089590750.921475311.7939019051.53514880.99450531.508821251.2270141950.68622983 6.73.5 0.4211.0586697940.83303380.403863210.8085780730.6297689780.306373420.688617290.5281514840.27319971 7.94.4 0.5681.399100261.10170860.520798691.0110694580.7997165410.40636060.905900430.7007853690.35452716 73.7 0.4411.1328437910.891526440.429553160.8536717540.6673879120.328123150.736037130.5656979540.29104575 8.74.5 0.581.4379210831.132374220.533972431.0335046830.8186981920.417789180.930629160.7205211630.36371653 4.12.7 0.340.7716989380.606821310.302539640.6275595750.4802766290.222408540.504560340.3832455760.20330304 Measurements in Meters SVL (m)HW (m)Pipe Length (m)Upper A Mid ALower AUpper BMid B Lower BUpper CMid C Lower C 0.016 30.0081 0.001264 0.0028231040.002193430.001008520.0018002250.0015002670.000913170.002024460.0015922920.00056412 0.01410.0060.0009630.0020745270.001563180.000784450.0015077770.0012467630.000676150.001659770.001237890.00054634 0.00430.00270.0003730.0007241690.000567740.000276370.000619630.0004557940.000191010.000486930.0003498110.00016525 0.01730.00920.0013580.0031369870.002459810.000975450.0020472520.0016550440.000836110.002362450.00186850.00094182 0.01580.00790.0012830.002793090.002209350.000988380.001758690.0013810890.000802320.001554450.0012637180.00070366 0.01080.00570.0009640.0019566150.001585390.000647750.0011796780.0009701710.000555780.000969170.0008264490.00054288 0.01680.00920.0014620.0033659330.002657390.00108850.0020209750.0016287490.000834470.001907230.0013935460.00047395 0.01460.00770.0011850.0028820240.002348770.001152750.0017206030.0014081540.000770530.001937520.0015596590.00087726 0.00930.00590.0010290.0022453850.001781690.000850560.001355860.0011447210.000679940.001519240.0012560380.00063331 0.01240.00710.0012540.0026425430.002089590.000921480.0017939020.0015351490.000994510.001508820.0012270140.00068623 0.00670.00350.0004210.001058670.000833030.000403860.0008085780.0006297690.000306370.000688620.0005281510.0002732 0.00790.00440.0005680.00139910.001101710.00052080.0010110690.0007997170.000406360.00090590.0007007850.00035453 0.0070.00370.0004410.0011328440.000891530.000429550.0008536720.0006673880.000328120.000736040.0005656980.00029105 0.00870.00450.000580.0014379210.001132370.000533970.0010335050.0008186980.000417790.000930630.0007205210.00036372 0.00410.00270.000340.0007716990.000606820.000302540.000627560.0004802770.000222410.000504560.0003832460.0002033 Table A.18: Pressure Calculations (continued)

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Vogel Diameter Resistance Calculations SVL (m) Upper AMid A Lower AUpper BMid BLower BUpper CMid CLower C 0.0163 818881.25522247173.90550278491.24952464.2210267248.9774804973.143096627.538091654.64513615394 0.0141 2139593.666636960.2781046542097667590.8216401063.28189596400.55221774.8116876389.1444791627.1 0.0043 55812331.19147733469.72631217524104126297355643672.611531154753273044400102507629820584200806 0.0173 577072.11791526425.98561724821.73181239.427448065.575114349560.31794043.384584675.7371023696.15 0.0158 867497.92382215917.09555324001.65518874.5514511824.31127415524.59042768.5520701783.2215355643.4 0.0108 2706681.9886279404.45422533479620483548.644778131.33415756902.14496358885034325.5456709955.5 0.0168 468713.02251206438.71642855766.23606494.298548936.707124076169.64546955.7515953030.21192289317 0.0146 706821.45691602280.47527616041.65563878.1212402207.591383373553460307.678241033.7882335994.6 0.0093 1665840.5444202128.81480905092.512529593.924660289.91198116261.57948621.117013172.8263222155.2 0.0124 1058256.2692706662.20971572170.84982923.779291313.14552753416.59956984.7322765681.7232702281.2 0.0067 13791816.7935976017.2765121798840529918.1110138336.2196634277177046314.72226535123109872828 0.0079 6100064.92415865832.1531772419122366902.257145954.43857202470.234706269.796914710.41479557157 0.007 11018943.2328726528.7253303088934170899.791475905.05156557028461833119.51772073082529152630 0.0087 5583020.96614516087.0329358516820919903.153126858.82783394840.631820195.288556919.31363820764 0.0041 39451977.49103185125.3167005674490207064262962955.157181367532158777736485624298190018945 Whole Pipe Resistances Pressure aP( erusserPetaR wolFecnatsiseR latoTediS enO)m( LVS C B A)m( LVS ) kPa 0.016353344546.390024686.33524803676.2 0.01633.17596E-0862973090.314.5716E-052878.878872.87887887 0.0141113430763213665054.6466889791 0.01411.5638E-081278935423.8285E-054896.379284.896379283 0.004328347633241199092472321882321504 0.00434.81859E-1041505958181.9565E-0581206.237381.20623734 0.017363828319.8124978865.377402415.25 0.01733.65879E-0854662920.424.9171E-052687.813252.687813246 0.015858407416.7147446223.3245100195.2 0.01582.79832E-0871471425.854.4006E-053145.185353.145185351 0.0108234320883481018582.1586707869 0.01088.051E-09248416358.68.0656E-0520036.31720.03631697 0.016844530917.9136231600.61212789303 0.01683.06213E-0865314025.954.7438E-053098.340993.098340991 0.014629925143.5156303440.894037336.06 0.01465.04486E-0839644310.343.9952E-051583.884241.583884243 0.009386773061.8235306145.3288183949.1 0.00931.92441E-08103927943.56.7171E-056980.956936.980956932 0.012475337089.367027653.42265424947.6 0.01243.19604E-0862577374.463.0524E-051910.0841.910083999 0.006770098582221170110253409572655 0.00672.19222E-09912317877 28309.249628.30924964 0.0079339690088936715326.81611178137 0.00794.63208E-09431771113.24.2461E-0518333.271418.33327144 0.00757277636116912170892768193058 0.0072.69842E-09741174812.72.8607E-0521203.112521.20311249 0.0087313684276857441602.61484197878 0.00875.02794E-09397776937.34.7779E-0519005.576319.00557634 0.0041181269384660713067729054459147 0.00418.26817E-1024189145261.8457E-0544646.956644.64695657 Table A.18: Pressure Calculations (continued)

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Areas (mm2) SVLHWPipe LengthUpper A Mid ALower AUpper B 4.72.887104440.000389610.802562530.484883870.167669440.705416189 53.042071790.0004140.9107283570.549262840.188036090.783741251 4.82.938925990.000397740.8378422740.505894530.174338890.731146414 5.43.24647850.000446521.0658258750.641391210.216853760.89340547 5.73.398240080.000470911.1903290630.715209280.239701910.979502327 5.13.093403720.000422130.9483360710.571620770.195063110.810601275 5.33.195603690.000438391.025884180.617684830.209472280.865435508 4.92.990580470.000405870.8738973180.527354140.18112790.757255543 5.23.144579870.000430260.9867211270.594428060.202208620.837833411 4.82.938925990.000397740.8378422740.505894530.174338890.731146414 6.63.846399860.000544081.606079720.960980880.314509811.25703874 6.83.944662360.000560341.7071019571.020555950.332395411.32254561 7.34.188394890.000600991.9734404841.177392630.379092741.492263618 7.84.429551380.000641642.2595169721.345523040.428600061.670341621 6.23.648470020.000511561.4134640550.847242850.280109571.130172522 7.14.09122260.000584731.8645398251.113303360.360075011.423363557 6.13.598682360.000503431.3672713820.819935260.271796661.099329448 7.94.477490740.000649772.319105891.380505360.438836281.706945767 6.63.846399860.000544081.606079720.960980880.314509811.25703874 7.24.139861040.000592861.9185956261.145122170.369527561.457645722 8.14.573088920.000666032.440660881.451826920.45964181.781132528 8.54.763199780.000698552.6932914091.599900070.502579481.933386349 9.25.092611180.000755463.1660082161.876462710.581944582.212090381 8.74.857732250.000714812.8243735881.676652950.52470852.011434895 9.55.232584510.000779853.3805558372.00178760.61759122.336236674 8.44.71580460.000690422.6289426611.562202820.491679721.894840783 9.35.139346460.000763593.2367260981.917784270.593718392.25316176 9.55.232584510.000779853.3805558372.001787 60.6175912 2.336236674 8.6 4.810508610.000706682.7584349171.638050080.513589131.972251424 9.85.371874260.000804243.6022908762.131194150.654210882.463164771 10.35.602569590.000844893.9878475372.355947170.717394022.680824068 11.56.149353790.000942454.9950049512.941683720.879896043.233782876 10.85.831534890.000885544.3934393022.59205170.783248172.906026769 11.36.05886240.000926194.8191074252.839515730.851754723.138666893 10.45.648497960.000853024.0673617352.402259690.730351782.725264622 10.65.740150260.000869284.2287957022.496247180.75658722.815047409 10.25.556572050.000836763.909134752.31008870.70454312.636685228 10.65.740150260.000869284.2287957022.496247180.75658722.815047409 11.36.05886240.000926194.8191074252.839515730.851754723.138666893 11.26.01352380.000918064.7323657732.789113790.837842083.091548748 12.76.687348390.001040016.118114133.592911181.057537213.828797986 13.46.997507290.001096926.8270094894.00307671.168064054.194816693 13.16.864897380.001072536.5183388573.824557481.120076454.036265256 12.66.642826590.001031886.0200804473.536138411.042161083.777638113 12.66.642826590.001031886.0200804473.536138411.042161083.777638113 13.87.173607860.001129447.2499200684.247484241.233485884.410120898 12.16.419385290.000991235.5420331343.259104830.966838583.52611397 13.46.997507290.001096926.8270094894.00307671.168064054.194816693 12.76.687348390.001040016.118114133.592911181.057537213.828797986 13.57.041607910.001105056.9315205684.06349471.184265624.248225878 14.17.305163740.001153837.575624364.435578091.283627134.574504443 15.37.827157330.001251398.9516237935.229022311.493344885.256611903 14.77.566986380.001202618.2489744584.824083911.386661044.910673869 15.27.783906960.001243268.8324787175.1603911.47531175.198282183 14.57.479899570.001186358.0212715264.692756621.351909774.797526091 14.97.653889740.0012188 78.479932878 4.95723704 1.421817855.024906996 14.27.348918920.001161967.6858169284.499188331.300545044.629849199 15.77.999724140.001283919.4363592525.508115281.566484555.492606768 14.27.348918920.001161967.6858169284.499188331.300545044.629849199 15.47.870363910.001259529.0715841545.298110341.511478865.31520974 Table A.19: Viscosity Pressure Calculations(mm)(mm) (mm)

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Mid B Lower BUpper CMid C Lower C 0.4248973070.14410880.45768360.2886329170.12183586 0.472702630.161225330.514180490.3233748620.13458185 0.4405945840.14971850.476173610.3000136230.12603118 0.5397358850.185378710.594278920.3724783620.15231163 0.5924369450.20448040.657902490.4113699450.16614661 0.4891107190.167121730.533695710.3353540660.13893635 0.5226285880.179198760.57374570.3599064360.14780163 0.4565301440.155424130.495006180.3115944950.13027999 0.5057531240.173112990.553551040.3475314660.14334307 0.4405945840.14971850.476173610.3000136230.12603118 0.7626966750.266771580.866825980.5384976450.21031662 0.8029566820.281615420.916897620.5688511870.22065904 0.9073782580.320294251.047818740.6480367080.24732706 1.0171046710.361191521.186888190.7318958740.27512978 0.6848022310.238170910.770645720.4800747960.19020058 0.864967360.304554910.994468750.6157987130.23652197 0.6658811420.231248750.747429850.4659477950.18529177 1.0396779010.369634751.215674170.7492240530.28082388 0.7626966750.266771580.866825980.5384976450.21031662 0.8860663210.31238011.020980520.6318240340.2419017 1.0854463650.386783321.274214260.784433650.29234386 1.1794514960.422123251.395153680.8570553940.31590495 1.3517673890.487281851.619103940.9911509180.35877554 1.2276772310.440311491.457545660.8944617820.3279428 1.428614450.516485371.719847211.0513271370.37777398 1.1556434160.413158411.364437580.8386255480.30995005 1.3771848640.496931591.652368491.011030070.36506714 1.428614450.516485371.719847211.0513271370.37777398 1.2034629870.431174341.426189850.8756675880.3219026 1.5072367310.546449261.823433331.1131150010.39714078 1.6421777320.598066952.002366011.2196541910.43022532 1.9855916340.730403892.463632561.4933101290.51363844 1.7819409330.651765312.189120111.3306116090.46430123 1.9264634270.707526042.383651661.4459532040.49935023 1.6697466640.608640772.039092551.2414933330.4369618 1.7254610990.630037482.113482761.2857006760.4505531 1.6148016750.587576361.965952311.1979917720.4235285 1.7254610990.630037482.113482761.2857006760.4505531 1.9264634270.707526042.383651661.4459532040.49935023 1.8971810 80.69620975 2.34412519 1.4225357240.49226342 2.3559534850.874483952.969368441.7919649950.60252251 2.5841478470.963867043.284707131.9775631560.65681374 2.4852667690.925082293.147737211.8970011080.63332934 2.3240792010.862034172.925538431.7661323890.59491184 2.3240792010.862034172.925538431.7661323890.59491184 2.7184981371.016688983.47157752.087348450.6886265 2.1674519940.800990082.710975851.639538930.55741036 2.5841478470.963867043.284707131.9775631560.65681374 2.3559534850.874483952.969368441.7919649950.60252251 2.6174673510.976953933.330970562.0047560440.66471354 2.8211297651.057133363.614903872.1714572490.71285766 3.247478361.225948424.215267242.5229520780.81291202 3.0311577851.14013883.90968732.3442029170.76226397 3.2109909341.211452984.16358972.4927453220.80438528 2.9604457451.112157693.810223952.285951990.74565624 3.1025689681.168431484.010350252.4031208820.77900966 2.85569441.070771953.663282442.1998295710.72100496 3.3951535571.28470244.424959872.6454340950.84735766 2.85569441.070771953.663282442.1998295710.72100496 3.2841386461.240521184.267243262.5533245090.82147272 Table A.19: Viscosity Pressure Calculations (continued)

PAGE 105

Perimeters (mm) SVLHWUpper AMid A Lower AUpper BMid B 4.72.887104443.8314066222.9463781622.060062654.210120193.298604881 53.042071794.0793475453.1308035182.180066794.444668193.474587796 4.82.938925993.9140306663.007877182.100134364.288503273.357460164 5.43.24647854.4102440733.3763827292.339129274.754716073.706634205 5.73.398240084.6586337343.5603414472.457766454.985379993.878860762 5.13.093403724.1620394683.1922318192.219930564.52245913.532869203 5.33.195603694.3274881373.3150209892.299460444.677479053.648888424 4.92.990580473.9966777953.0693521322.140135224.366684393.416119593 5.23.144579874.2447531373.2536374952.259727984.600061363.590968057 4.82.938925993.9140306663.007877182.100134364.288503273.357460164 6.63.846399865.404821484.1111624932.810612895.668705214.387197043 6.83.944662365.5708334154.2333683612.88844865.818935364.498605493 7.34.188394895.9861457694.5385919273.082201036.192159194.774875715 7.84.429551386.4018400144.84342273.274828486.562228565.048132585 6.23.648470025.073002043.8665397442.65433275.366530534.162735915 7.14.09122265.8199735344.4165511933.004839816.0432624.664742846 6.13.598682364.9900913223.8053384392.615130735.290614834.10626336 7.94.477490746.4850225064.9043440383.313226036.635884395.102442549 6.63.846399865.404821484.1111624932.810612895.668705214.387197043 7.24.139861045.9030519154.4775795213.043543246.117774614.719870462 8.14.573088926.6514296755.026143443.389897896.78285165.210734437 8.54.763199786.9844080285.2695741643.542763817.075452125.426049175 9.25.092611187.5676204115.6950660943.808829047.583462755.79901325 8.74.857732257.150976655.3912081933.618966047.221109095.533095249 9.55.232584517.8177535555.8772308433.922323597.799698495.957449322 8.44.71580466.9011433455.2087370633.504605757.002464965.372375421 9.35.139346467.6509861475.7557998993.8466957.655636985.851915831 9.55.232584517.8177535555.8772308433.922323597.799698495.957449322 8.6 4.810508617.0676858465.330397821 3.580883747.148333045.479621998 9.85.371874268.0679926526.0592875384.035514048.015090246.115086822 10.35.602569598.4852846546.3624843044.223516118.372278836.376117417 11.56.149353799.487870997.0890531114.671636429.221004246.994552225 10.85.831534898.9028484666.665404594.410744198.727326036.635127772 11.36.05886249.3206716596.9680614384.59723719.080343026.892226057 10.45.648497968.5687760876.4230900444.261022358.443455866.428077485 10.65.740150268.7357911466.5442687914.335943278.585556756.531758888 10.25.556572058.401804096.3018675094.185978938.301016186.324076578 10.65.740150268.7357911466.5442687914.335943278.585556756.531758888 11.36.05886249.3206716596.9680614384.59723719.080343026.892226057 11.26.01352389.2370868286.9075505584.559995599.009897066.840954531 12.76.6873483910.491863627.8141964215.1157945310.05881347.602728503 13.46.9975072911.078122078.2365941495.3732216510.54296357.953215034 13.16.8648973810.826816888.0556186095.2630391910.33586397.803374318 12.66.6428265910.408147237.7538187245.078922249.989383177.552410101 12.66.6428265910.408147237.7538187245.078922249.989383177.552410101 13.87.1736078611.413312768.4777767775.5198067610.8182078.152171584 12.16.419385299.9897003517.4517937114.894183419.641195397.299847083 13.46.9975072911.078122078.2365941495.3732216510.54296357.953215034 12.76.6873483910.491863627.8141964215.1157945310.05881347.602728503 13.57.0416079111.161907328.2969023315.4099023510.61186868.003042193 14.17.3051637411.66479158.6585773665.6295083811.02399068.300783169 15.37.8271573312.671409599.3810721686.066377511.84183458.890298255 14.77.5669863812.167962789.0199633045.8483217411.43394628.596503384 15.27.7839069612.587483129.3209061186.0300860911.77399278.841462348 14.57.4798995712.000207868.8995326835.775469811.29752878.498148442 14.97.6538897412.335748329.1403631465.9210895311.5701348.694644465 14. 27.34891892 1 1.748633778.7188280945.6660313411.09246428.350207518 15.77.9997241413.007188579.6216629856.2113431312.11265689.085135307 14.27.3489189211.748633778.7188280945.6660313411.09246428.350207518 15.47.8703639112.755343429.4412308326.1026487711.90962148.939083123 (mm)(mm)Table A.19: Viscosity Pressure Calculations (continued)

PAGE 106

Lower BUpper CMid CLower C 2.3845747633.35014082.786716922.218933035 2.5009953383.535170462.925706572.309303228 2.4235661583.411984842.833251542.249277898 2.6537627413.779635233.10829512.426859026 2.7666333743.96142053.243341812.513006167 2.5394422363.596519662.971636972.338995725 2.6158219473.718748693.062926862.397768395 2.4623714633.47366012.879579722.279399243 2.5777164133.657711263.017375582.368482331 2.4235661583.411984842.833251542.249277898 3.0974293634.499543853.639782962.762295518 3.16949054.617775723.726266182.816012582 3.3475579474.911395273.940147222.947911493 3.5228444355.202386474.15092233.076640451 2.9517779714.261650493.465111752.653094159 3.2766780124.794274433.854982212.895549077 2.9150320224.201866843.42107282.625407099 3.5575877435.26028654.192726353.102030562 3.0974293634.499543853.639782962.762295518 3.3121744924.852888193.897627822.921794802 3.6267733935.375799724.275997843.152471331 3.7639827135.605715674.441240673.252046993 4.000598416.004706224.726495483.422395273 3.8320288995.720138224.523236873.301209714 4.1007273356.17446844.847315373.493984218 3.7298220425.548372344.400088523.227311872 4.0340568676.061373164.76686093.446349041 4.1007273356.17446844.847315373.493984218 3.7980512275.662970584.482289643.276679067 4.2001327226.343528724.967323693.564775292 4.3642734246.623801415.165614813.681075745 4.7509791427.289369985.633388223.95232263 4.5265939336.902294395.36186163.795389123 4.6871973917.179100635.556178423.907839137 4.3968796826.679639275.205023883.704093227 4.4618773086.79110465.283600613.749893995 4.3315943966.567892395.1261243.657978827 4.4618773086.79110465.283600613.749893995 4.6871973917.179100635.556178423.907839137 4.6552094657.123870165.517464353.885492711 5.1285112477.945873256.090840394.21368893 5.3449315498.325039166.353398434.362097174 5.2525059138.162865736.241241034.298838978 5.0973733027.8914866.053083254.192253462 5.0973733027.8914866.053083254.192253462 5.4674306978.540532646.502112524.445665309 4.94082037.618689615.863324954.084156023 5.3449315498.325039166.353398434.362097174 5.1285112477.945873256.090840394.21368893 5.3756341318.378990696.390664724.383071249 5.5587701528.701614576.613044474.507778333 5.9197874279.341555997.051870714.751686546 5.740124907 9.022442086.8334134 4.630615866 5.889957651 9.288486047.015589964.731626732 5.6798655758.915693916.76017424.589871204 5.8001962769.12899996.906440264.671164289 5.5891171368.755208246.649909474.528378186 6.0386627359.553384327.196491984.831465159 5.5891171368.755208246.649909474.528378186 5.9495724689.394580467.088100894.771699891 Table A.19: Viscosity Pressure Calculations (continued)

PAGE 107

Hydraulic Diameter (mm) SVLHWUpper AMid A Lower AUpper BMid B 4.72.887104440.8378776870.6582778490.325561830.670210020.515244865 53.042071790.8930137450.7017531970.345009770.705331620.544182686 4.82.938925990.8562449760.6727595560.332052840.681959530.524914147 5.43.24647850.9666819860.7598560520.370828180.751595220.582453898 5.73.398240081.0220413370.8035288630.390113410.785899830.61093912 5.13.093403720.9114147790.7162647380.351476060.71695620.553782992 5.33.195603690.9482490980.7453163410.364385110.740087130.572918136 4.92.990580470.8746237380.6872514050.338535420.693666380.534559909 5.23.144579870.9298266310.7307858460.357934450.728541070.563361318 4.82.938925990.8562449760.6727595560.332052840.681959530.524914147 6.63.846399861.1886273950.9349967410.447603160.887002370.695384016 6.83.944662361.2257425990.9642968530.460309950.909132360.713960522 7.34.188394891.3186718541.0376721690.491976650.96396980.760127226 7.84.429551381.4117922141.1112166930.52350841.01815510.805925482 6.23.648470021.1144991030.8764868950.422116750.842385980.658030915 7.14.09122261.2814764981.0083011010.479326720.942116070.741706361 6.13.598682361.0959890660.8618789340.415729370.83115440.64864923 7.94.477490741.4304381441.1259449550.529799391.028918330.815043298 6.63.846399861.1886273950.9349967410.447603160.887002370.695384016 7.24.139861041.3000703051.0229832080.485654420.953056180.75092427 8.14.573088921.4677511451.1554202020.542366541.050373870.833238675 8.54.763199781.5424593741.2144435330.567443391.093010770.869473503 9.25.092611181.67344981.3179567560.611153271.166796990.932412002 8.74.857732251.5798533411.2439905030.579954051.114197210.887515704 9.55.232584511.7296814551.3624018870.629821771.19811640.959212154 8.44.71580461.5237722391.1996787730.561181211.082385010.860433849 9.35.139346461.6921876661.3327664660.617380261.177256320.941356577 9. 55.23258451 1.729681455 1.3624018870.629821771.19811640.959212154 8.64.810508611.56115311.2292141310.573700991.103614740.878500735 9.85.371874261.7859663641.4068942150.648453581.229263650.985913545 10.35.602569591.8798886311.4811492190.679428231.280809741.030205452 11.56.149353792.1058485961.6598457770.753394281.402789891.135507503 10.85.831534891.9739476951.5555254990.710309311.33192081.074246642 11.36.05886242.0681374051.6300176190.741101411.382620411.118050053 10.45.648497961.8986897051.4960149540.685611781.291065971.039033315 10.65.740150261.936308061.5257607930.69796781.311527021.056659395 10.25.556572051.8610930261.4662883330.673240941.270536121.021367566 10.65.740150261.936308061.5257607930.69796781.311527021.056659395 11.36.05886242.0681374051.6300176190.741101411.382620411.118050053 11.26.01352382.0492892881.6151101720.73494991.372512351.109307814 12.76.687348392.3325175981.8391711610.826880131.522564471.23953051 13.46.997507292.4650421591.9440446490.869544661.591513311.299674577 13.16.864897382.408219861.8990757470.85127731.562042731.273944664 12.66.642826592.3136031091.8242048420.820773411.512661211.23090731 12.66.642826592.3136031091.8242048420.820773411.512661211.23090731 13.87.173607862.5408644162.0040557110.893861641.630629151.3338768 12.16.419385292.2190988471.7494337360.790193991.462936421.187669807 13.46.997507292.4650421591.9440446490.869544661.591513311.299674577 12.76.687348392.3325175981.8391711610.826880131.522564471.23953051 13.57.041607912.4839914421.9590418410.875628091.601311151.308236187 14.17.305163742.597774462.049102480.91207051.659836121.359452335 15.37.827157332.825770482.2296054070.984669931.775607281.461133594 14.77.566986382.7117027252.1392920320.948416381.717927931.410414281 15.27.783906962.8067497322.2145447830.978633921.766021881.452696764 14.57.479899572.6737108632.1092148470.93631155 1.69861081.393454475 14.9 7.65388974 2.7497100822.1693829720.960510961.737199241.427347136 14.27.348918922.6167525792.0641252620.918134731.669547591.36796332 15.77.999724142.9018905052.2898807781.008789581.813840461.494816948 14.27.348918922.6167525792.0641252620.918134731.669547591.36796332 15.47.870363912.8447949562.2446693390.990703491.785181761.469563981 (mm)(mm)Table A.19: Viscosity Pressure Calculations (continued)

PAGE 108

Lower BUpper CMid CLower C 0.2417350110.546464910.414298150.219629634 0.2578578660.581788630.442115230.233112479 0.247104460.558236490.423560870.224127368 0.2794201720.628927270.479334620.251043224 0.2956378640.664309670.507340850.264458739 0.2632416360.593569080.451406510.237599999 0.2740228720.617138450.470016360.246565308 0.2524787770.570011080.43283330.228621625 0.268630.605352370.460706940.242084254 0.247104460.558236490.423560870.224127368 0.3445070670.77059010.591790940.304553397 0.3554078090.794233130.610639350.313434742 0.3827198850.853377650.657880710.33559632 0.4101135020.91257210.705285060.357701575 0.3227490890.723330760.554181030.286760389 0.3717849660.829713660.6389640.326738674 0.3173189780.711521690.544797290.282305579 0.4156015580.92441670.71478460.362116206 0.3445070670.77059010.591790940.304553397 0.3772507740.841544640.648419050.331168639 0.42658670.94811140.733801730.370939272 0.4485921240.995522260.771906280.388561354 0.487208961.078556640.838804070.419326825 0.4596118731.019238070.790992650.397360763 0.5037987881.114166980.867554150.432485043 0.443086460.983666920.762371520.384158777 0.4927363261.090425190.848382270.423714642 0.5037987881.114166980.867554150.432485043 0.4541006051.007379310.781446680.392962008 0.5204114191.149791170.896349880.445627843 0.5481480161.209194470.944440680.46749956 0.6149501961.351904251.060328220.519834521 0.5759432541.268633290.992648980.489331884 0.6037945321.3281061.04096960.511126703 0.5537024591.221079450.954073110.471869113 0.5648182941.244853610.97335190.480603557 0.5425959181.197310910.934812950.463128432 0.5648182941.244853610.97335190.480603557 0.6037945321.3281061.04096960.511126703 0.5982199111.316208821.031296720.506770655 0.6820567651.494797791.176826110.571966772 0.7213316261.578230241.245042750.602291706 0.7044883371.542466731.215784550.589302691 0.6764536351.482883411.167096050.567629649 0.6764536351.482883411.167096050.567629649 0.7438148121.625930211.284104790.619593648 0.6484672861.42332921.118504560.545924648 0.7213316261.578230241.245042750.602291706 0.6820567651.494797791.176826110.571966772 0.726949721.590153611.254802830.606618967 0.7606958571.6617163 81.31343877 0.632557862 0.828373273 1.804952941.431082440.68431452 0.7945045231.733316661.372200260.658455802 0.8227244061.793011121.421260560.680007388 0.7832281751.709445831.352599460.649827596 0.8057875451.757191491.391814480.667079651 0.7663263611.67364721.323223770.636876981 0.8509846981.852729761.470402020.701532668 0.7663263611.67364721.323223770.636876981 0.8340237451.816895721.440907540.688620607 Table A.19: Viscosity Pressure Calculations (continued)

PAGE 109

Measurements in Meters SVLHWUpper AMid A Lower AUpper BMid B 0.00470.00288710.0008378780.0006582780.000325560.000670210.000515245 0.0050.003042070.0008930140.0007017530.000345010.000705330.000544183 0.00480.002938930.0008562450.000672760.000332050.000681960.000524914 0.00540.003246480.0009666820.0007598560.000370830.00075160.000582454 0.00570.003398240.0010220410.0008035290.000390110.00078590.000610939 0.00510.00309340.0009114150.0007162650.000351480.000716960.000553783 0.00530.00319560.0009482490.0007453160.000364390.000740090.000572918 0.00490.002990580.0008746240.0006872510.000338540.000693670.00053456 0.00520.003144580.0009298270.0007307860.000357930.000728540.000563361 0.00480.002938930.0008562450.000672760.000332050.000681960.000524914 0.00660.00384640.0011886270.0009349970.00044760.0008870.000695384 0.00680.003944660.0012257430.0009642970.000460310.000909130.000713961 0.00730.004188390.0013186720.0010376720.000491980.000963970.000760127 0.00780.004429550.0014117920.0011112170.000523510.001018160.000805925 0.00620.003648470.0011144990.0008764870.000422120.000842390.000658031 0.00710.004091220.0012814760.0010083010.000479330.000942120.000741706 0.00610.003598680.0010959890.0008618790.000415730.000831150.000648649 0.00790.004477490.0014304380.0011259450.00052980.001028920.000815043 0.00660.00384640.0011886270.0009349970.00044760.0008870.000695384 0.00720.004139860.001300070.0010229830.000485650.000953060.000750924 0.00810.004573090.0014677510.001155420.000542370.001050370.000833239 0.00850.00476320.0015424590.0012144440.000567440.001093010.000869474 0.00920.005092610.001673450.0013179570.000611150.00116680.000932412 0.00870.004857730.0015798530.0012439910.000579950.00111420.000887516 0.00950.005232580.0017296810.0013624020.000629820.001198120.000959212 0.00840.00471580.0015237720.0011996790.000561180.001082390.000860434 0.00930.005139350.0016921880.0013327660.000617380.0011772 60.000941357 0.0095 0.00523258 0.0017296810.0013624020.000629820.001198120.000959212 0.00860.004810510.0015611530.0012292140.00057370.001103610.000878501 0.00980.005371870.0017859660.0014068940.000648450.001229260.000985914 0.01030.005602570.0018798890.0014811490.000679430.001280810.001030205 0.01150.006149350.0021058490.0016598460.000753390.001402790.001135508 0.01080.005831530.0019739480.0015555250.000710310.001331920.001074247 0.01130.006058860.0020681370.0016300180.00074110.001382620.00111805 0.01040.00564850.001898690.0014960150.000685610.001291070.001039033 0.01060.005740150.0019363080.0015257610.000697970.001311530.001056659 0.01020.005556570.0018610930.0014662880.000673240.001270540.001021368 0.01060.005740150.0019363080.0015257610.000697970.001311530.001056659 0.01130.006058860.0020681370.0016300180.00074110.001382620.00111805 0.01120.006013520.0020492890.001615110.000734950.001372510.001109308 0.01270.006687350.0023325180.0018391710.000826880.001522560.001239531 0.01340.006997510.0024650420.0019440450.000869540.001591510.001299675 0.01310.00686490.002408220.0018990760.000851280.001562040.001273945 0.01260.006642830.0023136030.0018242050.000820770.001512660.001230907 0.01260.006642830.0023136030.0018242050.000820770.001512660.001230907 0.01380.007173610.0025408640.0020040560.000893860.001630630.001333877 0.01210.006419390.0022190990.0017494340.000790190.001462940.00118767 0.01340.006997510.0024650420.0019440450.000869540.001591510.001299675 0.01270.006687350.0023325180.0018391710.000826880.001522560.001239531 0.01350.007041610.0024839910.0019590420.000875630.001601310.001308236 0.01410.007305160.0025977740.0020491020.000912070.001659840.001359452 0.01530.007827160.002825770.0022296050.000984670.001775610.001461134 0.01470.007566990.0027117030.0021392920.000948420.001717930.001410414 0.01520.007783910.002806750.0022145450.000978630.001766020.001452697 0.01450.00747990.0026737110.0021092150.0009363 10.00169861 0.001393454 0.0149 0.007653890.002749710.0021693830.000960510.00173720.001427347 0.01420.007348920.0026167530.0020641250.000918130.001669550.001367963 0.01570.007999720.0029018910.0022898810.001008790.001813840.001494817 0.01420.007348920.0026167530.0020641250.000918130.001669550.001367963 0.01540.007870360.0028447950.0022446690.00099070.001785180.001469564 Table A.19: Viscosity Pressure Calculations (continued)

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Lower BUpper CMid CLower C 0.0002417350.000546460.00041430.00021963 0.0002578580.000581790.000442120.000233112 0.0002471040.000558240.000423560.000224127 0.000279420.000628930.000479330.000251043 0.0002956380.000664310.000507340.000264459 0.0002632420.000593570.000451410.0002376 0.0002740230.000617140.000470020.000246565 0.0002524790.000570010.000432830.000228622 0.000268630.000605350.000460710.000242084 0.0002471040.000558240.000423560.000224127 0.0003445070.000770590.000591790.000304553 0.0003554080.000794230.000610640.000313435 0.000382720.000853380.000657880.000335596 0.0004101140.000912570.000705290.000357702 0.0003227490.000723330.000554180.00028676 0.0003717850.000829710.000638960.000326739 0.0003173190.000711520.00054480.000282306 0.0004156020.000924420.000714780.000362116 0.0003445070.000770590.000591790.000304553 0.0003772510.000841540.000648420.000331169 0.0004265870.000948110.00073380.000370939 0.0004485920.000995520.000771910.000388561 0.0004872090.001078560.00083880.000419327 0.0004596120.001019240.000790990.000397361 0.0005037990.001114170.000867550.000432485 0.0004430860.000983670.000762370.000384159 0.0004927360.001090430.000848380.000423715 0.0005037990.001114170.000867550.000432485 0.0004541010.001007380.000781450.000392962 0.0005204110.001149790.000896350.000445628 0.0005481480.001209190.000944440.0004675 0.000614950.00135190.001060330.000519835 0.0005759430.001268630.000992650.000489332 0.0006037950.001328110.001040970.000511127 0.0005537020.001221080.000954070.000471869 0.0005648180.001244850.000973350.000480604 0.0005425960.001197310.000934810.000463128 0.0005648180.001244850.000973350.000480604 0.0006037950.001328110.001040970.000511127 0.000598220.001316210.00103130.000506771 0.0006820570.00149480.001176830.000571967 0.0007213320.001578230.001245040.000602292 0.0007044880.001542470.001215780.000589303 0.0006764540.001482880.00116710.00056763 0.0006764540.001482880.00116710.00056763 0.0007438150.001625930.00128410.000619594 0.0006484670.001423330.00111850.000545925 0.0007213320.001578230.001245040.000602292 0.0006820570.00149480.001176830.000571967 0.000726950.001590150.00125480.000606619 0.0007606960.001661720.0013134 40.000632558 0.000828373 0.00180495 0.001431080.000684315 0.0007945050.001733320.00137220.000658456 0.0008227240.001793010.001421260.000680007 0.0007832280.001709450.00135260.000649828 0.0008057880.001757190.001391810.00066708 0.0007663260.001673650.001323220.000636877 0.0008509850.001852730.00147040.000701533 0.0007663260.001673650.001323220.000636877 0.0008340240.00181690.001440910.000688621 Table A.19: Viscosity Pressure Calculations (continued)

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Diameter Resistance SVLViscosityPipe LengthUpper A Mid ALower AUpper B 0.00470.001010.0003896132530374.6185383627.1142717639879463536.69 0.0050.001010.00041426788551.9270249657.9120242010868834855.46 0.00480.0035340.00039774106545169.82795673254710826842264783860.7 0.00540.0035340.0004465273626313.521928600393399982037201479803 0.00570.0069480.00047091122175457.33197804385755649229349453208.4 0.00510.0102680.00042213255933955.16709619451.1572E+10668377268.8 0.00530.0102680.000438392268385405943524041.0403E+10611329278 0.00490.014620.0004058741315154410837569011.8407E+101044219569 0.00520.014620.00043026342870815.88986238351.5614E+10909750447 0.00480.0234830.00039774707979689.118576908593.1303E+101759456537 0.00660.001010.0005440811216601.4829295697.655779117436169716.89 0.00680.001010.0005603410214943.7126667978.751360784333753952.12 0.00730.0035340.0006009928618504.9374636834.71477120467100216716.8 0.00780.0035340.0006416423255995.8960593082.2123005194285973044.26 0.00620.0069480.0005115693863683.352453775234561273934287588794.8 0.00710.0069480.0005847361380822.031601453443135802568210115282.4 0.00610.0102680.00050343145968842.23816805117050862147441324682.2 0.00790.014620.0006497792446568.462408232924912712210345337318.7 0.00660.0234830.00054408260791537.26811394721.2969E+10840963823.5 0.00720.0234830.00059286198563066.15179547321.0197E+10687530265.8 0.00810.001010.000666035905620.71715378551.731674057322516434.43 0.00850.0035340.0006985517769254.2846239681.497013901370473585.65 0.00920.0035340.0007554613870348.0936052341.377971798558689027.56 0.00870.0069480.0007148132482050.2984497190.11788694584131299255.7 0.00950.0069480.0007798524664167.864078160.71403008486107135876.9 0.00840.0102680.0006904253577086.421394438692912371949210441912.1 0.00930.0102680.0007635938959384.571012488182198848106166311416.4 0.00950.014620.0007798551898407.211348334352952214172225435595.9 0.00860.023483 0.00070668113829412.1 296159929 6241573552455791800.2 0.00980.0234830.0008042475632114.611964054654351948850336991685.6 0.01030.001010.000844892783896.9517224143.8416315759112919424.06 0.01150.001010.000942451972110.3635109387.4712037893710015422.68 0.01080.0035340.000885548398316.9821778415.950089280840515501.53 0.01130.0035340.000926197289691.87218891112.544209557936493446.19 0.01040.0069480.0008530218580745.6448209805.7109286378686913129.98 0.01060.0069480.0008692817505792.745408148.2103690277083170752.1 0.01020.0102680.0008367629179277.9675730243.21703981164134337975.6 0.01060.014620.0008692836835735.3595547945.72181853554175008116.8 0.01130.014620.0009261930157129.3678151687.91828929646150971755.3 0.01120.0234830.0009180649804852.771290851053010605117247525357.4 0.01270.001010.001040011445836.7863740506.3291547980.47963724.429 0.01340.001010.001096921222528.5793160323.178956675.37035829.77 0.01310.0035340.001072534591467.9431187317729407078625939670.04 0.01260.0069480.0010318810195151.0626378778.864365921555793347.39 0.01260.0102680.0010318815066754.6238983491.795122234182453380.98 0.01380.0102680.0011294411336608.712929341274016394866832593.77 0.01210.014620.0009912324348674.0563036474.91514422399128908067.9 0.01340.014620.0010969217696403.7945746459.11142917418101845377.5 0.01270.0234830.0010400133616421.0386968623.62128535865185160535.4 0.01350.0234830.0011050527771236.88717828601798526557160802462.1 0.01410.001010.001153831042599.5352693199.8568613514.36255506.13 0.01530.0035340.001251392825997.5867291338.9419167109118127238.6 0.01470.0069480.001202616296169.4461625415642077364139086335.59 0.01520.0069480.001243265671097.43214633358.138370796036182415.11 0.01450.0102680.001186359711829.05425076996.164576911959618804.41 0.01490.0102680.001218878919812.40423022815.759909271655989272.27 0.014 20.01462 0.001 1619614762095.2938128915.397403145689084765.35 0.01570.014620.0012839110784945.7527815736.673848164070655456.48 0.01420.0234830.0011619623711236.9161243592.31564513043143090119.3 0.01540.0234830.0012595218399874.7447468908.51250961587118655801.5 (m) (St) (m)Table A.19: Viscosity Pressure Calculations (continued)

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Mid B Lower BUpper CMid C Lower C 227487153.846951919181797887165442013126890453672 194268743.83853543598148703403445902481.85769254831 754349838.51.536E+1058972975317793548842.2696E+10 558626243.31.0547E+1041092810512179020801.6187E+10 956898955.51.7451E+1068450325020121414292.7254E+10 18777324923.6777E+10142267962042532500295.5412E+10 17023008503.2528E+10126437578437579818924.9623E+10 29607987235.9497E+10229013583068882955448.8496E+10 25444290634.9218E+10190855842356890457697.4623E+10 50125628911.0207E+113918682450118235967001.5081E+11 95751462.54158946764063496610.4182545438.12602498221 88743448.73144519094757948353.71658417812389156320 259208199.14033385923163165684461960975.46822210741 218997179.93265891876133213831373387114.15643319788 772380489.41.3346E+1052901593815353587802.1416E+10 546949548.78663791366349270835993046811.51.4524E+10 11897218062.0773E+1082173628323908113313.3159E+10 877090491.21.2974E+1053002456514827447112.251E+10 22262689063.6956E+10147632762742442718046.0509E+10 17839441752.8006E+10113098587932088007944.7159E+10 56858786.0882764866433918589.294527972.911447651415 175994352.62483805380102404784283312565.84412510222 143915209.9193053220780383384.9219733356.63518256782 326141707.74534668768187502898516916899.68116533800 260778804.93426908514143261617389712760.16310250678 526974222.87493857065308508447855052251.61.3262E+10 4068080555419358316225955382616651580.89910881875 548731451.87210909970301451473820034621.81.3278E+10 11351884391.5901E+1065654479418131723042.8355E+10 814411715.51.0491E+1044027443211920352051.9512E+10 30866420.2238511484116262864.143700146.99727875017 23328120.8227119396011610637.430681635.39531103694 95745595.69115882016149225531.4131326395.82223928235 85345719.35100339059542864303.3113572855.81953945499 207186393.12569054466108618409291442237.14870717213 197396532.12417934749102472296274157459.94612450020 321675969.84038692430170340965458403572.27609236677 415362305.55087824702215622477576882853.29705529547 353071425.34150982031177327706469845826.98083385171 580064718.86858691777292674948776515613.91.3318E+10 18129678.4619775929 38572138.96 22313608.58 399885621 15820417.131667310677275703.4218785353.74343027466 58631881.9262696148427281790.270682126.531280508291 127247042.8139507309460411702157442763.82813771428 188050177.9206168833289278548.6232674481.64158290879 149260965.2154365353867608535173782989.43206131222 296755682.33339101492143866762377251404.16647389053 229004453.92413473466105317608271922645.24965407485 421523999.34598001470199306474518802445.79297538660 360953262.63785978202165363361426475066.67807853629 13901682.251418009356227241.2815954528.37296566618 39532985.9438266171216976798.342959648.17821667864 86031586.2485439603237716646.396022879.091811082364 79028182.1176818238534052573.186255551.251645990568 131639933131888091758121580.8148279787.62783339540 122852758.8120954253153484381.1135887011.92575090947 197651828.8200698250788215111.5225769604.44207038032 153175744.2145832744264907329163605418.63157551573 317473180.33223664174141693260362636636.16757446930 258383482.52490606301110585640279559518.45359184190 Table A.19: Viscosity Pressure Calculations (continued)

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Whole Pipe Resistance SVLViscosityA B C 0.00470.00101154509040050021426097614443700 0.0050.00101129945831841166471986363860716 0.00480.0035345096939337163795708662.5065E+10 0.00540.0035343666468390113072904201.7816E+10 0.00570.0069486197605125187572428332.995E+10 0.00510.01026812498916269393229022766.1088E+10 0.00530.01026811224323430348417784045.4645E+10 0.00490.0146219903693975635019970269.7675E+10 0.00520.0146216855864083526717754478.2221E+10 0.00480.023483338685417241.0884E+111.6655E+11 0.00660.0010159830347317213888192848540270 0.00680.00101550490765.515676883482612946454 0.00730.003534158037580743928108397447337400 0.00780.003534131390102035708621016149920733 0.00620.0069484900515140144061311142.348E+10 0.00710.006948335732873494208561971.5866E+10 0.00610.0102687578511500224041250003.6372E+10 0.00790.014625245982070141959667182.4523E+10 0.00660.02348313910851936400231422266.623E+10 0.00720.02348310913142268304770992025.1499E+10 0.00810.00101338024745907023884.21576097977 0.00850.003534103414794927302733184798227571 0.00920.003534829640674.621331364443818373523 0.00870.006948190567382549921097328820953597 0.00950.006948149175081537948231966843225054 0.00840.010268310539290482312732001.4426E+10 0.00930.010268233905630859924777871.0753E+10 0.00950.01462313894601579850770181.44E+10 0.00860.0234836651562894174921162793.0825E+10 0.00980.0234834623986430116422871242.1145E+10 0.01030.00101173165631.3428900685787838028 0.01150.00101127460435.1304537503.4573395967 0.01080.003534531069541.312950812582404480162 0.01130.003534468276383.811252297602110382658 0.01040.006948115965433828631539895270777860 0.01060.006948109981671126985020334989079776 0.01020.010268180889068544947063758237981215 0.01060.01462231423723556781951241.0498E+10 0.01130.01462193723846446550252118730558704 0.01120.023483318949507576862818531.4387E+10 0.01270.0010196734323.48 223852696.2430771369 0.01340.0010183339526.96189587314369088524 0.01310.003534310535430.8711533035.51378472208 0.01260.006948680233145.215781134843031625894 0.01260.010268100527258723321918904480243909 0.01380.01026878079396917597470973447522746 0.01210.01462160180754837647652427168507219 0.01340.01462120636028127443232975342647738 0.01270.023483224912090952046860051.0016E+10 0.01350.023483189808065443077339278399692057 0.01410.0010172349313.68161958123.1318748388 0.01530.003534201788427.4440321936.9881604310 0.01470.006948443323966.5979513953.61944821889 0.01520.006948404012416883392981.91766298693 0.01450.010268680557944.415101396542989740908 0.01490.010268631035343.913883845622764462340 0.01420.01462102692246722937191014521022748 0.01570.01462777082322.716821586433386064321 0.01420.023483164946787236842274737261776826 0.01540.023483131683037028676455845749329348 (m) (cSt)Table A.19: Viscosity Pressure Calculations (continued)

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Pressure Viscosity ) 0.00470.001019.78455E-1020440387922.1814E-0544589.35144.58935101 0.0050.001011.1696E-0917099791992.4935E-0542637.76842.63776802 0.00480.0035342.97144E-1067307384111.4485E-0597496.005697.49600564 0.00540.0035344.1731E-1047926053551.5407E-0573837.34373.83734301 0.00570.0069482.48054E-1080627625012.4858E-05200423.068200.423068 0.00510.0102681.21807E-10164193952223.5187E-05577748.502577.748502 0.00530.0102681.36093E-10146957913151.9239E-05282738.077282.7380767 0.00490.014627.62275E-11262372410021.6177E-05424440.337424.4403372 0.00520.014629.04744E-11221056891581.6419E-05362956.772362.9567716 0.00480.0234834.47178E-11447249377769.2053E-06411707.162411.7071615 0.00660.001012.60338E-09768233282.72. 1111E-0516218.556716.21855672 0.00680.001012.83715E-09704932145.22.7611E-0519463.61419.46361399 0.00730.0035349.94682E-1020106933861.8768E-0537737.476137.73747613 0.00780.0035341.20374E-0916614877011.9716E-0532757.493132.75749313 0.00620.0069483.16064E-1063278384492.4209E-05153189.151153.1891514 0.00710.0069484.67032E-1042823649812.8598E-05122468.755122.4687548 0.00610.0102682.0408E-1098000613402.1308E-05208818.266208.8182657 0.00790.014623.01843E-1066259596861.525E-05101048.459101.0484595 0.00660.0234831.11971E-10178618041361.4672E-05262059.5262.0594995 0.00720.0234831.43862E-10139022205132.25E-05312795.956312.7959565 0.00810.001014.69535E-094259534804.378E-0518648.041618.64804164 0.00850.0035341.54165E-0912973082792.9145E-0537810.524637.81052456 0.00920.0035341.93603E-0910330439913.0072E-0531066.050831.06605077 0.00870.0069488.38431E-1023854071015.3064E-05126578.884126.5788836 0.00950.0069481.08E-0918518517423.4965E-0564749.676764.74967675 0.00840.0102685.12829E-1038999380212.883E-05112433.764112.4337642 0.00930.0102686.87392E-1029095488333.171E-0592262.453292.2624532 0.00950.014625.13259E-1038966713402.0501E-0579885.503379.88550334 0.00860.0234832.3995E-1083350558292.1791E-05181629.475181.6294745 0.00980.0234833.49451E-105723269583 1.8074E-05103442.379 103.4423791 0.0103 0.001019.37566E-09213318395.47.6111E-0516235.975616.2359756 0.01150.001011.28732E-08155361101.74.1539E-056453.54256.4535425 0.01080.0035343.07104E-09651246198.53.8295E-0524939.448324.93944833 0.01130.0035343.49805E-09571747754.52.6427E-0515109.544615.10954458 0.01040.0069481.40132E-0914272294003.9627E-0556556.490756.5564907 0.01060.0069481.48026E-0913511175124.3704E-0559049.878259.04987821 0.01020.0102688.96698E-1022304055532.9512E-0565824.03365.824033 0.01060.014627.03476E-1028430250472.3311E-0566274.803466.27480341 0.01130.014628.45561E-1023652948982.465E-0558304.712458.30471239 0.01120.0234835.13137E-1038975911372.87E-05 111861.605 111.8616047 0.01270.001011.71262E-08116779914.63.143E-053670.334983.670334982 0.01340.001011.99831E-08100084572.33.1366E-053139.22763.139227599 0.01310.0035345.3511E-09373754831.52.5324E-059464.963069.464963058 0.01260.0069482.43361E-09821824977.64.4484E-0536557.651436.55765139 0.01260.0102681.64674E-0912145220022.835E-0534432.184134.43218414 0.01380.0102682.13907E-09934983831.43.2192E-0530099.009230.09900916 0.01210.014621.02941E-0919428518062.6271E-0551040.502551.04050247 0.01340.014621.3805E-0914487489583.193E-0546258.182146.25818205 0.01270.0234837.36596E-1027151908271.8233E-0549505.303149.50530307 0.01350.0234838.78041E-1022777990003.3681E-0576717.42676.71742598 0.01410.001012.31335E-0886454568.213.8285E-053309.896263.309896262 0.01530.0035348.36105E-09239204494.92.8565E-056832.897626.832897625 0.01470.0069483.79079E-095275949074.9945E-0526350.928626.35092863 0.01520.0069484.17333E-09479234052.15.3797E-0525781.512925.78151291 0.01450.0102682.46605E-09811013513.84.8781E-0539562.154439.56215442 0.01490.0102682.66669E-09749992643.93.9522E-0529640.913329.6409133 0.01420.014621.63095E-0912262826102.2541E-0527642.184527.64218453 0.01570.014622.17667E-09918835868.13.631E-0533362.966933.36296695 0.01420.0234831.01539E-0 91969684989 3.5768E-05 70452.334870.45233481 0.01540.0234831.28205E-0915600006942.7968E-0543629.751443.62975139 (m)(St) SVLVisc.One SideTotal ResistanceFl Rte (m/s)Press. (Pa)Pressure (kPa)Table A.19: Viscosity Pressure Calculations (continued)

PAGE 115

4.711.01 0.1832 0.1867 0.1855 511.01 0.1768 0.1952 0.1784 6.621.01 0.296 0.356 0.2904 6.821.01 0.1654 0.1492 0.1184 8.131.01 0.1112 0.2496 0.1728 10.341.01 0.1008 0.324 0.1408 11.541.01 0.2832 0.2768 0.296 12.751.01 0.1382 0.4654 0.268 13.451.01 0.163 0.5956 0.3176 14.161.01 0.232 0.292 0.2424 4.813.534 0.1312 0.2272 0.264 5.413.534 0.1624 0.2976 0.2848 7.323.534 0.3272 0.312 0.388 7.823.534 0.3856 0.3552 0.448 8.533.534 0.4336 0.2538 0.4576 9.233.534 0.4216 0.2592 0.4976 10.843.534 0.5196 0.329 0.5907 11.343.534 0.6822 0.3486 0.7302 13.153.534 0.7782 0.4776 0.4122 15.363.534 0.6042 0.3292 0.9064 5.716.948 0.2158 0.2306 0.2438 6.226.948 0.1762 0.2158 0.2474 7.126.948 0.2856 0.2582 0.26 8.736.948 0.1316 0.1592 0.1554 9.536.948 0.3402 0.2854 0.2894 10.446.948 0.3341 0.2792 0.2838 10.646.948 0.2012 0.2438 0.2679 12.656.948 0.3682 0.3021 0.3066 14.766.948 0.3722 0.3341 0.3411 15.266.948 0.389 0.3476 0.3503 5.1110.268 0.105 0.1496 0.1241 5.3110.268 0.1902 0.2134 0.2406 6.1210.268 0.1992 0.284 0.2736 8.4310.268 0.2236 0.3032 0.2955 9.3310.268 0.2552 0.3776 0.3008 10.2410.268 0.1888 0.32 0.2224 12.6510.268 0.42 0.4576 0.4584 13.8510.268 0.4632 0.474 0.4684 14.5610.268 0.1652 0.2282 0.2788 14.96 10.268 0.187 0.2524 0.3486 4.9114.62 0.0972 0.1688 0.1677 5.2114.62 0.0904 0.1382 0.1804 7.92 14.62 0.2504 0.3184 0.2936 9.5 314.62 0.2872 0.3406 0.2854 10.6414.62 0.1976 0.3106 0.3584 11.3414.62 0.3106 0.3854 0.3028 12.1514.62 0.3098 0.3788 0.3142 13.4514.62 0.2632 0.3212 0.2794 14.2614.62 0.2512 0.3514 0.5056 15.7614.62 0.3134 0.3804 0.3266 4.8123.483 0.404 0.462 0.4228 6.6223.483 0.516 0.4168 0.4968 7.2223.483 0.2824 0.2864 0.3616 8.6323.483 0.364 0.2928 0.3912 9.8323.483 0.244 0.4224 0.2968 11.2423.483 0.2682 0.324 0.3166 12.7523.483 0.4842 0.4514 0.782 13.5523.483 0.2718 0.3306 0.3198 14.2623.483 0.3052 0.3214 0.3358 15.4623.483 0.7464 0.6244 0.668 IndSize ClassVisc. (cSt)DMO (s) DMC (s) DHD (s)Table A.20: Viscosity Data

PAGE 116

0.1988536.2857628577.28573278628.20957 4183.441198 0.1876543.6995416590.11133768452.641913 3092.573423 0.3112694.9755463509.71228036823.442744 5001.705648 0.2468733.1345513688.19435247632.248687 4910.837873 0.1928761.8242408725.52614737483.188616 3114.11046 0.1488701.6984398515.62393795501.833296 2263.115232 0.312 756.3581871930.71817474478.462918 2937.843908 0.46561211.3496631068.2945244833.21949 2602.903472 0.49821395.1994761201.3864664691.003259 2342.785492 0.4344647.40959121003.7443443395.463392 2642.100031 0.3072 648.206501731.22016785290.472853 3265.490798 0.3336656.8095867610.28092894465.632654 2463.329717 0.396 919.636551951.81967022866.7548 3183.472094 0.4088957.2654724975.87128032582.419843 3192.986272 0.3072712.8076515750.11326871674.598712 3317.641493 0.328 498.0629256571.25548471216.492354 1906.039183 0.3134 811.3356711688.04233141561.385826 2465.679069 0.48 887.3059648883.87987481300.385357 2544.970253 0.60021062.4577351233.0989611365.295477 2224.261437 0.6434758.24578541088.3448661255.004893 2303.552621 0.2209683.5978185711.00295935604.129056 4357.124379 0.2514951.29464341058.2834645401.385728 4408.328567 0.25121083.002859 1112.1949635810.43924 4288.239783 0.1736687.3757636692.55039585222.339684 4317.346313 0.2934833.1039583851.18426724997.294301 3993.297782 0.2892832.1049622851.10582835103.324355 4055.498951 0.2684966.12356621021.3953534833.006348 3964.228 0.32581586.1957131633.1895734694.21156 3778.006466 0.3504993.19403651132.1958184360.19056 3504.439517 0.3389872.0029587955.29682224288.008341 3689.498954 0.1362712.3967637721.03868256782.387574 4763.186548 0.2611702.2194876715.12049598410.597872 4831.397828 0.28 1173.8950211160.9066086061.203576 4659.243432 0.30611147.2905031158.195967934.105892 4582.395912 0.3152 1524.784741520.7057228331.867597 4152.155996 0.3792 1323.945921522.3996828048.942399 4530.469006 0.5112 2008.598911390.2591285803.052785 4405.719879 0.5032 2100.348532129.2959125647.194068 4213.00582 0.3528944.19947251266.122895718.329532 4137.176834 0.45021022.3858631562.0492565466.329487 4050.95719 0.2821721.3956626702.10964247418.194554 4273.181506 0.2989 586.0124354 707.55903876491.936162 4242.571387 0.5368 1118.987683853.3799796499.722617 3962.489543 0.50041305.1054981334.4843265847.205833 3501.269306 0.50321056.3361441236.5487685346.902594 3400.130912 0.51461107.298587 1114.2104855471.230959 3633.103496 0.525 2056.2195842068.1958735366.048188 3479.02386 0.48941432.1039591472.0458136371.329684 3880.294599 0.74421231.3845241683.0013464902.403404 3503.295486 0.52241582.0386831766.2948015213.496928 3400.148677 0.4834677.1940976681.20950971823.189486 2207.198587 0.44781003.5743731245.2968731945.119487 2408.487473 0.3248 1022.45654997.41274713603.492059 3612.965703 0.41681235.7290091204.8352233792.713576 4561.578922 0.5896 578.476295698.13269472711.937297 1597.988911 0.43721098.289583 1117.3858293413.498688 2834.003857 0.80261783.2465242118.3856533677.285756 3951.396593 0.46822078.2965822092.1868273209.385897 2416.295872 0.469 1632.4398681888.0158793169.284969 2276.136821 0.66241594.4401951681.3052342136.385876 2553.668487 DHE (s)Gape (um)Hyoid (um)VMO (um/s) VMC (um/s)Table A.20: Viscosity Data (continued)

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7533.269784 3361.385013 7204.842657 2322.421879 6246.757484 4038.65669 5811.833968 2788.104823 4359.686546 2947.55253 3860.452139 1529.513999 4667.537834 2598.544306 3987.378548 2294.195863 3783.286675 2411.294386 3538.934632 2364.225387 3323.824355 2804.862238 2438.778439 1912.783041 2562.790761 2410.01526 2253.084921 2552.217556 1680.768951 2538.433967 1203.257795 1736.321115 1164.692599 2195.284869 1210.486744 1841.284582 1131.007985 2055.284766 1200.688829 1691.794057 4438.135695 4176.798315 4277.884737 4211.058677 4143.143899 4055.863498 4456.936895 3988.602984 4231.138289 3845.963869 3704.537681 4011.971384 3812.439599 3804.552059 3653.145014 3799.136322 3341.138643 3561.023792 3480.497326 3682.197636 5809.479766 5294.007484 5617.295726 5266.258715 4312.643913 4895.334312 5367.004292 5166.20693 6454.787709 5062.122954 7713.290501 4215.473258 3040.517097 3148.668015 4743.470111 3688.104587 4536.685749 3587.41044 4481.497855 3471.104867 4186.477784 2489.285687 3922.086119 2367.224869 3768.031739 1790.550217 3462.001894 2418.329586 3449.832943 2456.936214 3407.184033 2394.105839 3512.597903 2377.289603 3803.105877 2631.395894 3328.985467 2261.396587 3888.032868 2346.614978 2011.386753 2633.105767 2506.385673 2781.496745 2669.323544 3225.833744 3345.296577 3084.535474 2696.486977 1200.747323 2598.028487 2709.193487 2712.496775 2639.193857 2463.112968 2481.006382 2423.029386 2399.045868 2517.039868 2538.067655 VHD (um/s) VHE (um/s)Table A.20: Viscosity Data (continued)

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 4 Normality Test: Passed(P = 0.447) Equal Variance Test: Passed(P = 0.853) Group Name N Missing MeanStd DevSEM 1.010100 -0.704 0.759 0.240 3.534100 -0.677 0.830 0.263 6.948100 -0.250 0.840 0.265 10.268100 0.645 1.027 0.325 14.620100 0.447 0.702 0.222 23.483100 0.536 0.995 0.315 Source of Variation DF SS MS F P Between Groups 5 19.190 3.838 5.108 <0.001 Residual 54 40.574 0.751 Total 59 59.764 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 0.942 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 10.268 vs. 1.010 1.349 3.479 0.00100 0.003 Yes 10.268 vs. 3.534 1.322 3.409 0.00124 0.004 Yes 23.483 vs. 1.010 1.240 3.198 0.00232 0.004 Yes 23.483 vs. 3.534 1.212 3.128 0.00284 0.004 Yes 14.620 vs. 1.010 1.151 2.970 0.00444 0.005 Yes 14.620 vs. 3.534 1.124 2.900 0.00539 0.005 No 10.268 vs. 6.948 0.895 2.309 0.0248 0.006 No 23.483 vs. 6.948 0.786 2.027 0.0476 0.006 No 14.620 vs. 6.948 0.698 1.800 0.0775 0.007 No 6.948 vs. 1.010 0.454 1.171 0.247 0.00 9 N o 6.948 vs. 3.534 0.427 1.100 0.276 0.010 No 10.268 vs. 14.620 0.197 0.509 0.613 0.013 No 10.268 vs. 23.483 0.109 0.282 0.779 0.017 No 23.483 vs. 14.620 0.0883 0.228 0.821 0.025 No 3.534 vs. 1.010 0.0272 0.0701 0.944 0.050 NoMaximum Gape Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 5 Normality Test: Passed(P = 0.873) Equal Variance Test: Passed(P = 0.590) Group Name N Missing MeanStd DevSEM 1.010100 -0.945 0.709 0.224 3.534100 -0.629 0.846 0.267 6.948100 -0.247 0.929 0.294 10.268100 0.701 0.669 0.212 14.620100 0.478 0.606 0.192 23.483100 0.647 0.980 0.310 Source of Variation DF SS MS F P Between Groups 5 24.893 4.979 7.745 <0.001 Residual 54 34.712 0.643 Total 59 59.606 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 0.998 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 10.268 vs. 1.010 1.646 4.592 0.0000267 0.003 Yes 23.483 vs. 1.010 1.593 4.442 0.0000446 0.004 Yes 14.620 vs. 1.010 1.423 3.969 0.000215 0.004 Yes 10.268 vs. 3.534 1.330 3.710 0.000490 0.004 Yes 23.483 vs. 3.534 1.277 3.560 0.000782 0.005 Yes 14.620 vs. 3.534 1.107 3.087 0.00319 0.005 Yes 10.268 vs. 6.948 0.948 2.644 0.0107 0.006 No 23.483 vs. 6.948 0.894 2.494 0.0157 0.006 No 14.620 vs. 6.948 0.725 2.021 0.0483 0.00 7 No 6.948 vs. 1.010 0.698 1.948 0.0567 0.00 9 N o 6.948 vs. 3.534 0.382 1.066 0.291 0.010 No 3.534 vs. 1.010 0.316 0.881 0.382 0.013 No 10.268 vs. 14.620 0.223 0.623 0.536 0.017 No 23.483 vs. 14.620 0.170 0.473 0.638 0.025 No 10.268 vs. 23.483 0.0538 0.150 0.881 0.050 NoMaximum Hyoid Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. Normality Test: Failed(P < 0.050) Equal Variance Test: Passed(P = 0.397) Group Name N Missing MeanStd DevSEM 1.010100 -0.791 0.989 0.313 3.534100 0.959 0.835 0.264 6.948100 0.00274 0.641 0.203 10.268100 -0.388 0.830 0.262 14.620100 -0.467 0.627 0.198 23.483100 0.679 0.930 0.294 Source of Variation DF SS MS F P Between Groups 5 23.746 4.749 7.066 <0.001 Residual 54 36.294 0.672 Total 59 60.040 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 0.994 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 3.534 vs. 1.010 1.750 4.772 0.0000143 0.003 Yes 23.483 vs. 1.010 1.470 4.009 0.000188 0.004 Yes 3.534 vs. 14.620 1.426 3.890 0.000277 0.004 Yes 3.534 vs. 10.268 1.346 3.672 0.000552 0.004 Yes 23.483 vs. 14.620 1.147 3.127 0.00284 0.005 Yes 23.483 vs. 10.268 1.067 2.910 0.00524 0.005 No 3.534 vs. 6.948 0.956 2.608 0.0118 0.006 No 6.948 vs. 1.010 0.793 2.164 0.0349 0.006 No 23.483 vs. 6.948 0.677 1.845 0.0705 0.007 No 6.948 vs. 14.620 0.470 1.282 0.205 0.00 9 N o 10.268 vs. 1.010 0.403 1.099 0.276 0.010 No 6.948 vs. 10.268 0.390 1.065 0.292 0.013 No 14.620 vs. 1.010 0.323 0.882 0.382 0.017 No 3.534 vs. 23.483 0.280 0.762 0.449 0.025 No 10.268 vs. 14.620 0.0797 0.217 0.829 0.050 NoDuration of Mouth Opening Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Normality Test: Passed(P = 0.457) Equal Variance Test: Passed(P = 0.203) Group Name N Missing MeanStd DevSEM 1.0101000.0859 1.188 0.376 3.534100 0.241 0.653 0.206 6.948100 -0.617 0.646 0.204 10.268100 -0.160 1.125 0.356 14.620100 -0.193 0.774 0.245 23.483100 0.811 1.141 0.361 Source of Variation DF SS MS F P Between Groups 5 11.659 2.332 2.581 0.036 Residual 54 48.780 0.903 Total 59 60.439 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = 0.036). Power of performed test with alpha = 0.050: 0.505 The power of the performed test (0.505) is below the desired power of 0.800. Less than desired power indicates you are more likely to not detect a difference when one actually exists. Be cautious in over-interpreting the lack of difference found here. All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 23.483 vs. 6.948 1.427 3.358 0.00144 0.003 Yes 23.483 vs. 14.620 1.003 2.361 0.0219 0.004 No 23.483 vs. 10.268 0.970 2.283 0.0264 0.004 No 23.483 vs. 1.010 0.897 2.110 0.0395 0.004 No 3.534 vs. 6.948 0.858 2.019 0.048 5 0.00 5 No 23.483 vs. 3.534 0.570 1.340 0.186 0.005 No 1.010 vs. 6.948 0.531 1.249 0.217 0.006 No 10.268 vs. 6.948 0.457 1.075 0.287 0.006 No 3.534 vs. 14.620 0.434 1.021 0.312 0.007 No 14.620 vs. 6.948 0.424 0.998 0.323 0.009 No 3.534 vs. 10.268 0.401 0.943 0.350 0.010 No 3.534 vs. 1.010 0.327 0.770 0.445 0.013 No 1.010 vs. 14.620 0.107 0.251 0.802 0.017 No 1.010 vs. 10.268 0.0737 0.173 0.863 0.025 No 10.268 vs. 14.620 0.0331 0.0779 0.938 0.050 NoDuration of Mouth Closing Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 2 Normality Test: Passed(P = 0.181) Equal Variance Test: Passed(P = 0.098) Group Name N Missing MeanStd DevSEM 1.010100 -0.958 0.821 0.260 3.534100 1.184 0.635 0.201 6.948100 -0.430 0.515 0.163 10.268100 -0.249 0.744 0.235 14.620100 -0.278 0.488 0.154 23.483100 0.732 0.997 0.315 Source of Variation DF SS MS F P Between Groups 5 31.800 6.360 12.196 <0.001 Residual 54 28.159 0.521 Total 59 59.960 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 1.000 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 3.534 vs. 1.010 2.142 6.633 0.0000000162 0.003 Yes 23.483 vs. 1.010 1.690 5.235 0.00000278 0.004 Yes 3.534 vs. 6.948 1.614 4.998 0.00000646 0.004 Yes 3.534 vs. 14.620 1.462 4.526 0.0000334 0.004 Yes 3.534 vs. 10.268 1.432 4.436 0.0000455 0.005 Yes 23.483 vs. 6.948 1.162 3.599 0.000694 0.005 Yes 23.483 vs. 14.620 1.010 3.127 0.00284 0.006 Yes 23.483 vs. 10.268 0.981 3.037 0.00368 0.006 Yes 10.268 vs. 1.010 0.710 2.198 0.0323 0.007 N o 14.620 vs. 1.010 0.681 2.107 0.0398 0.009 N o 6.948 vs. 1.010 0.528 1.636 0.108 0.010 No 3.534 vs. 23.483 0.452 1.399 0.168 0.013 No 10.268 vs. 6.948 0.182 0.562 0.576 0.017 No 14.620 vs. 6.948 0.152 0.472 0.639 0.025 No 10.268 vs. 14.620 0.0292 0.0906 0.928 0.050 NoDuration of Hyoid Depression Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 3 Normality Test: Passed(P = 0.071) Equal Variance Test: Passed(P = 0.390) Group Name N Missing MeanStd DevSEM 1.010100 -0.741 1.027 0.325 3.534100 0.399 0.624 0.197 6.948100 -0.994 0.508 0.161 10.268100 -0.321 0.715 0.226 14.620100 0.761 0.476 0.150 23.483100 0.902 0.823 0.260 Source of Variation DF SS MS F P Between Groups 5 31.926 6.385 12.297 <0.001 Residual 54 28.040 0.519 Total 59 59.966 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 1.000 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 23.483 vs. 6.948 1.896 5.884 0.000000262 0.003 Yes 14.620 vs. 6.948 1.755 5.447 0.00000129 0.004 Yes 23.483 vs. 1.010 1.642 5.096 0.00000455 0.004 Yes 14.620 vs. 1.010 1.502 4.660 0.0000211 0.004 Yes 3.534 vs. 6.948 1.394 4.325 0.0000661 0.005 Yes 23.483 vs. 10.268 1.223 3.795 0.000375 0.005 Yes 3.534 vs. 1.010 1.140 3.538 0.000838 0.006 Yes 14.620 vs. 10.268 1.082 3.359 0.00144 0.006 Yes 3.534 vs. 10.268 0.721 2.237 0.0295 0.007 N o 10.268 vs. 6.948 0.673 2.089 0.0415 0.00 9 N o 23.483 vs. 3.534 0.502 1.558 0.125 0.010 No 10.268 vs. 1.010 0.419 1.301 0.199 0.013 No 14.620 vs. 3.534 0.362 1.122 0.267 0.017 No 1.010 vs. 6.948 0.254 0.787 0.435 0.025 No 23.483 vs. 14.620 0.141 0.436 0.664 0.050 NoDuration of Hyoid Elevation Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 6 Normality Test: Failed(P < 0.050) Equal Variance Test: Failed(P < 0.050) Group Name N Missing MeanStd DevSEM 1.010100 0.565 0.354 0.112 3.534100 -1.555 0.828 0.262 6.948100 0.301 0.103 0.0324 10.268100 0.869 0.317 0.100 14.620100 0.632 0.182 0.0575 23.483100 -0.809 0.741 0.234 Source of Variation DF SS MS F P Between Groups 5 46.385 9.277 37.041 <0.001 Residual 54 13.524 0.250 Total 59 59.909 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 1.000 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 10.268 vs. 3.534 2.424 10.832 3.744E015 0.003 Yes 14.620 vs. 3.534 2.187 9.771 1.543E013 0.004 Yes 1.010 vs. 3.534 2.121 9.475 4.448E013 0.004 Yes 6.948 vs. 3.534 1.856 8.293 3.326E011 0.004 Yes 10.268 vs. 23.483 1.679 7.500 0.000000000635 0.005 Yes 14.620 vs. 23.483 1.441 6.439 0.0000000334 0.005 Yes 1.010 vs. 23.483 1.375 6.143 0.000000100 0.006 Yes 6.948 vs. 23.483 1.110 4.961 0.00000735 0.006 Yes 23.483 vs. 3.534 0.74 6 3.332 0.00156 0.007 Yes 10.268 vs. 6.948 0.568 2.539 0.014 0 0.009 No 14.620 vs. 6.948 0.331 1.478 0.145 0.010 No 10.268 vs. 1.010 0.304 1.357 0.181 0.013 No 1.010 vs. 6.948 0.265 1.182 0.242 0.017 No 10.268 vs. 14.620 0.237 1.061 0.293 0.025 No 14.620 vs. 1.010 0.0662 0.296 0.769 0.050 NoVelocity of Mouth Opening Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 7 Normality Test: Failed(P < 0.050) Equal Variance Test: Failed(P < 0.050) Group Name N Missing MeanStd DevSEM 1.010100 -0.296 0.922 0.292 3.534100 -0.998 0.634 0.201 6.948100 0.682 0.104 0.0328 10.268100 1.029 0.149 0.0470 14.620100 0.394 0.191 0.0604 23.483100 -0.813 1.240 0.392 Source of Variation DF SS MS F P Between Groups 5 34.225 6.845 14.361 <0.001 Residual 54 25.739 0.477 Total 59 59.964 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 1.000 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 10.268 vs. 3.534 2.026 6.563 0.0000000211 0.003 Yes 10.268 vs. 23.483 1.842 5.965 0.000000194 0.004 Yes 6.948 vs. 3.534 1.679 5.439 0.00000133 0.004 Yes 6.948 vs. 23.483 1.495 4.842 0.0000112 0.004 Yes 14.620 vs. 3.534 1.392 4.509 0.0000355 0.005 Yes 10.268 vs. 1.010 1.324 4.289 0.0000746 0.005 Yes 14.620 vs. 23.483 1.208 3.911 0.000259 0.006 Yes 6.948 vs. 1.010 0.977 3.166 0.00254 0.006 Yes 1.010 vs. 3.534 0.702 2.274 0.0270 0.007 N o 14.620 vs. 1.010 0.690 2.235 0.0296 0.00 9 N o 10.268 vs. 14.620 0.634 2.054 0.0448 0.010 No 1.010 vs. 23.483 0.517 1.676 0.0995 0.013 No 10.268 vs. 6.948 0.347 1.123 0.266 0.017 No 6.948 vs. 14.620 0.287 0.931 0.356 0.025 No 23.483 vs. 3.534 0.184 0.597 0.553 0.050 NoVelocity of Mouth Closing Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 8 Normality Test: Passed(P = 0.196) Equal Variance Test: Failed(P < 0.050) Group Name N Missing MeanStd DevSEM 1.010100 0.804 0.369 0.117 3.534100 -1.681 0.688 0.217 6.948100 0.358 0.124 0.0391 10.268100 0.923 0.566 0.179 14.620100 0.212 0.260 0.0823 23.483100 -0.612 0.480 0.152 Source of Variation DF SS MS F P Between Groups 5 48.732 9.746 47.053 <0.001 Residual 54 11.186 0.207 Total 59 59.918 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 1.000 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 10.268 vs. 3.534 2.605 12.796 5.538E018 0.003 Yes 1.010 vs. 3.534 2.485 12.209 3.688E017 0.004 Yes 6.948 vs. 3.534 2.039 10.018 6.419E014 0.004 Yes 14.620 vs. 3.534 1.893 9.303 8.286E013 0.004 Yes 10.268 vs. 23.483 1.536 7.545 0.000000000537 0.005 Yes 1.010 vs. 23.483 1.416 6.958 0.00000000482 0.005 Yes 23.483 vs. 3.534 1.069 5.251 0.00000262 0.006 Yes 6.948 vs. 23.483 0.970 4.767 0.0000145 0.006 Yes 14.620 vs. 23.483 0.82 5 4.052 0.000164 0.007 Yes 10.268 vs. 14.620 0.711 3.49 3 0.00096 0 0.009 Yes 1.010 vs. 14.620 0.592 2.906 0.00529 0.010 Yes 10.268 vs. 6.948 0.565 2.778 0.00750 0.013 Yes 1.010 vs. 6.948 0.446 2.191 0.0328 0.017 No 6.948 vs. 14.620 0.146 0.715 0.478 0.025 No 10.268 vs. 1.010 0.119 0.587 0.560 0.050 NoVelocity of Hyoid Depression Analysis

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One Way Analysis of Variance Data source: Viscosity Data in Xenopus Data.SNB Dependent Variable: Stud. Res. 9 Normality Test: Failed(P < 0.050) Equal Variance Test: Passed(P = 0.323) Group Name N Missing MeanStd DevSEM 1.010100 -0.362 0.737 0.233 3.534100 -0.954 0.472 0.149 6.948100 1.013 0.0780 0.0247 10.268100 1.306 0.433 0.137 14.620100 -0.604 0.433 0.137 23.483100 -0.400 0.854 0.270 Source of Variation DF SS MS F P Between Groups 5 42.965 8.593 27.459 <0.001 Residual 54 16.899 0.313 Total 59 59.864 The differences in the mean values among the treatment groups are greater than would be expected by chance; there is a statistically significant difference (P = <0.001). Power of performed test with alpha = 0.050: 1.000 All Pairwise Multiple Comparison Procedures (Holm-Sidak method): Overall significance level = 0.05 Comparisons for factor: Viscosity ComparisonDiff of MeanstUnadjusted PCritical Level Significant? 10.268 vs. 3.534 2.260 9.034 2.197E012 0.003 Yes 6.948 vs. 3.534 1.966 7.860 0.000000000166 0.004 Yes 10.268 vs. 14.620 1.910 7.635 0.000000000383 0.004 Yes 10.268 vs. 23.483 1.706 6.819 0.00000000811 0.004 Yes 10.268 vs. 1.010 1.668 6.667 0.0000000143 0.005 Yes 6.948 vs. 14.620 1.616 6.461 0.0000000308 0.005 Yes 6.948 vs. 23.483 1.412 5.645 0.000000628 0.006 Yes 6.948 vs. 1.010 1.374 5.493 0.00000109 0.006 Yes 1.010 vs. 3.534 0.592 2.367 0.0215 0.00 7 No 23.483 vs. 3.534 0.554 2.215 0.0310 0.009 N o 14.620 vs. 3.534 0.350 1.398 0.168 0.010 No 10.268 vs. 6.948 0.294 1.174 0.246 0.013 No 1.010 vs. 14.620 0.242 0.969 0.337 0.017 No 23.483 vs. 14.620 0.204 0.817 0.418 0.025 No 1.010 vs. 23.483 0.0381 0.152 0.880 0.050 NoVelocity of Hyoid Elevation Analysis


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Ryerson, William G.
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The role of abiotic and biotic factors in suspension feeding mechanics of Xenopus tadpoles
h [electronic resource] /
by William G. Ryerson.
260
[Tampa, Fla] :
b University of South Florida,
2008.
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Thesis (M.S.)--University of South Florida, 2008.
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Includes bibliographical references.
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Text (Electronic thesis) in PDF format.
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ABSTRACT: As a comparison to the suction feeding mechanics in aquatic environments, I investigated buccal pumping in an ontogenetic series of suspension feeding Xenopus laevis tadpoles (4-18 mm snout-vent length) by examining the morphology, kinematics, fluid flow, pressure generated in the buccal cavity, and effects of viscosity manipulation. Investigation of the dimensions of the feeding apparatus of Xenopus revealed that the feeding muscles exhibited strong negative allometry, indicating that larger tadpoles had relatively smaller muscles, while the mechanical advantage of those muscles did not change across the size range examined. Buccal volume and head width also exhibited negative allometry: smaller tadpoles had relatively wider heads and larger volumes. Tadpoles were imaged during buccal pumping to obtain kinematics of jaw and hyoid movements as well as fluid velocity.Scaling patterns were inconsistent with models of geometric growth, which predict that durations of movements are proportional to body length. Only scaling of maximum hyoid distance, duration of mouth closing, and duration of hyoid elevation could not be distinguished from isometry. The only negatively allometric variable was maximum gape distance. No effect of size was found for duration of mouth opening, duration of hyoid depression, and velocity of hyoid elevation. Velocity of mouth opening, velocity of mouth closing, and velocity of hyoid depression decreased with increasing size. Fluid velocity increased with size, and is best predicted by a piston model that includes head width and hyoid depression velocity. Reynolds number increased with size and spanned two flow regimes (laminar and intermediate) ranging from 2 to over 100. Pressure was found to be greatest in the smallest tadpoles and decreased as size increased, ranging from 2 kPa to 80 kPa.The viscosity of the water was altered to explore changes in body size, independent of development (higher viscosity mimicked smaller tadpole size). Viscosity manipulations had a significant effect on the kinematics. Xenopus initially increased velocity and distance of movements as viscosity increased, but these values declined as viscosity increased further. These results suggest that abiotic factors such as fluid viscosity may set a lower size limit on suspension feeding.
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Mode of access: World Wide Web.
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Advisor: Stephen M. Deban, Ph.D.
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Ontogeny
Scaling
Viscosity
Biomechanics
Morphology
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Dissertations, Academic
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x Biology
Masters.
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t USF Electronic Theses and Dissertations.
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u http://digital.lib.usf.edu/?e14.2790