AGE Ai\TD GRO\.JTH OF THE RED GROUPER EPDVEPHELVS ,":iOFIO (VALENCIENNES), FRON THE EASTERN GULF O F NEXICO by Hartin Andreas Noe Jr. THESIS Presented to the faculty of the Departm ent of Zoology of the University of South F lorida i n partial fulfillment of the requirements for the degree of Mas ter o f Arts Unive rsity of South F lorid a April, 1 96 7
AGE AND GROWTH OF THE RED GROUPER, EPINEPHELUS MORIO (VALENCIENNES), FROM THE EASTERN GULF OF MEXICO APPROVED: Supervising professor
TABLE OF CONTENTS INTRODUCTION METHODS AND MATERIALS Procedures Processing of samples Otolith description Otolith counts and measurements RESULTS Age and growth Length-weight relationship Catch composition DISCUSSION SUMMARY LITERATURE CITED APPENDIX I, TABLES APPENDIX II, FIGURES 1 2 3 4 6 7 9 9 . 17 18 19 22 25 30 33
LIST OF TABLES Table 1. Listing of collection data and otolith annuli counts. Table 2. Back-calculated lengths of age groups 1 through 15. Table 3. Listing of empirical lengths, mean weights and calculated weights of red grouper. LIST OF FIGURES Figure 1. Map of the collection areas offshore of the central west coast of Florida. Figure 2. Drawing of the lateral concave and dorsal aspects of a hypothetical 10 year old otolith. Figure 3. Photographs of otoliths from age groups 1, 3, 6, 8, 10, and 15. Figure 4. The relationship of otolith radius to standard length. Figure 5. The relationship of otolith radius and otolith weight to standard length for 128 selected pairs of otoliths. Figure 6. The mean marginal increment of otoliths from age groups 1 through 10 during all months. Figure 7. Vector diagram showing absolute growth of the mean empirical standard length and the mean empirical otolith radius of each age group. Figure 8. Vector diagram showing absolute growth of the mean back calculated lengths and the mean increments o f back calculate d l engths
Figure 9. Walford growth transformation of the absolute empirical growth curve. Figure 10. Walford growth transformation of the calculated growth curve. Figure 11. Frequency histogram of all accurately _aged fish. Figure 12. The relationship of total to standard length. Figure 13. The relationship of length to weight for 205 red grouper. Figure 14. Frequency polygon showing the distribution of standard length of red grouper from the sport and commercial catches. Figure 15. Frequency polygon showing the distribution of age of red grouper from the sport and commercial catches.
INTRODUCTION The red grouper, EpinepheZus mopio (Valenciennes), is one of the most common of the large serranids in the Gulf of Mexico, and composes the major portion of the commercial and sport catch of. grouper on Florida coasts (Jarvis, 1935; Moe, 1963). Of the food fishes landed in Florida in 1965, groupers were ranked second highest in pounds produced (8,446,443 lbs.) and third highest in dockside value ($927,988) according to the Florida landing reports by Jones and Smith (1966). Groupers also form an important part of the food fish resources throughout the Caribbean. Despite their commercial and sport value, knowledge of the life history of groupers is very limited. A brief summary of some of the more important papers contributing to grouper biology within the area of their special significance is included below. Contributions to basic biology and ecology have been made by Bardach (1958a and 1958b), Longley and Hildebrand (1941), Randall and Brock (1960), Smith (1959) and a synoptic treatment of biological data was developed by Smith (1961). Migration and movement of tagged groupers was reported by Randall (1961 and 1962), Springer and McErlean (1962), Topp (1963), B eaumariage and Wittich (1966) and Moe (1966 and 1967). The grouper fishery of Florida has been described by Jars (1935) and Moe (1963). McErlean (1963) investigated methods of .aging gag grouper, Mya tePopePaa miaPoZepis, and contributed to other aspects of the biol_ogy of that species. This study was conducted at the Florida Board of Conservation Marine Laboratory as a part of the r esearch activities of this institution. I Ext end my gratitud e to Mr. Robert M. Ing l e Director o f Research, f o r his
-2-encouragement and aid during the course of the study. My sincere appreciation is given to Mr. Phillip Heemstra for assisting with the field work and to Mr. Arthur Wittich and Mr. Michael Wollam for counting one set of otolith annuli. Harry's Seafood Market and Fisherman's Cooperative Association were the primary sites of collections and my appreciation is extended to the managements of these fish houses for their gracious cooperation. Dr. John C. Briggs of the University of South Florida provided counsel during the study and critically read the manuscript. Dr. Frank E. Friedl and Dr. Joe R. Linton also critically read the manuscript. The major purposes of this paper are twofold: (1) to establish a method for .aging red grouper and provide proof of the validity of the method; and (2) to describe the relationship of age and growth and length and weight for red grouper taken in the sport and commercial catches off the Florida west coast. METHODS AND MATERIALS Since the late nineteenth century, fishes have been aged by counting the marks on various hard parts of the fish. These marks are apparently caused by annual physiological changes in the rate and nature of growth. Such annual check marks occur on the bones and scales of most temperate and arctic fishes and have apparently been observed in some tropical and subtropical species. The annular nature of these check marks is suspect in subtropical and tropical fish because, in colder regions, annual fluctuations in water temperature are considered to be the primary cause of growth rate change. Scales, bones, and otoliths (calcareous concretions of the labyrinth)
-3-may all exhibit growth checks and can be used to determine age. Scales are usually the favored _aging tools as they are easy to obtain and can be visually projected onto a screen for counting and measurement. Three pairs of otoliths, the sagitta, lapillus, and asteriscus, occur in pairs, one on each side, in the labyrinth of teleosts. The sagittae are by far the largest of the three and are the otoliths used in aging of fish. Removal of otoliths is a simple matter of dissection whereas bones must be laboriously cleaned of muscle and cartilage before they can be examined for annuli. The bones most often used in age determination are the vertebral centrum and the large flattened scapular, opercular and branchiostegal bones. Fin rays and spines are also useful in _age.determinations when examined in thin cross section. Otoliths were chosen to determine the _age of red grouper for the following.reasons. Grouper scales are tiny, embedded structures with no visible annular marks and thus are completely inadequate for age determination. Otoliths of the grouper are flattened, leaf-like structures that display readily discernible growth checks under reflected light. Sectioning, grinding, and mounting are not necessary. McErlean's (1963) preliminary work and the clarity of the growth checks eliminated the necessity of working with bones other than otoliths. Procedures: Standard length (SL), total length (TL), weight, otoliths and gonadal tissue were taken from red grouper obtained from the sport and commercial catches off the Florida west coast. Figure 1 illustrates the general areas in which the fish were taken. Sampling was officially begun in October, 1963 and continued on a regular monthly basis until November, 1964. Some incidental samples taken before and after this
-4-period are also included to supplement the data. Table 1 lists each monthly collection which has been used in some capacity in this paper. Collections from the commercial catches were made at the same time each month to obtain.the greatest possible regularity of time inter-vals between catches. Sport catches of grouper were more sporadic than commercial catches and obtaining adequate samples was difficult due to limitations of time and geography; thus the sport catch col-lections were numerically limited and were distributed throughout the month. Otoliths were also collected from fish shipped to Pinellas County from the Florida Keys. These samples were not used in the de-velopment of growth curves since populations of red groupers in the Florida Keys may have different growth characteristics from the west coast populations. The Florida Keys collections were not numerous enough to permit the development of comparative data and were used only in.the development of the proportional relationship between the otolith radius and the standard length of the fish. Miscellaneous col-lections of .juveniles have also been included to provide data on the smallest size ranges. These small red grouper are not usually taken by hook and line and are extremely difficult to obtain. Red grouper taken by trawling in July of 1965 are included in the analysis of age and growth for this reason. Processing of samples: Large numbers of groupers could be handled only when local fish . houses were processing the catches from commercial vessels. Close contact was maintained with both the commercial fishermen and fish house operators and it was possible to make collections at the fish houses and to identify the fishing vessel which produced the catch and the
-5-general locality of capture. The fish were usually kept on ice aboard the fishing vessel for three to five days before landing and in the fish house for several days before dressing. The grouper were always gutted aboard the fishing vessel; how-ever, the gonads were seldom removed during g utting since they are firmly attached to the dorsal side of the body cavity by mesentaries. The fish were filleted at the fish house immediately upon removal from cold storage. The head with the spine and body cavity intact were then obtained for otolith and gonad collections. An effort was always made to secure fish from all size ranges present in the catch. A test series of 25 fish were measured before and after filleting to determine the effect of this operation on SL and TL measurements. When measuring filleted c arcasses, the spine was always lifted slightly above the level of the measuring board by pulling the caudal fin away from the head. The slope of the spinal column then approximated tha t of a fish measured in the round. Variations in SL and T L before and after filleting rarely exceeded 10 mm when this procedure was followed. Measurements after filleting were neither consistently above or below measurements in the round. A standard fish measuring board graduated in millimeters was used to measure SL and TL. Standard length was measured f rom the t i p of the protr ud i ng lower jaw to the posterior edge of the hypural plate at the end o f the spinal c olumn and the total l e n g t h meas u reme n t extended to the longest rays of the caudal fin. Weights o f ungutted fish were obtaine d when e ver possible O t oliths w e r e removed in t he following manner: two cuts w e r e made
-6-in the head with a hacksaw to open the cranium; a vertical cut from the top of the head down to a point just posterior to the orbits, and an oblique cut from the insertion of the dorsal fin to the same point posterior to the orbits. A large, heavy-bladed knife was used to pry out this wedge of tissue and bone and expose the brain. The brain was spooned out and the otoliths were removed with forceps from the otic capsules on the floor of the cranium. All traces of the enveloping sacculus were removed from the otoliths and they were then placed in a numbered vial in either a weak detergent solution (Del-0-Dex) or in water. Upon return to the laboratory, the otoliths were carefully washed and placed with a label into a vial of glycerol for clearing and permanent storage. Otolith description: The otolith (sagittae) of the red grouper is essentially similar to the otolith of the gag, described by McErlean (1963) and the otolith of the snook, Centropomus described by Volpe (1959). It has the general form of a rather thin, elliptical, concave saucer composed of a brittle white material. Each sagitta is a mirror image of its mate. Very little variation in form or size was noted between members o f a pair. The convex surface of each sagitta is oriented toward the central axis of the fish and bears a deep groove, the suZcus acousticus. This groove appears as an opaque scar and a marginal notch on the concave side. The dorsa-posterior quadrant of the sagitta o f mature red grouper is greatly convoluted, which produces an irregular margin in that area. The history of the sagitta is best displayed on the concave side. The kernel point at the center of the sagitta can be seen as a tiny, translucent area surrounded by a dense white ring. This central translucent
-7-area has a tendency to. become opaque in larger otoliths, due to thickening. Broad translucent zones and narrow opaque zones radiate outward from the central core area. The narrow, opaque zones were interpreted as annuli since examination of small individuals indicated that the first narrow opaque zone was formed after the first year of life. Figures 2 and 3 .illustrate the sagittae diagrammatically and photographically. Otolith counts and measurements: The .otolith was immersed concave side upwards in a black-bottomed' watch glass containing glycerol, and then examined by reflected light with a binocular dissecting microscope. Measurements were made with an ocular micrometer. A bright light source was directed on the otolith surface at about a 45 degree angle from the horizontal plane. A plastic lens from a pair.of polaroid glasses was taped over the light source and aided considerably in distinguishing the closely spaced annuli of older specimens. Annuli on each otolith were counted one time by three different biologists. The .otolith was examined a fourth time if the counts did not closely correspond, and if an accurate count could not be determined, an approximate count was recorded. Approximate counts were not used in the determination of growth characteristics but they will have value when reproductive patterns are analyzed. Counts were easily made on otoliths with less than twelve annuli. Difficulty in determining an accurate count was most often encountered with older, thicker otoliths of fifteen or more annuli. The annuli of red grouper otoliths are sharply delimited rings rather than broad zones. This allows ready identification of annual marks, but also masks the presence of false or supernumerary rings.
-8-These false rings are probably caused by the occurrence of poor growth conditions either before or after the period of normal annulus formation. Unseasonal changes in water temperature, scarcity of food, physical injury, and unseasonal sexual development may all alter the normal annual growth patterns. False rings were not difficult to distinguish because they usually had the following characteristics: they occurred very close to a normal annulus, were less distinct than normal annuli, and tended to merge with the more distinct annuli or disappear as they were traced along the otolith. Most of the approximate counts of otoliths of greater than ten annuli were caused by the presence of false rings. Counts along several radii were always made when the annuli of larger otoliths were indistinct. A count was considered approximate when a consistent value could not be obtained from these recounts. Red grouper were placed in age groups corresponding to the number of annuli present on the otolith. The marginal area bracketed and labeled B in Figure 2 is the area of smoothest growth and has a more regular margin than other areas. This was the area from which all counts and measurements were made. It is bounded anteriorly by the marginal notch of the sulc us acousticus and posteriorly by the point of greatest width terme d the latera l projection (area Eon Figure 2). Two measurements were made on all otolith pairs during the third reading. (1) Otolith r a d ius: this measurement was m a d e with an ocular micrometer at 20 X along the line D on Figure 2. One ocular micrometer unit at 20 X equaled 0.0675 mm. This line was chosen f o r t his measurem ent because the symmetry o f various sized otoliths was most consistent in this area. The radial measurement of both otoliths of a pair was
-9-determined and then averaged to obtain one value for each set. Only one otolith was measured if one member of a pair was broken or malformed. Computations were facilitated by expressing the otolith radius in ocular micrometer units rather than the metric equivalent. (2) Marginal increment: this measurement was made with an ocular micrometer at 80 X and usually only on the left otolith of each pair. One ocular micrometer unit at 80 X equaled 0.0171 mm. The area between the outermost annulus and the otolith margin is represented by this measurement. Whenever possible, this measurement was made along the line of radial measurement described above. Occasionally, the marginal increment was measured above or below this point when the margin varied in thickness. Two other types of measurements were made on selected otolith pairs. Two hundred two pairs of otoliths representing age groups 1 through 15 were chosen on the basis of clarity of annuli for use in back-calculation of body length. The radius of each otolith was measured from the kernel point to each successive annulus. Weight to the hundredth of a gram was also obtained for each pair of these otoliths. RESULTS Age and growth: Van Oosten (1929) was one of the first to establish positive cri-teria that must be met before the growth marks on scales or bones can be considered annuli. Succinctly, these are as follows. 1. The scale (or bone) must remain constant in number and identity throughout the life of the fish. 2. The growth of the scale (or bone) must be proportional to the overall growth of the fish. 3. The growth check marks must be formed yearly and at approximately
-10the same time of the year. 4. Body lengths at the time of prior annulus formation calculated from measurements of these existing annuli must be in agreement with empirical body lengths of younger age groups of fish whose ages were determined by the number of annuli present on scales or bones. Use of otoliths as an aging tool fulfills number one above, since otoliths can be found in larval and juvenile fish, and otoliths were present in the smallest red groupers it was possible to examine, 41 mm SL. The relationship of otolith radius to standard length is illustrated in Figure 4. The 1354 dots that compose the scatter plot in Figure 4 were taken from otolith radius and SL measurements of fish from both the regular (central west coast) and the Florida Keys collections. The Florida Keys collections were included to increase the number and range of measurements graphed. The regression lines were derived by the method of least squares and without the use of a computer it was to limit the number of cases used in the calculations. The mean, median, and the median on each side of the center median were determined for the range of values on each ocular micrometer unit (expressed on they axis of Figure 4). This reduced the number of cases involved in the calculations but preserved the central tendencies of the original scatter plot. Red grouper of almost all size ranges are represented on this graph; thus, the relationship of otolith radius to SL can be followed through juvenile ontogeny, maturity, and on into senility. This overall relationship is curvilinear, being slightly sigmoid in expression. This sigmoid
-11-expression is apparently due to unobtrusive changes in the symmetry of the otolith that occur with increasing age. The relative thickness (mass) of the otolith increases with age at greater rate than the linear dimensions of the otolith (as does the weight of the fish compared with body length, Figure 13). This is illustrated by Figure 5 in which the weight and average radius of 128 pairs of otoliths, drawn from age groups 1 through 15, were plotted against standard length. Regression lines and correlation coefficients were calculated for those 94 pairs of values that fell within the area of most rapid and consistent growth. The coefficient of correlation for otolith weight was slightly higher than that for the otolith radius, r=0.971 and r=0.959, respectively. This comparison, illustrated in Figure 5, shows that the growth of the otolith is more directly proportional to the increase in length and weight of the fish than is indicated by just the relationship of otolith radius to standard length. The absolute mean growth increment of otolith radius and standard length for each .age group were plotted on a vector diagram in Figure 7. The range of values for the otolith radii was fitted to the same range of standard length values to allow comparison of growth rates. The rate of growth of the otolith radius was found to be directly comparable to the growth rate of standard length between 200 and 400 mm standard length. The growth rate of the otolith radius then became relatively slower than the growth rate of standard length, although both growth rates retained a proportional relationship to each other. The calculation of regression lines describing the relationship between the otolith radius and standard length (Figure 4) were delimited at the point growth rate change indicated in Figure 7, 430 mm SL,
-12-and at the point of maximum linear growth, about 600 mm SL. The regression line for the 77 dots falling in the range below 400 mm SL is described by the equation Y=9+1.336X, and the equation Y=l4.9+1.137X described the regression line for the 116 dots within the range of linear growth of the otolith radius of fish between 430 mm and 680 mm SL. The regression equation calculated for the combination of both of the groups was Y=l2.6+1.185X. The coefficient of correlation was calculated for all three sets of data (r=0.9867, r=0.9184, r=0.9860, respectively), and in all cases it was great enough to demonstrate a high linear correlation and to establish the proportional increase in otolith radius and standard length. Figure 6 illustrates the mean marginal increment measurement of otoliths from age groups 1 through 10 during all months of the year. The marginal increment measurement is expressed in ocular micrometer units (1 unit equals 0.0171 mm). The accuracy of this measurement declined as the width of the marginal increment decreased, thus _age groups over 10 were not graphed. These series of graphs (Figure 6) show the time of annulus formation for each age group depicted. The younger age groups of 1 through 4 form their annulus earlier in the year, March to May, than the older age groups of 5 to 10, which form their annulus in May to July. This lag in time of annulus formation in older _age groups is probably a reflection of the slower metabolic rate and the shorter growth period of the older large fish. The pattern of annuli formation is readily apparent in these graphs despite the relative sparsity of specimens in the smallest size ranges of the youngest age groups. The time of annulus formation coincides with both the latter part of the spawning season and the inception of
-13-warm summer water temperatures. Annuli were observed to first appear on the anterior edge of the otolith, but were not counted unless they were also in evidence along the delimited radius. Although the per-iod of annulus formation extends from to July, this variation represents the range of annulus formation for all age groups. Annu-lus formation in fish of the same age group occurs in a limited per-iod within the more extended time of annulus formation of the entire population. The preceding data shows that the otolith radius increases in proportion to the length of the fish and that the growth checks on the otolith are formed yearly. It remains to be shown that body lengths calculated from prior annuli agree with empirical body lengths of the same age group. Table 2 presents the calculated lengths o f age groups 1 through 15 derived from radial measurements of all annuli on 202 pairs of otoliths. The direct proportionality formula, including a correction factor, was utilized for back calculation of previous body lengths. This formula is expressed as follows. S I L' = C + (L C) s L' represents the calculate d fish length, S' is the otolith radius to the annulus, the observed fish length is represented by L and the ob-served otolith radius is S. The correction factor, C, is the intercept of the regression line, calculated from the scatter plot of the otolith radius on standard length, with the Y axis. These regression lines are graphically depicted in Figure 4. A correction factor of 9 was used when back calculations were made from fish with an observed length less than 420 mm SL. Fish in the age groups of 1 through 4 fell within this
14-size range. A correction factor of 15 was used when back calculations were made from fish with an observed length greater than 420 mm SL. Fish in age groups 5 through 15 fell into this size range. The correction factor described above was originally developed to compensate for the body length attained by salmon before the formation of scales (Rounsefell and Everhart, 1953). This same correction factor, however, can also compensate for slight changes in proportionality between the growth of the body length and the scale and/or otolith radius. It is necessary to calculate two regression lines, one along each linear portion of the.curve, when the inflection point of the curvilinear relationship occurs toward the center of the curve. If the proportionality is curvilinear along its entire length, a logarithmic transformation must be employed to obtain a linear relationship. Figure 7 illustrates the absolute growth curve formed from plotting the mean of all observed lengths in each age group. The curve levels off sharply at about 625 mm SL after an age of 13 years is attained. The erraticism of the curve from age 18 through age 24 occurs because the curvilinear expression of mean values becomes a scatte r plot o f individual cases as the number of fish in each year class drastically diminishes. Figure 7 also illustrates the growth of the otolith radius on a scale proportional to the standard length scale. The absolute growth curves d erived from the grand averages of bac k -calculate d standard lengths a nd from the mean increments o f back-calculate d lengths are plotted in Figure 8. Only ages 1 through 15 are represente d because the annuli on otoliths of fish older than 15 years w ere too c lose to allow reasona b l y accurate radial measureme nts t o each annulus These growth curves (Figures 7 and 8) are almost identical, and illustrate the close
-15-agreement of empirical and calculated body lengths. Figures 9 and 10 are Walford. graphical growth transformations of the absolute growth curves developed from the empirical and calculated lengths of each age group. Although Ford (1933) was the first to develop this relationship, Walford (1946) first developed graphic.representation (Ricker, 1958). Length at age (n) is plotted along the abscissa and length at age (n+l) is plotted along the ordinate. The result is a graphic transformation of growth curve into a straight line. Representative values must be used to fit the line accurately. Selection of the larger fish in the youngest .age groups will result in abnormally high mean values for these .age groups and the subsequent depression of the left end of the Walford line. Only the points representing the mean empirical lengths of groups 2 .through 17 were used to fit the line in Figure 9 for this reason. The mean empirical length of .age group 1 was not included because it was primarily derived from the larger fish of that .age group, and .age groups above 17 were not included because they greatly deviated from.the established curve. The Walford lines of Figures 9 and 10 were both calculated by the method of least squares. All age groups (1 through 15) used in establishing the back-calculated growth curve, Figure 8, were used in fitting the Walford line in Figure 10. Two constants can be immediately obtained from the Walford line and a line drawn at 45 through the zero point. These constants are (k), the slope of the fitted Walford line, and the asymptotic or ultimate attainable length of the population under the statistically defined conditions of growth. The constant ) represents the asymptote of the. growth curve. The rate of. growth is defined by the constant
-16-(k), for as the value of (k) increases toward 1, the ultimate length is approached at a much slower rate. The constants derived from the Walford transformation of the empirical growth curve were (k=0.8249) and =645.193 mm). The constants derived from the Walford transformation of the calculated growth curve were (k=0.8386) and =671.623 mm). Comparison of these constants demonstrates a very high degree of agreement between the empirical and back-calculated lengths of age groups 1 through 15, essentially the period of major length attainment by the population. The range and distribution of standard lengths in each age group is illustrated by a frequency histogram in Figure 11. All 1176 fish accurately aged in age groups 0 through 24 and 26 are included in this graph. An attempt was made to demonstrate the amount of growth each age group realized throughout the year by coding the time of capture into the histogram. Those fish taken during the six months subsequent to the time of annulus formation, March through August, are represented by clear areas and those fish taken during the six months prior to annulus formation, September through February, are represented by stippled areas. The majority of the largest fish were taken during the latter half of the season in age groups 1 through 6, and biannual growth is clearly evidenced in age groups 1 and 2. After about age group 7, however, genetically and environmentally produced variations in growth rate, coupled with a slowed growth rate, obscure the biannual progression of modal growth. The relationship of standard length to total length is graphically depicted in Figure 12. This r elationship is highly linear and it was not necessary to calculate a regression line. Standard and total lengths
-17-are expressed in both English and metric units to facilitate estimation and conversion of various lengths. Fish of all lengths were plotted until the relationship was expressed over the entire size range present in the collections. The measurements of 215 individuals were utilized. Length-weight relationship: The length-weight relationship of morio is graphically expressed in Figure 13. The red grouper has a typical perciform morphology and would be expected to approximate the cube law relationship (weight increases by the cube of the length), and such is the case. A total of 204 individuals with a weight range of 0.1 to 20 pounds and a standard length range of 100 to 700 mm were used to establish the weight-length relationship. The length-weight equations were calculated from the mean weights of each 50 mm length group. Table 3 lists these empirical length groups, their mean weights and their calculated weights. The close agreement of calculated and empirical weights confirms the accuracy of the equations. The length-weight relationship expressed logarithmically is (logW= + 2.9294 logL) and can be expressed exponentially as (W = 0.2918 L2.9294). The calculated weights are expressed as the curvilinear regression line in Figure 13 and the average weights are represented by open circles in the same figure. Weights and lengths are given in both English and metric units. The expression of this relationship allows the calculation of the coefficient of condition, estimation of either length or weight when only one of these values is known, comparison of the weight-length relationships of different species and different populations of the same species, enters into fishery production computations, and can aid in the selection of the proper mesh size for
-18-fish nets. Catch composition: Figure 14.depicts the frequency distribution of.standard length of all but 9 fish taken from the commercial and sport catches. The otoliths of the 9 fish not included in this graph were very abnormal and radial measurements could not be taken and were omitted for this reason. Standard lengths were arranged in 25 mm groups and plotted on a frequency polygon in Figure 14. Absolute values were plotted rather than percentages since the sample was extensive. The sport catch is.represented by. 250 individuals and the commercial catch is represented by 1014 fish. The commercial catches are composed of fish in.the largest size ranges of the population. This is probably areflection of both the predominance.of large fish in deeper waters and the selection of large fish by commercial fishermen. Conversely, the sport catches are predominantly composed of fish in the small size ranges of the population. This is a a reflection of the predominance of small fish on the near-shore areas frequented by sport vessels. Figure 15 depicts the frequency distribution of _age of all accurately aged fish from the sport and commercial catches. Absolute values were plotted since the data were extensive and the graphic presentation clearly expressed the distribution pattern. The sport catch is represented by 246 individuals and the commercial catch by 880 individuals. Predominantly young fish compose the sport catch while the commercial catch is composed almost entirely of fish in age groups 6 to 15. Moe (1966 and 1967) discussed the depth-size relationship of red grouper evident in tagging data. Fish over 400 mm TL were infrequently encountered on the near-shore areas visited by sport fishing boats and fish
-19-under 500 mm TL were infrequently encountered on the offshore commercial fishing grounds. These size ranges agree well with the distribution of lengths found in the sport and commercial catches depicted above in Figure 14. Moe (1967) found that young grouper tagged on the near-shore sport fishing grounds moved to the offshore commercial fishing grounds after a period of about three years. Previous studies indicated that red grouper on the near-shore areas did not move; however, this conclusion was based on short term tag recoveries. Moe (1966) demonstrated that red groupers on the deep offshore areas moved frequently and extensively. Movement of up to 45 miles with a depth increase of 20 fathoms was recorded. DISCUSSION The annual nature of growth checks on the scales and bones of temperate fishes has long been accepted. Extensive annual variation in water temperature is considered the major causative factor in the formation of these marks. Studies such as the present one demonstrate that the growth checks on the hard parts of certain species of tropical and subtropical fishes are annual in nature, and introduce the possibility that many tropical fish form annual growth marks. The exact physiological basis for the formation of annual growth marks is an important area of investigation that has not yet been fully entered. The structure and composition of t h e otolith has been the subject of extensive research efforts. Carlstrom (1963) summarizes the past work on otolith composition and states that calcium carbonate in the f orm o f arago n ite is t h e principal, i f not only, c r y s t alline compon e n t of teleost otoliths. The specific gravities of two red grouper
-20otoliths were determined by weighing them in air and in water. Spe cific gravities of 1.77 and 1.82 were obtained for these otoliths. These values fall between the specific gravity of calcite (1. 71) and aragonite (1.95), and since the otolith also contains some organic matter (probably about 5 to 15 percent), it is reasonable to assume that the otoliths of red grouper conform to the teleost pattern and are composed of aragonite. The crystalline growth and structure of the otoliths of certain teleosts has been carefully investigated by Irie (1955, 1957, and 1960) using microradiography, electron microscopy, and x-ray diffraction. His work has shown that the otolith grows by the formation of microcrystal grains of Caco 3 on the otolith surface. During periods of slow growth, the micro-crystal grains are formed very slowly and much protein fills the grooves between crystal grains. This type of growth forms the opaque zones of the otolith. During rapid growth the microcrystal grains of Caco 3 are formed rapidly and abundantly and very little protein fills the grooves between these crystal grains. This type of growth forms the translucent zones of the otolith. Significantly, Irie (1960) found that the formation of crystal grains of CaC03 was greatly affected by season even when the temperature and salinity of the rearing water was kept constant. The alternating zones of opaque and translucent growth observed in red grouper otoliths are probably formed in the same manner as described by Irie (1960) in MyLio and LateoLabrax. Walford line plots have not been developed for any other species of Florida fish, thus it is not possible to compare growth rates of various species or different populations of red grouper. This graphic trans-
-21-formation of growth curve can be used to define slight variations growth rates between subpopulations of one species and to compare the growth characteristics of different species. The ultimate length derived from this plot is related to the ultimate yield of the population; thus the growth transformation can be used in the estimation of population parameters and .the effects of exploitation. growth.relationships have been developed for very few Florida marine fishes and for the most part, these studies have not been exhaustive with respect to _age and growth. Broadhead (1958) aged black mullet, from west and northwest Florida by the scale method: Klima and Tabb (1959) aged spotted weakfish, Cynoscion from northwest Florida by the scale method: Klima (1959) _aged Spanish mackerel, ScomberomoPUs from southern Florida by otolith examination: Volpe (1959) _aged snook, Centropomus undeci from southwest Florida by otolith examination (scales were also examined, but the annuli were vague and complicated): Tabb (1961) _aged spotted weakfish, Cynoscion from east-central Florida by the scale.method: Croker (1962) _aged gray snapper, Lutjanus griseus, from south Florida by the scale method: and McErlean (1963) aged gag grouper, Mycteroperca from the west Florida coast by otolith examination. Except for McErlean (1963), none of the above authors utilized a correction factor in back calculation of previous body lengths, and growth curves.were not developed in three of the above studies. None of the above authors distinguished the time of annulus formation for each _age group included in the study. Generally, the time of annulus formation was reported as occurring from December through March for the inshore fish and April through July for the only offshore species
-22-investigated, the. gag grouper. McErlean's (1963) data on time of annulus formation in .age groups 3 and 4 of the gag grouper .agrees well with the time of annulus formation of age groups 3 through 10 of the red grouper, Figure 6. A great variation in the growth rate of individuals in each age group is evident in Figure 11. This variation is probably a result of both genetic potential and environmental conditions. A genetic variation in growth rate potential may have a selection value in a population of fishes. During periods of good environmental conditions, fish with an inherently rapid growth rate would develop faster, mature more quickly, and have greater survival potential than fish with an inherently slow growth rate. However, during adverse environmental conditions, fish with an inherently slow growth rate may be better able to survive and reproduce than their hyperactive cousins. A population with such a genetic variation of growth rates would thus be able to compensate for the vicissitudes of the environment. Future studies with the growth of this species will include determination of the growth rate of transformed males (this species is a protogynous hermaphrodite) and large females, and determination of the growth characteristics of populations in the Florida Keys and the northern Gulf of Mexico. Other aspects of the biology of this species such as reproduction, larval life, ecology, migrations, parasitism, and behavior should also be investigated. SUMMARY The purposes of this paper are twofold: (1) to establish a method for aging red grouper and provide proof of the validity o f the method; (2} to describe the relationships of age and growth, and length and
-23-weight for red grouper taken in the sport and commercial catches off the Florida west coast. Otoliths were used to determine age because the annuli were discernible Without grinding or sectioning and because grouper scales have no annuli. The otoliths of 1425 fish were obtained for this study. Processing of otoliths consisted of cleaning them upon removal from the fish and then placing them in glycerol for storage and clearing. Annuli on each otolith. were counted three times and then examined a fourth time if the counts did not closely correspond. Either an accurate or an approximate .age was assigned to each fish, but only the 1176 fish that were accurately aged were used to establish the relationships of .age growth. An ocular micrometer was used to measure the radius and the marginal increment (distance from the last annulus to the edge of the otolith) of each otolith. Two hundred two pairs of otoliths representing .age groups 1 through 15 were chosen on the basis of clarity of annuli for use in back calculation of body length. The radius of each otolith was measured to each successive annulus and body lengths at the time of prior annulus formation were calculated by the direct proportionality formula, including a correction factor. The relationship of otolith radius to standard length was expressed as a scatter plot and two regression lines were calculated to determine the proper correction factor for the back calculations. Two regression lines were necessary because the overall relationship was sigmoidally curvilinear. Coefficients of correlation were calculated for these data and they demonstrated a high linear correlation, r=0.9867 and r=0.9184, in each case.
-24-The time of annulus formation was determined from the variation of the mean marginal increment of the otoliths from each .age group during all months. The younger .age groups of 1 through 4 form their annulus earlier in the year, March to May, than the older .age groups of 5 to 10, which form their annulus from May to July. A close .agreement was obtained between.the mean empirical standard lengths of each .age group and the mean back calculated lengths of each .age group. growth transformation plots were developed for both the empirical and calculated data, and the constants derived from these plots provide a basis for comparison of the empirical and calculated growth curves. These constants are (k), the slope of the fitted Walford line, and the asymptotic or ultimate attainable length of the population under the statistically defined conditions o f growth. These values were (k=0.8249; k=0.8386) and =645.193 mm; .623) for the empirical and calculated growth curves, respectively. The relationship of grouper was calculated from lengths andweights of 204 individuals. The length-weight relationship expressed logarithmically is (log W= -1.4343+2.9294 log L) and can be expressed exponentially as (W=0.2918 12.9294). The age and standard length distribution of .red grouper from the sport and commercial catches is illustrated on separate frequency polygons. The commercial catches are composed of older larger fish and the sport catches are composed of younger, smaller fish. This distribution is probably a reflection of the predominance of small fis h on the near-shore areas frequented by sport v essels and the selecti o n of large fish by the commercial fishermen.
-25-LITERATURE CITED BARDACH, J. E. 1958a. On the movements of certain Bermuda reef fishes. Ecotogy, 39(1): 139-146. BARDACH, J. E. 1958b. Bermuda fisheries research program, final report. Bermuda Trade Devetop. Board, Hamilton, Bermuda: 1-59. BEAUMARIAGE, D. S. and A. C. WITTICH 1966. .Returns from the 1964 Schlitz tagging program. Fta. Bd. Conserv., Tech. Ser. No. 47: 1-50. BROADHEAD, G. C. 1958. Growth of the black mullet (MUgit cephatus L.) in west and northwest Florida. Fta. Bd. Conserv., Tech. Ser. No. 25: 1-31. CARLSTROM, D. 1963. A crystallographic study of vertebrate otoliths. Biot. Butt., t25(3): 441-463. CROKER, R. A. 1962. Growth and food of the gray snapper, Lutjanus griseus, in Everglades National Park. Trans. Amer. Fish. Soc., 9t(4): 379 -383. FORD, E. 1933. An account of the herring investigations conducted at Plymouth during the y ears from 1924-1933. J Mar. Biot. Ass., t9; 305-384.
-26-IRIE, I. 1955. The crystal texture of the otolith of a marine teleost Pseudosciaerza. JoUI'. Fac. Fish. Animal. Hus. Hiroshinrz Univ., 7,(1): 1-14. IRIE, I. 1957. On the forming.season of annual rings (opaque and translucent zones) in the otoliths of.several marine teleosts. JoUI'. Fac. Fish. Animal. Hus., Hiroshima Univ., Z(3): 311-317. IRIE, I. 1960. The growth of the fish otolith. JoW'!. Fac. Fish.AnimaZ Hus. Hiroshima Univ., 3 (1).: 203-221. JARVIS, N. D. 1935. Fishery for red snappers and groupers in the Gulf of Mexico. Invest. Rep. U.S. Bur. Fish., 26: 1-29. JONES, H. and J. SMITH 1966. Summary of Florida commercial marine landings, 1965. FZa. B d Conserv Fla. Landings Rpt., 1965: 1-61. KLIMA, E. F. 1959. Aspects of the biology and the fishery for Spanish mackerel, Scomberomorus macuZatus (Mitchill), of southern Florida. FZ.a. Bd. Conserv., Tech. Ser. No. 27: 1-39. KLIMA, E. F. and D. C. TABB 1959. A contribution to the biology of the spotted weakfish, cynoscion nebuZ.osus (Cuvier) from northwest Florida, with a description of the fishery. FZa. Bd. Con s erv., T e c h Ser. No. 30: 1-25.
-27LONGLEY,_ W. H. and S. F. HILDEBRAND 1941. Systematic catalogue of the fishes of Tortugas, Florida. Carnegie Inst. Wash., Pub. 535: 1-331. MCERLEAN, A. J. 1963. A study of the age and growth of the gag, Mycteroperca microZepis Goode and Bean (Pisces: Serranidae) on the west coast of Florida. FZa. Bd. Conserv., Tech. Ser. No. 41: 1-29. MOE, M. A., JR. 1963. A survey of offshore fishing in Florida. FZa. Bd. Conserv., Prof. Pap. Ser. No. 4: 1-117. MOE, M. A., JR. 1966. Tagging fishes in Florida offshore waters. FZa. Bd. Conserv., .Tech. Ser. No. 49: 1-40. MOE, M. A., JR. 1967. Prolonged survival and migration of three tagged reef fishe s in the Gulf of Mexico. Trans. Amer. Fish. Soc. (in press). RICKER, W. E. 1958 Handbook of computations for biological statistics of fish populations. Fish. Res. Bd. Canada, Bull. No. 119: 1-300. RANDALL, J. E. 1961. Tagging reef fishes in the Virgin Islands. Proc. Gulf Carib. Fis h. Inst., Fourteenth Annual Sessions 1961: 201 -241 RANDALL, J. E. 1962 Additional recoveries of tagged reef fishes from the Virgin I s l ands. Proc. GuZf Cari b Fish. Inst., Fifteenth Annual Sessions 1962: 155-157.
-28-RANDALL, J. E. and V. E. BROCK 1960. Observations on the ecology of Epinepheline and Lutjanid fishes of the Society Islands, with emphasis on food habits. Trans. Amer. Fish. 89(1): 9-16. ROUNSEFELL, G. A. and W. H. EVERHART 1953. Fisheries science, its methods and applications. John Wiley & Sons, Inc., New York. 444 pp. SMITH, C. L. 1959 Hermaphroditism in some serranid fishes from Bermuda. Pap. Mioh. Aaad. XLIV: 111-119. SMITH, C. L. 1961. Synopsis of biological data on groupers (EpinepheLus and allied genera) of the western north Atlantic. P.A.O. Pish. BioL. 23(1): 1-62. SPRINGER, V. G. and A. J. MCERLEAN 1962. A study of the behavior of some tagged south Florida coral reef fishes. Amer. MidL. 6?(2): 386-397. TABB, D. C. 1961. A contribution to the biology of .the spotted Cynosoion nebuLosus (Cuvier) of east-central Florida. PLa. Ed. Tech. Ser. No. 35: 1-24. TOPP, R. W. 1963. The tagging of fishes in Florida 1962 program. PLa. Ed. Prof. Pap. Ser. No. 5: 1-76.
-29-VAN OOSTEN, J. 1929. Life history of the lake herring (Leuaiahthys artedi LeSueur) of Lake Huron as revealed by its scales with a critique of the scale method. BuZZ. Bur. Fish., 44: 265-428. VOLPE, A. V. 1959. Aspects of the biology of the common snook, Centropomis undeaimaZis .(Bloch) of southwest Florida. FZa. Bd. Conserv., Tech. Ser. No. 31: 1-37. WALFORD, L. A. 1946. A new graphic method of describing the growth of animals. BioZ. BuZZ., 90(2): 141-147.
-30Table 1. Listing of collection data and otolith annuli counts.
TABLE I. Total collection and annuli count data. total no reading approximate accurate collected possible count count H:Lscellaneous 13 5 8 January 1964 64 6 58 February 1964 68 7 61 }!arch 1964 81 10 71 }larch Keys 6 6 April 1964 102 8 94 May 1964 107 14 93 June 1964 108 8 100 June 1965 50 8 42 June Keys 26 1 25 July 1964 lOS 17 88 July 1963 32 4 28 July Keys 14 1 13 August 1964 106 7 99 August 1963 25 4 21 August Keys 28 28 September 1964 102 14 88 September 1963 36 1 6 29 September Keys 13 13 October 1964 101 1 9 91 October 1963 55 4 7 44 f\ovember 1964 52 2 50 November 1963 65 2 7 56 December 1963 66 11 55 Grand Totals 1425 12 152 1261 Regular collection totals 1275 12 137 1126 Keys collection totals 87 2 85 July 1965 collection totals 50 8 42 Miscellaneous collection totals 13 5 8
Table 2. -31-Back calculated lengths for age groups 1 through 15. Both the mean length at capture of the fish used i n back calculation and the mean length at capture of the entire age group are listed in this table. The mean lengths of the fish selected for back calcu-lation were consistently larger than the mean lengths of the entire age group. This may be a result of the selection of otoliths for clarity and regularity of annuli since those fish with the most rapid and regular growth rate would probably have easily counted annuli.
. \BLE II. Back calculated lengths for age groups 1 through 15 .c .c Q) Q) AGE GROUPS OOJ..4 OOJ..40. c :s c :s Q) Q) 0 ..... 0. ..... c ,.... 1 2 3 4 C1! Q) 00 5 6 c (J c C1! C1! ,.... Q) Age Group N Q) Q) 0 00 C1! C1! 1 25 221 210 145 2 21 275 262 139 230 3 21 345 328 156 245 304 4 15 407 385 163 259 323 375 5 15 425 423 166 255 308 368 406 6 15 476 465 180 265 331 377 417 456 7 15 560 487 179 268 329 377 418 459 8 21 529 520 184 283 346 388 423 459 9 12 547 541 179 281 342 383 417 452 10 12 586 563 187 283 352 400 435 469 11 7 620 573 187 269 351 396 441 463 12 7 631 597 184 272 330 374 411 448 13 6 632 621 191 275 331 373 422 457 14 5 642 618 187 284 339 367 401 445 15 5 641 618 180 263 325 359 393 428 . Grand Average of r.llcu1ated lengths 174 267 332 378 417 454 increment 1f Grand Average 93 65 46 39 37 ''e1n increment 91 62 44 38 36 Growth by 174 265 327 371 409 445 t 'L'3n increment = 202 202 177 156 135 120 105
6 7 8 9 10 11 13 14 15 456 459 486 459 494 515 452 479 513 533 469 493 531 558 579 463 508 538 560 590 612 448 484 514 543 572 602 624 457 492 521 543 570 584 605 619 445 470 494 532 552 573 601 621 635 428 462 490 517 538 565 579 600 613 634 454 485 515 541 567 587 602 613 624 634 37 31 30 26 26 20 15 11 11 10 36 32 29 27 25 23 21 18 14 21 445 477 506 533 558 587 602 620 634 655 105 90 75 54 42 30 23 16 10 5
-32-Table 3. Listing of empirical lengths, mean weights, and calculated weights of grouper.
TABLE III. Listing of empirical lengths, mean weights and calculated weights Number of fish empirical length mean weight calculated weight nnn inches grams lbs grams lbs 4 125 4.9 57 .13 60.08 .13 6 175 7.0 162 .36 160.9 .35 34 225 8 9 349 .77 336.2 .74 27 275 10.8 663 1.46 604.9 1.33 32 325 12.8 1005 2.22 987.2 2.18 26 375 14.8 1444 3.18 1501 3.31 14 425 16.7 2122 4.68 2166 4.78 25 475 18.7 2948 6.50 3000 6.62 17 525 20.7 3812 8.40 4022 8.87 10 575 22.6 5125 11.30 5251 11.58 6 625 24.6 6900 15.22 6704 14.78 3 675 26.6 8617 19.00 8397 18.52
-33-Figure 1. Map of the collection areas offshore of the central west coast of Florida. Red grouper obtained for this study were taken within the area delimited by the heavy solid line, and the vast majority of these were taken north of the heavy broken line. The sport catch was obtained almost entirely from areas within 15 fathoms and the commercial catch was usually taken from areas offshore of 15 fathoms.
0 0 0 CX) N 0 0 0 ,._ N
-34-Figure 2. Drawing of the lateral concave and dorsal aspects of a hypothetical 10 year old otolith. The long axis of the otolith is about 20 mm. The suZcus acousticus is indicated by (A). (B) represents the area of smoothest, most consistent growth where the annuli were most easily counted. The first annulus is shown within the lines (C). (D) demarks the line of measurement of the otolith radius, and (E) brackets the lateral projection or widest point of the otolith.
LEFT OTOLITH OF E PINPHELUS MORI 0 (I 0 YEAf\S) ANT\IOA J B c VIEW DORSAL VIEW
-35-Figure 3. A. Otolitm (9.5 mm long) from a fish in age group 1. Note the large marginal increment. The second annulus is just beginning to appear on the anterior tip of the otolith. B. Otoliths (13.5 mm long) from a fish in age group 3. C. Otoliths (15.0 mm long) from a fish in age group 6. D. Otoliths (16.3 mm long) from a fish in age group 8. E. Oto liths (19.0 mm long) from a fish in age group 10. Note the abnormal formation of the sulcus acousticus of the left otolith. F. Otoliths (19.0 mm long) from a fish in age group 15. G. Otoliths from a fish in age group 15 showing both concave and convex surfaces. Note the sculpturing of the lateral convex surface.
A c D
E F G
-36-Fi&ure 4. The relationship of otolith radius to standard length. The squares represent the mean of all SL measurements along each ocular micrometer unit of otolith radial measurement. The circles represent the central median and the median on each side of the central median of all SL measurements along each ocular micrometer unit of otolith radial measurement (only the center median is expressed when less than 10 SL measurements occurred on any one unit of otolith radial measurement). These mean and median values were the points used in calculation of the regression lines.
4 mm Otolith Radius in mm and micrometer units 3mm 0 0 100 Standard Length in mm ,0 o. N=77 Y=9+1.336X r=0.9867 I 0 ''I' ''''I & ;0 I ' 'I Q "' :- .. p 0 G& : O .... "!-o-;..(>0: ... -. -,QI :I (J. e . Total Nl354 N= 116 Y=I4.9+1.137X r= 0 9184 N=l93 Y=l2.6 + 1.185 X r=0.9860 0 e-w e ... D 1!1 Iii D 0 0
-37-Figure 5. The relationship of otolith radius and otolith weight to standard length for 128 selected pairs of otoliths. Regression lines were calculated for those 94 pairs of values that occurred within the area of greatest linear growth.
7 6 4 3 otolith radius in mm 100 SL in mm 0 0 Y= 17. 8 + 1.075 X r=0.959 0 0 N=94 l 400 N=34 0 0 0 0 0 : :. Y=37. 2 + 1.932 X r=0.971 500 1.3 : 0 0 0 0 q, 9o 41 a i %% 0 8> 0 0 0 0 0 0 0 in grams 600 700
-38-Figure 6. The mean marginal increment of otoliths from .age groups 1 through 10 during all months. The f .igure by each monthly value indicates the number of fish contributing to the mean. Missing monthly means are bypassed with a broken line. Ocular micrometer units are expressed along the ordinate. One ocular micrometer unit equals 0.0171 mm; .thus 5 units equal 0.0855 mm, 10 units equal 0.171 mm, and 25 units equal 0.4275 mm.
55 6 2 ocular micrometer units 2 7 I I I 4 I I 23 / age group I N=48 2 age group II N=69 Jan. Feb. Mar Apr. May June July Aug. Sept Oct. Nov Dec
7 20 6 0---20 ocular micrometer units 4 Q \ \ \ \ \ \ \ \ \ \ \ 3 age group m N=59 age group Til N=63 age group Il N = 42 8 2 7 D 6 Jan Feb. Mar Apr. May June July Aug Sept. Oct. Nov. Dec.
I 5 6 8 J 10 2 7 18 4 7 J 1 0 5 J F M A M 4 5 age group 3ZI N=58 age group N = 135 age group N=l63 age group N =157 J J age group N =122 A X s II 14 1 0 --8----o 8 II 0 N D 1 0 5 Jan. Fe b Mar. Apr. May June July Aug. Sept. Oct. N o v Dec.
-39-Figure 7. Vector diagram showing absolute growth of the mean empirical standard length and the mean empirical otolith radius of each age group. The figure by each point on the curve indicates the number of fish contributing to the mean. One ocular micrometer unit equals 0.0675 mm; thus 30 ocular micrometers equal 2.025 mm, 50 units equal 3.375 mm, 80 units equal 5.400 mm and 100 units equal 6.750 mm.
700 122 157 163 135 SL 1n mm Age 3 6 100 3 44 90 27 45 ,. . 80 ... 70 60 N= 1170 50 growth curve from mean S L of each age group growth curve from mean otolith radius of each age group otolith radius 40 30 in ocular micrometer units 2 3 4 5 6 7 8 9 10 II 12 13 1 4 15 16 17 18 19 20 21 22 23 24
-40Figure 8. Vector diagram showing absolute growth of the mean back-calculated lengths and the mean increments of back-calculated lengths. Age groups 1 through 15 are represented in the back calculated lengths.
700 SL in mm Age growth curve from mean back calculated lengths growth curve from mean increments of back calculated lengths 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20
-41-Figure 9. Walford growth transformation of the absolute empirical growth curve. Only those points connected by solid lines (derived from age groups 2 through 17) were used to fit the Walford line. Age groups 1 and 18 to 24 were not used because they were not truly representative of the population.
700 600 500 400 SL at age N -t-I 300 200 100 SL at age N 100 200 300 k=0.8249 400 0 Joo =645.193 Wolford growth transformation for absolute growth curve 500 600 0 0 700
-42-Figure 10. Walford growth transformation of the calculated growth curve. Age groups 1 through 15 are represented.
700 600 500 400 SL at age N +I 300 200 100 100 200 S L at oge N 300 k =0.8386 400 Wolford growth transformation plot for calculated growth curve 500 600 700
-43-Figure 11. Frequency histogram of all accurately aged fish. Age groups 0 through 24 and 26 are represented.
0 H PI a. a. a. a. a. 0. :::J :::J :::J :::J :::J :::J 0 0 CX) e (1) 0 (1) 0 ,., 0 C\J t;,LO .... v (l) t;,LO .... .... 01 01 01 (l) 01 v II II II II II II IDZ II) z Cl> z Cl> z Q) z 01 01 D' D' D' 0 0 0 0 0 0 10 10 10 0 10 10 0 10 10 0 10 10 0 10 a. a. :::J :::J I() 0 CX) 0 t;,LO .... ,., 01 II II II) z D' 0 0 0 10 10 0 10 a. :::J ,., 0 .... (l) 01 II Q) z D' 0 g. :::J <( D' :::J 0 .... u .... 0 :E ,n c: u II) 0 u 0 .0 Q) 1.1.. D' :::J 0 .... a. Q) (J) ,n c: 0 u .!! 0 u L] 10 2 10 ...1 c:E en E
-15 age group lX -10 N= 157 -5 n age group X N= 122 -15 -10 -5 age group ::xr N=45 1-10 f-5 _R_flt rt--.. ..JJ::I .R,.,n age gro'up :xrr N=27 -10 -5 .n.. Fl .r::::l age group :xm -10 N=44 5 ,..I:Il!TI ,,... _,..... ,..... -10 age group :x::I2: -5 N=54 age group ::x:l[ '-5 N=26 J"-,. n f-5 age group Xlli N=26 -R::rll= f-5 oge group m N=14 r--5 age group m N=6 -n.....-. r--2 age group XIX N=l r---2 age group :XX N=3 -= r-2 age group XXI N=3 r>-2 age group ::x:x:n: N=3 -2 a g e group :x::x:rrr N=l -2 age group m N= I -2 f requency age group :xx'ili N= I 0 collections, March through Aug. SL m collections, in Sept. through Feb. mm oooooooooooooooooooooooooooooooooooooooooo
-44-Figure 12. The relationship of total to standard length. Lengths are represented in both English and metric units.
_25 _15 Total Length 10 . . Inches 15 mm l100 . .... : lzoo .. .... .. r .. .: .. Standard LenQih 115 1300 1400 ,-: ,I' ... .. : ....... : : N =215 .. ... . ...... : :: : ... t ... ... . ...
-45-Figure 13. The relationship of length to weight for 205 red grouper. One specimen, over 700 mm SL, was not included in the calculations. Lengths and weights are expressed in both English and metric units.
-201bs 9000 gm -19 lbs -18 lbs 8000 gm 17 lbs -16 lbs 7000 gm -15 lbs 6000 gm -131bs -12 lbs 5000 gm II lbs -10 lbs 9 lbs 4000gm 8 lbs 7 lbs 3000 gm 6 lbs 5 lbs 2000 gm 4 lbs 3 lbs weight 0 2 1 SL in mm 2 2 2 3 2 4 log W = -1.4343 + 2 9292 log L . .. ,.. 10" 15" I I 1200 1250 1300 1350 1400 1450 2 5 2 6 2 7 2 8 log length, m m "' 3 0 I]_ 1. o N=205 0 indicates mean weight of each 50 mm length group calculated length-weight curve W=0.2718 L 2 '9292 20" 25" 28" I I I lsoo 1550 lsoo 16so 1700 1750
-46-Figure 14. Frequency polygon showing the distribution of standard length of red grouper from the sport and commercial catches. The sport catch is represented by 250 individuals and the commercial catch is represented by 1014 individuals.
130 frequency S L in mm N= 1264 Total catch Commercial catch Sport catch A. ', : / ... .. ...... ... ', ... .. ... ,. ', ........ ... __ .,.. . . ... ...._ _____ .... -.....
-47-Figure 15. Frequency polygon showing the distribution of age of red grouper from the sport and commercial catches. The sport catch is represented by 246 accurately aged individuals and the commercial catch is represented by 880 accurately aged individuals.
N =ll26 Total catch Commercial catch Sport catch