Aspects of Growth in Captive Killer Whales (Orcinus Orca)

MARINE MAMMAL SCIENCE, 16(1):110-123 (January 2000) 0 2000 by the Society for Marine Mammalogy zyx zyxw ASPECTS OF GROWTH IN CAPTIVE KILLER WHALES (ORCINUS ORCA) STEVEN T. CLARK DANIEL K. ODELL C. THADLACINAK zyxw zyxwvu zyxwvuts zyxwv Seaworld, Inc., Corporate Zoological Operations, 7007 SeaWorld Drive, Orlando, Florida 32821-8097, U.S.A. E-mail: steve.clark@anheuser-busch.com ABSTRACT Morphometrics from 25 captive killer whales (1 1 captive-born) were collected at SeaWorld parks from 1984 to 1995 to determine age-specific growth parameters. For sexes combined, the body-volume index was the most accurate predictor of body weight. However, predicting weight from total length was appropriate, although it may underestimate weight of pregnant animals. Among captive-born calves, a Gompertz model was the best predictor of weight and length at age. Estimates for length and weight at birth were done using data from in utero and neonatal calves. For ages 1-5 yr, models indicate that males grew in both weight and length at slower rates. Growth rates in males may surpass those of females at approximately 5-6 yr of age. Key words: cetacean age and growth, Gompertz, body-volume index, captive cetaceans. Documentation of growth rates for free-ranging killer whales (Orcznus m a ) is an important part of understanding their life history. Any study intending to document growth rates has two basic components. There must be some accurate determination of size (e.g., body length or weight) and age. In general, among odontocetes, counting dentinal growth layer groups (GLGs) is one of the methods by which age is estimated (Kasuya et af. 1974, Perrin et af. 1976, Lockyer 1978, Perrin and Henderson 1984, Myrick et af. 1988, Hohn et af. 1989, Read et af. 1993, Amano et af. 1996, Fernandez and Hohn 1998) and has been used in killer whale studies as well (Christensen 1982, 1984). Photogrammetric analyses (Bigg 1982, Heimlich-Boran 1986) or information gathered during whaling operations can be used to determine killer whale size and estimated age through allometric relationships (Tomilin 1957, Nishiwaki and Handa 1958, Olesiuk et af. 1990, Guinet and Bouvier 1995). All of the methods described have their limitations and may be subject to 110 zyxwvutsrq zyxw zyx CLARK ETAL.: KILLER WHALE G R O W T H 111 bias, most likely due to the difficulties in gathering information from wild marine mammals (Anderson and Fedak 1987, Gales 1989, Deutsch et af. 1990). The analysis of GLGs may be biased depending on the skill and expertise of the investigator (Hohn 1990). Gathering information about allometric growth rates through photogrammetric techniques requires predictions from structures visible to the investigator and assumes allometric growth between these structures. Finally, since the focus of many whaling operations was not necessarily scientific in nature, data such as length, weight, and sex may have been occasionally misinterpreted and samples of teeth (for GLG analysis) may have been lost. Gathering accurate age, growth, and allometric information from wild populations of killer whales is difficult. Thus, analyses of data from captive populations can provide a valuable tool to add to our knowledge of life history parameters of killer whales and other odontocetes (e.g., Kasuya et af. 1986, Duffield and Miller 1988). zyxwvu zyxwvut MATERIALS AND METHODS SeaWorld parks have maintained killer whales since 1965 (Duffield et af. 1995). Data for this study were collected through December 1995 on 25 animals (16 females, of which 7 were captive-born; 9 males, 4 captive-born). Because the exact birth dates of the captive-born animals are known, a time series of their size-at-age may be used to establish baseline growth patterns for their wild counterparts. Animals of unknown age were used to compute allometric relationships between weight and body-volume index and between weight and total length. As part of Seaworld’s husbandry program, all animals were measured at 24-wk intervals, at which time a suite of 11 measurements (based on Norris 1961) was recorded. Weights were collected approximately monthly by having whales slide out onto a hydraulic scale (Model 747-915-40; Emery Winslow Scale Company, Seymour, CT). The parameters total length (TL), girth at the anterior origin of the dorsal fin (GAODF), and body weight were analyzed. A body-volume index (BV), originally developed for Steller sea lions (Ewzetopias jabatus) (Castellini and Calkins 1993), was calculated using the formula: BV = T L X (GAODF)2. Linear relationships between body weight and BV were explored. All analyses involving age were carried out only for the captive-born killer whales. Numerous models have been suggested to describe growth as a function of age. We tested the von Bertalanffy, logistic, and Gompertz models in attempts to characterize growth. Due to the prevalence of the Gompertz model in cetacean age and growth studies (Perrin and Henderson 1984, Doidge 1990, Read and Gaskin 1990, Read et af. 1993, Ferrero and Walker 1995, Fernandez and Hohn 1998) and its appropriateness for this particular dataset (as indicated by analysis of residuals), we used it as well to allow for interspecific comparisons. The model used follows Fitzhugh (1975): zy WT or zyxw T L = Winf or LinfX [exp(-6 X exp(-k X t))] 112 zyxwvutsr zyxwvut zyxwvu zyx zyxwvuts zyxwv zy MARINE MAMMAL SCIENCE, VOL. 16, NO. 1, 2000 where WT or TL is the weight or total length of the animal, W,nfor Linfis the asymptotic weight or length growth value for this particular dataset, exp is the natural logarithm, b is the integration constant, k is the growth rate constant, and t is age (in days). Model-predicted weights and total lengths were used to evaluate sexual differences in growth rates. Only ages 1-6 yr were used for this comparison, as the oldest known-age male in the dataset was 6 yr old. The difference between weight or total length at 6 yr and 1 yr of age was then divided by 5 (the number of yearly intervals) to obtain an approximation of the overall mean yearly growth rate during this time period. Analyses to estimate weight and length at birth were based upon a smaller dataset (n = 4 ) of three in utero calves before or at term and one calf that died at 11 d of age. Weight and length at birth were estimated directly from the model by substituting an age of 0 d into the equation; therefore, there was no variance associated with this estimate. The Gompertz model begins describing growth at conception (Laird et al. 1965, Jolicoeur et al. 1992). Hence, this allowed us to use developmental ages (evaluated as minus days of age; e.g., a calf estimated at three days prior to birth would have an age of “ - 3 ” ) calculated from determination of estimated time of conception through analysis of female serum progesterone data (Walker et al. 1988, Duffield et al. 1995) of the three in utero calves as age variables in order to determine growth parameters. Due to the small size of our dataset (two males and two females), sexually dimorphic differences in weight and length at birth were not evaluated. This study is unique in that it includes a mixture of cross-sectional (size of all animals in a dataset at particular ages) and longitudinal (multiple measurements of individual animals over a period of time) dimensions. To deal with this combination of data types we used a technique employed recently in a study which contained similarly mixed data (Read et al. 1993) and described in Sokal and Rohlf (1995) as jackknifing. Specifically, the jackknifing technique is a non-parametric approach to obtain model parameter estimates from a mixture of longitudinal and cross-sectional data. It consists of separating the dataset into categories, removing a particular category, then estimating model parameters on the reduced dataset. The previously removed category is then replaced and another category of data is removed. Read et al. (1993) separated their dataset into categories of size. In this study, categories were based on individual animals. Model parameters were initially obtained for the entire dataset of all animals, then a particular animal’s data (e.g., animal 7806) were removed, the model was run again, the removed animal’s data were replaced, another particular animal’s data were removed and the model was run again. These iterations produced parameter estimates which are used to calculate pseudovalues for each model run by the formula: pseudovalue = n * St - (n - 1) * Sr-l; where n is number of categories in the dataset, St is the parameter estimate based upon the entire dataset, St-l is the parameter estimate based upon the dataset minus the removed animal’s data. Pseudovariances associated with parameter estimates from each model run were calculated by the formula: pseu- zyxwvutsrq zyxwvuts zyxwvut CLARK ET A L . : KILLER WHALE G R O W T H 113 dovariance = (pseudovalue obtained from a particular run - average of all pseudovalues from the entire dataset)*. Overall parameter estimates and variances were calculated by averaging the pseudovalues and pseudovariances from each model run. Standard errors and 95% confidence limits were determined from the overall variances (Sokal and Rohlf 1995). All analyses presented in this study were done using the SYSTAT statistical package (version 6.1 for Windows, SPSS, Inc., 1996). RESULTS In the analyses of weight and total length at age, models were determined from datasets containing in excess of 250 and 1,000 data points, respectively. In order to minimize confusion in App. Fig. 3-5, average weights and total lengths at various age intervals were plotted. Plots of individual trajectories and Gompertz parameter estimates of growth in weight and total length for all captiveborn calves are provided in the appendix. Body volume index and weight-A linear relationship existed between body weight and body volume index (r2 = 0.99) (Table 1, App. Fig. 1). The gap in data between -70 and 80 m3 is due to the fact that few animals in the SeaWorld collection were in this size range at the time of these analyses. Most were older individuals of unknown age or smaller animals (known-age, captiveborn calves) that had not yet achieved that size. Totul length and weight-The relationship between body weight and total length was exponential (r2 = 0.97) (Table 1, App. Fig. 2). The poorer fit with animals at total lengths 1 3 5 0 cm was probably due to the limited data at these smaller sizes. In order to investigate the possibility that the data from the three in utero and one neonate calves exerted a degree of leverage on the curve, dragging it downward, models were run after removing these animals. The results of these reduced models did not significantly change the model parameter estimates. Age and weight-Weight-at-age was described by a Gompertz relationship (r2 = 0.90) (Table 1). Analyses of the dataset of calves <6 mo of age places weight at birth at 153.8 kg. Separate curves were fitted for males and females (Table 1, App. Fig. 3). For ages 1-6 yr, males grew slower than females (182.0 kg/yr us. 247.9 kg/yr, respectively). Among males, closer inspection of Appendix Figure 4 revealed what may be an accelerated growth rate somewhere between 5 and 6 yr of age for the only captive-born male that was that old. Examination of length at 6 yr of age for this animal revealed that it was clearly outside the estimated 95% confidence intervals for asymptotic weight in Table 1. Age and total length-A Gompertz function was used to describe the relationship (r2 = 0.90) between age and total length (Table 1). Direct computation from the dataset of calves <6 mo of age yielded an estimated length at birth of 232.6 cm. Males grew more slowly than females for ages 1-6 yr (27.7 cm/yr us. 36.0 cm/yr). However, as is evident in Appendix Figure 4 (and similar to App. Fig. 3), male growth rate appeared to increase at about 5-6 yr of age and may have became greater than the female growth rate as the zyxwvut 114 zyxw zyxwvuts MARINE MAMMAL SCIENCE. VOL. 16. NO. 1. 2000 Tabk 1. Jackknife estimates, standard errors, and 95% confidence intervals for allometric and growth equations for captive killer whales at SeaWorld parks. zyxwvuts zyxwvu zyxwv zyxwvu Parameter estimates Equation 95% confidence intervals Standard errors Body volume index (m3)and weight (kg) b, * body volume index weight = 6, bo - 109.7 10.5 bl 43.2 0.3 Total length (cm) and weight (kg) weight = a * total lengthb a 6.0-(j 2.3-6 b 3.2 0.4 Age (days) and weight (kg) weight = W,nf* lexp (-b * exp)(-k * age))] sexes combined (>6 mo) W,"f 3,097.4 883.1 b 2.0 1. o - 2 k 5.0-4 2.0-3 sexes combined (<6 mo) Wt"f 313.2 23.6 b 0.7 8.0-* k 1.0-2 4.0-? males (6 mo-5 yr) W'"f 1,225.9 52.3 b 1.3 0.1 b 2.0-3 3.0-3 females (all ages) W,"f 2,763.0 273.6 b 2.3 0.2 k 7.0-4 1.0-4 Age (d)and total length (cm) total length = L,,, * lexp(-b * exp(-k * age))] sexes combined (>6 mo) L1nf 552.6 11.4 b 0.8 3.0-' k 1.0-3 1.0-3 sexes combined (<6 mo) Lmf 347 .O 261.7 b 0.4 0.7 k 4.0-3 4.0-3 males (6 mo-5 yr) L,nf 413.3 8.0 b 0.6 0.1 k 3.0-? 5.0-? females (all ages) Lmf 544.2 9.6 b 0.8 3.0-' 1.0-3 1. o - 3 k + (- 131.5)-(-87.9) 42643.7 1.2-6- 10.8-6 2.4-3.9 zyxwvut 1,153.7-5,04 1.1 1.8-2.3 9 .0-5-8. 2-4 238.1-388.3 0.2-4.7 (- 2.7-3b2.3-2 1,080.7-1,371.1 1.O-1.7 1.2 ?-2 - zyxwvut 2,132.1-3,393.9 1.8-2.8 7.7-4-1.2-3 5 27.4-577.7 0.7-0.8 5.0-4-1.0-3 (-485.7&1,179.7 (- 1.8b2.6 (-8.7-3b1.7-2 391.0-435.5 0.3-0.9 1.6-?-4.4521.5-566.9 0.7-0.9 1.2- 3-7 .6- zyxwvutsrq zyxwvuts zyxw CLARK ET A L . : KILLER WHALE G R O W T H 115 average total length at age 6 was greater than the 95% confidence intervals computed for asymptotic length in Table 1. DISCUSSION zyx zyxw zyxw For the captive killer whales in this study, the body-volume index is an accurate predictor of weight. This is useful because of the logistic difficulties of obtaining weight data from animals (alive or dead) in the field or in oceanaria. Determining girth of a live animal in the field is difficult, and a relationship which predicts weight from a variable that is more easily measured (e.g., total length) is necessary. However, a problem may arise when attempting to estimate the weight of female whales that might be pregnant. As would be expected, pregnant killer whales increase in girth up until parturition, rapidly declining following birth of the calf (App. Fig. 5). Therefore, using only total length as a predictor of weight could yield an underestimate. The use of the body-volume index would eliminate this problem and should be used to estimate weight of killer whales (particularly adult females) when practical. Up until the age of 6 yr, rate of growth in total length for male and female captive-born animals was similar to that estimated by Bigg (1982) (37 cm/ yr) for a similar time period in wild eastern North Pacific animals. Likewise, Duffield and Miller (1988) estimated growth rates of 21 and 39 cm/yr for wild-caught captive killer whales of Atlantic origin (their analysis supported separating North Atlantic killer whales into two groups) and 38 cm/yr in captive animals from the North Pacific. The contrasts seen in growth rates among the animals in this and previous studies may be attributable to a variety of factors including, but not limited to, differences in nutrition, energy requirement, overall health, genetic background (the genetic origin of our captive-born calves is almost exclusively Iceland), and/or parasite load. We found for ages 1-6 yr that the male growth rate was lower than that for females. This is in contrast to Christensen (1984, fig. 4), who appears to have suggested that growth rates of male and female North Atlantic killer whale are similar up to about 15 yr old. However, comparing this work to our results may be misleading, as the regression line was fit by eye and does not contain any males between the ages of 2 and 8 yr (an important time frame in our study). Overall, Seaworld’s male killer whales grew at slower rates in weight and length than females, at least up until about 5 or 6 yr old. The greater weights and total lengths of males seen in Figures 4 and 6 may be the result of greater birth weights and lengths. Our inadequate dataset of animals <6 mo of age did not allow this to be examined. Clearly, the magnitude of increase in the male curves in both figures began to decrease (or decay) more rapidly than in females. If these trends continued, males would end up shorter and lighter than females. How can we explain the overall greater weight and total length of adult male killer whales at SeaWorld parks (t-test, weight: t = 5.61; P < 0.01, total length: t = 3.98; P < O.Ol), as well as among adult males examined in studies of wild populations (Fraser 1934, 1938; Nishiwaki and 116 zyxwvutsr zyxwvu zyxwv zyxwvuts MARINE MAMMAL SCIENCE. VOL. 16. NO. 1. 2000 Handa 1958; Mikhalev et al. 1981, Ivanshin 1981, Christensen 1984, Duffield and Miller 1988) (Table 2)? Several investigators have reported an adolescent male growth spurt in length in odontocetes (Best 1970, Cockcroft and Ross 1990, Read et al. 1993). For North Atlantic killer whales, Christensen (1984) reported this growth spurt at -550-610 cm total length, which corresponds to an estimated age of 15 yr (based upon GLG counts). None of our known-age males have reached these lengths or age. An adolescent growth spurt may also account for the differences seen in the relationship between age and weight of adult males and females. What may be an accelerated growth rate in our oldest captive-born male is presumably too early to be considered an adolescent growth spurt, as this animal was just 6 yr old at the time of these analyses. Due t o the limited sample size (only one animal), precise growth modeling beyond 5 yr of age in males was inappropriate. Since this animal’s weight and total length at this age were clearly outside the asymptotic weight and length 95% confidence intervals, it was reasonable to assume that a significant change in growth rate may have occurred. Confirmation of this will only be substantiated by further data collection. However, the apparent increase in growth rate a t approximately 5-6 yr of age was noteworthy. Perhaps growth spurts in maturing male killer whales are not limited to a single event; indeed, organismal growth appears to be a complex mixture of varying growth rates throughout ontogeny (Laird 1967). Alternatively, since this animal was not born a t a SeaWorld park and was not obtained until it was approximately 3 yr old, this increase in growth may be related to its dietary or health history. Duffield and Miller (1988) provided an alternative explanation for the attainment of larger sizes in male killer whales. They did not find accelerated male growth in total length upon reaching reproductive maturity; they suggested that the overall larger size reached by males was because they continued to grow after female growth had ceased. They suggested that the point at which growth rate decreases is different for males and females, with male growth slowing at about 12-16 yr and female growth slowing earlier, somewhere around 9-12 yr. Similar results have been described for other odontocetes (Read et al. 1993, Read and Tolley 1997). As the captive-born male killer whales get older, it will interesting to observe whether they exhibit either an adolescent growth spurt or continue to grow steadily after female growth has ceased. In spite of the lack of data, model-calculated length at birth (232.6 cm) was within the range of estimates reported by other investigators (range: 213244 cm; Fraser 1934, Scheffer and Slipp 1948, Jonsgird and Lyshoel 1970, Bigg 1982, Perrin and Reilly 1984, Heimlich-Boran 1986, Duffield and Miller 1988, Olesiuk et al. 1990), but shorter than the 274 cm reported by Nishiwaki and Handa (1958). Further work should attempt to obtain data from animals less than 6 mo of age to refine estimates of the age and growth parameters. Upon examining the models, it was apparent that the gap in data between birth and 6 mo was significant. There is a consistently poorer fit at smaller sizes (weight and length) and lower ages (<6 mo) (Fig. 2, 3, 5). Growth during the first 6 mo zyxwvu zyxwvutsrq zyxwvut zyxw CLARK ETAL.: KILLER WHALE GROWTH 117 118 zyxwvutsr zyxwvu zyxwv zyxwvu MARINE MAMMAL SCIENCE, VOL. 16, NO. 1, 2000 must be substantial in order to reach the sizes predicted by the model from the birth sizes estimated. Specifically, the larger size of 6 mo-old males, in spite of a growth rate from 6 m o to 5 yr of age that was slower than that of females, suggests that either males were born and remained larger than females at least until 2 yr old or that growth in males from birth to 6 mo was greater than i n females. These are questions that can only be examined as data on the first 6 mo of growth become available. Information gained from this study may be useful in validating allometric relationships used by investigators in field studies. For instance, HeimlichBoran (1986) correlated blowhole-to-dorsal-fin-tip length with total length in order to provide a predictor of total length from photogrammetric information. Future captive-born calves will afford us the opportunity to examine this relationship more closely. Heimlich-Boran (1986) and Olesiuk et a/. (1990) examined change in the height-to-width (width = base length) ratio of the dorsal fin as an indicator of male sexual maturity, a relationship that should be examined in captiveborn males as they enter puberty. In conclusion, because of the logistic problems involved with obtaining accurate estimates of age and size from wild animals, age and growth parameters from captive killer whales may provide significant insight into their life history. In spite of the likely influences of genetics, differences in nutrition, parasitic infestations, energetics, prey availability, and various other environmental conditions between captive animals and wild animals, the models presented provide baseline information for examining the dynamics of age and growth in captive and wild killer whales. ACKNOWLEEMENTS We would like to extend our thanks to C. Tompkins, T. Turner, D. Force, and M. Scarpuzzi of the animal training staff at the SeaWorld parks in California, Florida, Ohio, and Texas for the collection of data. Additionally, our appreciation is extended to Bruce Ackerman, Douglas DeMaster, Deborah Duffield, Ronald Kastelein, John E. Reynolds 111, and Randall Wells for review of an earlier draft of this manuscript. N6lio B. Barros is all-deserving of thanks and appreciation for his careful editing of manuscript drafts and insightful comments pertaining to its science. Thank you to Megan Stolen for the many discussions dealing with growth models and her constant support. Finally, we are appreciative of comments on an earlier version of this manuscript from R. Ferrero and an anonymous reviewer. This is SeaWorld technical contribution No. 9603-F. LITERATURE CITED AMANO, M., N. MIYAZAKI AND F. YANAGISAWA. 1996. Life history of Fraser’s dolphin, Lagenodelpbis bosei, based on a school captured off the Pacific coast of Japan. Marine Mammal Science 12:199-214. S. S., AND M. A. FEDAK.1987. The energetics of sexual success of grey ANDERSON, seals and comparison with the costs of reproduction in other pinnipeds. Symposium of the Zoological Society of London 57:319-341. zyxwvutsrq zyxwv zyxwvuts CLARK ETAL.: KILLER WHALE G R O W T H 119 BEST,P. B. 1970. The sperm whale (Physeter cutodon) off the west coast of South Africa: 5. Age, growth and mortality. Investigational Report of the Division of Sea Fisheries of South Africa 79:l-27. BIGG,M. A. 1982. 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ROHLF.1995. Biometry, 31d edition. W. H . Freeman and Company, New York, NY. zyxwvutsrq zyxw 121 CLARK ETAL.: KILLER W H A L E G R O W T H zy TOMILIN, A. G. 1957. Zveri SSSR i prilezhashchikh, stran. IX. Kitoobraznye, (Mammals of the USSR and adjacent countries, Volume 9: Cetacea), Moscow: ANSSR, Israel (Israel Program for Scientific Translations, Jerusalem, 1967). WALKER, L. A., L. CORNELL, K. D. DAHL, N. M. CZEKALA, C. M. DARGEN, B. JOSEPH, A. J. W. HSUECH AND B. L. LASLEY. 1988. Urinary concentrations of ovarian steriod hormone metabolites and bioactive follicle-stimulating hormone in killer whales (OvcinuJ orcu) during ovarian cycles and pregnancy. Biology of Reproduction 39: 1013-1020. I zy Received: 8 August 1997 Accepted: 13 April 1999 zyxw APPENDIX individual trajectories of growth in weight and total length with age plotted for each captive-born calf. Identification numbers those listed as per Duffield et ul. (1995). Gompertz parameter estimates indicated in each figure. 0 7 X zyx zyxwvu zyxwvutsrqpon zyxwv 831 h v . .gi .. - y = -109.7+ 4 3 . 2 ~ ; r2 = 0.99 01 0 f -+I----$ 10 20 ---t---t----t-+---t---i----i 30 40 50 60 70 80 90 100 110 Body volume index (m 3 , Appendix Figure 1 . Linear relationship between body weight (kg) and body volume index (m’) = TL X (GADOF)z]in captive killer whales from SeaWorld parks, sexes combined (males: n = 9; females: n = 16). 122 zyxw zyxwvuts zyxw .f MARINE MAMMAL SCIENCE, VOL. 16, NO. 1, 2000 zyxwv zyxwv . 5'- ~ - - - - - y = 6 . 0 ' 6 ~'; h /i;l r2 = 0.97 g4 0 7 X v , ~ -3. c fU,2 m0 1 . - - - ~ - - - - - - _ _ _ - zyxwvut Jf: -/dm - - ~ _ _ _ II I i 01 \- ' . X *A *m -&-t--t--$ -t . i in utero * 11 day old ..a- I 50 100 150 200 250 300 350 400 450 500 550 600 650 700 Total length (cm) Appendix Figure 2. Exponential relationship between body weight (kg) and total length (cm) in captive killer whales from SeaWorld parks, sexes combined (males: n = 9; females: n = 16). 2000 1700 - 1400 P, Y E 1100 .-P, 2 zyxw 800 500 males are filled symbols females are unfilled symbols 200 0 500 1000 zyxw 1500 2000 2500 3000 3500 4000 Age (days) Appendix Figure 3. Gompertz non-linear relationship between weight (kg) and age (days) for captive killer whales from SeaWorld parks (males: n = 4; females: n = 7). Due to number of data points (n > 250), only average weights at various age intervals plotted for empirical data. Male growth model plotted until 5 yr of age (1,825 d). zyxwvutsrq zy zyxwvuts zyxwvu zyxwvutsrqponmlkjihg 123 CLARK ETAL.: KILLER WHALE G R O W T H 500 - co c. 400 _ _ ~ females: y = 544 2exp[-0 r 2 = 0.92 males y = 413 3exp[-0 6exp(-O.O03x)], r 2 = 091 350.- ~ ~~ males are filled symbols females are unfilled symbols 300 0 t I ~ 500 1500 1000 2500 2000 3000 3500 Age (days) zyx 4000 Appendix Figure 4. Gompertt non-linear relationship between total length (cm)and age (d) between sexes for captive killer whales from SeaWorld parks (males: n = 4; females: n = 7). Due to number of data points ( n > 1,000), only average total lengths at various age intervals plotted for the empirical data. Male growth model plotted until 5 yr of age (1,825 d). calf born I 280 0 0 7 zyxwvu * - 0 0 m 0 0 m 0 0 l m - 0 0 x T b - ---. i 0 0 - C - 0 0 U m C I 0 0 m U 0 0 C m U 0 0 b m - m I 0 0 I m d 0 0 b Time (days) Appendix Figure 5 . Relationship between girth at anterior origin of dorsal fin (GAODF) (cm) and time (d) during pregnancies for female killer whale (7806) from SeaWorld parks.