2013 SOUTHEASTERN NATURALIST 12(1):27–40 Growth in Body Length and Mass of the Florida Panther: An Evaluation of Different Models and Sexual Size Dimorphism Tad Bartareau1,*, Dave Onorato2, and Deborah Jansen3 Abstract - Knowledge of growth in body dimension and mass is important to understanding fundamental elements of wildlife biology and ecology. We evaluated five classical growth models (Gompertz, Logistic, Monomolecular, Richards, and von Bertalanffy) in describing body length and mass growth curves as a function of age to determine which best fit wild Puma concolor coryi (Florida Panther). When used for inferences on body length and mass growth curves of both genders, the von Bertalanffy function proved to be the best-fitting theoretical equation to our data set because it used the fewest parameters derived directly from metabolic laws, had lowest residual standard deviation of data points about fitted model, with lower Akaike Information Criterion value, and largest Akaike weight. The von Bertalanffy model estimated that male asymptotic body length was 9.4% longer and mass was 33.2% heavier than for females. Both genders grew in body mass for a longer duration than length. Male-biased sexual size dimorphism develops in part because males grew faster and for a more prolonged period. Our results should prove useful in future studies of Panther energetics, reproduction, and in developing conservation and management policies for this species. Introduction Growth in body dimension and mass is a fundamental element in the biology and ecology of all species that influences important life-history traits such as minimum size or age at reproductive maturity (Stearns 1992). Growth trends are heritable and affected by environmental factors, but one cannot continuously measure changes in body size of an individual during growth. Therefore, a practical method for estimating the growth curve of a species is the use of body size-at-age measurements fitted to algebraic models that describe how individuals grow as a function of age (Ratkowsky 1983). This approach gives one the opportunity to interpolate non-observed measurement intervals and describe consistent changes in the underlying growth processes. Growth models are also useful in wildlife research because they summarize growth data with uniform model parameters that provide quantitative indices for asymptotic size and relative growth rate. These variables can be used to reveal variation caused by the environment and facilitate comparison between genders and among populations, or of the same population at dif ferent times (Ratkowsky 1983). 1Habitat and Species Conservation, Florida Fish and Wildlife Conservation Commission, 298 Sabal Palm Road, Naples, FL 34114. 2Fish and Wildlife Research Institute, Florida Fish and Wildlife Conservation Commission, 298 Sabal Palm Road, Naples, FL 34114. 3Big Cypress National Preserve, 33100 Tamiami Trail East, Ochopee, FL 34141. *Corresponding author - Tad.Bartareau@myfwc.com. 28 Southeastern Naturalist Vol. 12, No. 1 Puma concolor L. (Puma), also known as Mountain Lion, Cougar, or Panther, is a sexually dimorphic species with males larger in body dimension and mass than females (Currier 1983, Gay and Best 1995). The territory of dominant males usually encompasses the home ranges of several females who are predominantly, but not exclusively, mating partners of the resident male (Logan and Sweanor 2001, Maehr et al. 1991). Males are aggressive, and their reproductive success is correlated with fighting ability and territory ownership (Logan and Sweanor 2001, Maehr et al. 1991). Females are generally less aggressive or territorial (Logan and Sweanor 2001, Maehr et al. 1991), and their reproductive success is dependent on energetic investment in rearing offspring (Ackerman et al. 1986, Laundré 2005, Robinette et al. 1961). Body mass tends to increase with increasing latitude throughout the range of the Puma (Iriarte et al. 1990), but no apparent geographic variation in relative sexual size dimorphism among adult skulls was detected (Gay and Best 1995). The causes responsible for both why and how sexual size dimorphism arises in this species are generally thought to be associated with intraspecific and interspecific interactions (Gay and Best 1995), although the root causes are still not well understood. Assumptions about Puma growth characteristics (Maehr and Moore 1992, Zullinger et al. 1984), reproductive productivity (Robinette et al. 1961), energetics (Ackerman et al. 1986), and prey requirements (Laundré 2005) have been based on body-mass growth curves. Historically, the generalized Richards function has been the model of choice for describing Puma body length and mass growth curves (Laundré and Hernández 2002, Maehr and Moore 1992). However, when a particular model is chosen independently of the data and used to approximate the growth curve as a basis for inference, uncertainty in the model’s selection is assumed to be zero (Akaike 1981, Burnham and Anderson 2002). If model selection uncertainty is overlooked, then precision can be overestimated and the accuracy of predictions could suffer (Burnham and Anderson 2002). Despite the importance of testing concordance among different growth models fitted to the same data set (Ratkowsky 1983, Zullinger et al. 1984), few studies have done so. Puma concolor coryi Bangs (Florida Panther) is a rare and endangered Puma subspecies that is native to the southeastern United States (Onorato et al. 2010). We used an information-theoretic approach (Akaike 1981, Burnham and Anderson 2002) to evaluate five classical models (Gompertz, Logistic, Monomolecular, Richards, and von Bertalanffy) in describing body length and mass growth curves as a function of age to determine which best fit wild Florida Panthers (hereafter Panther). Then, we compared gender differences in growth curves using the best model from these alternatives and examined the ontogeny of sexual dimorphism in this species. Methods Study site The study area encompassed the current breeding range of the Panther, bordered by the Caloosahatchee River to the north, coastal mangrove swamps of the 2013 T. Bartareau, D. Onorato, and D. Jansen 29 southern Everglades National Park to the south, and the urban centers of Miami– Fort Lauderdale and Naples–Fort Myers to the east and west, respectively (Onorato et al. 2010). Habitat types included several varieties of upland and lowland forests, open-canopy marshes and prairies, and agricultural lands (Land et al. 2008, Onorato et al. 2011). The climate of south Florida is characterized by a wet season during summer and autumn and a dry season during winter and spring. Data collection Panthers were captured and monitored with radiotelemetry from 1982 to 2012 by biologists from the Florida Fish and Wildlife Conservation Commission and National Park Service using methods described by Jansen et al. (2010) and the Florida Fish and Wildlife Conservation Commission (2011). Successive locations of radiocollared females in the same location were noted as a potential indication of the commencement of denning behavior and resulted in investigative trips to the area to search for neonatal den sites. Kittens examined in neonatal dens were implanted with passive integrated transponders. From this undertaking, standard growth data were recorded for 139 female and 155 male wild Panthers first examined as kittens in neonatal dens. These Panthers included 27 females and 21 males eventually recaptured for radiocollaring as larger dependent kittens, subadults, or adults. Growth data included body length (cm) and/or mass (kg) and age (yr). Body length was measured as the distance from the tip of the nose to the end of the last tail vertebra along the contour of the spine while the Panther was aligned laterally. Body mass was measured with calibrated spring scales. The age (yr) of kittens examined in dens was estimated to within a few days based on a combination of the movement patterns of radiocollared dams immediately prior to establishing the neonatal den and developmental characteristics of kittens when examined in dens (e.g., size, mobility, tooth development, eye opening). Maehr and Moore (1992) excluded data from recaptures in growth-curve construction to avoid potential autocorrelation. However, doing so violates a basic assumption of random samples for each age class because kittens would be excluded from future samples in older age classes (i.e., equal probability of being sampled; Zar 1999). Therefore, growth data for individual Panthers in multiple years were considered to be independent. As did Laundré and Hernández (2002), we considered all Panthers in the population at a given age to be representative of that age regardless of prior sampling. Data analyses We used a two-parameter body mass-length power function to compare body shape allometry by gender: Mass = aLengthb. The coefficient evaluates the rate of change, while the exponent is a measure of mass at unit length indicating an isometric relationship when b = 3 or one that is positive or negative allometric when b > 3 or b < 3, respectively. The correlation coefficient (r2) of data points about a fitted curve was used to assess the general goodness of fit for body mass and dimension data to power function. 30 Southeastern Naturalist Vol. 12, No. 1 The five growth models chosen in the study represent diminishing returns behavior (monomolecular), sigmoidal with a fixed point of inflection (Gompertz, logistic, von Bertalanffy), and sigmoidal with a variable point of inflection (Richards), as described in Ratkowsky (1983). Each of the four 3-parameter models can be derived from the generalized Richards model (Richards 1959) that encompasses different growth functions for particular values of an additional shape parameter (m) which determine the position of the inflection point. All models used were from general forms of the equations and have similar properties (e.g., unweighted nonlinear regressions; behavior describing body size to an asymptotic function of age as the response variable; asymptotic body size and maturing index have the same biological meaning). Equations 1–5 are the monomolecular (Brody 1945), Gompertz (Gompertz 1825), logistic (Verhulst 1838), von Bertalanffy (von Bertalanffy 1957), and Richards (Richards 1959) growth models, respectively: [1] A(t) = A∞ · [1 - be–Kt] [2] A(t) = A∞ · e[–e–K(t–I)] [3] A(t) = A∞ · [1 + e–K(t–I)] –1 [4] A(t) = A∞ · [1– e–K(t–T)]p [5] A(t) = A∞ · [1 + be–Kt] – (1/m) The parameter A(t) is an observed body length (cm) or mass (kg) at age t (yr), and A∞ is the estimated asymptotic size of the sampled population. The parameter K is the estimated relative growth rate or “maturing index” that describes the rate at which asymptotic body length or mass is reached (yr–1). The parameter b is an integration constant that represents a time-scale factor, and I is the age (yr) at the inflection point. T is a fitting constant and is interpreted as the hypothetical age (yr) of an individual at zero body length or mass, assuming the equation to be valid at all ages. The exponent p determines the model for body length ( p = 1) and mass ( p = 3). The monomolecular model is the simplest equation used in this study and it describes the progress of an irreversible first-order reaction (Brody 1945). The Gompertz model arises from an equation that describes self-limited growth where the rate decreases exponentially with time (Gompertz 1825). The logistic model is more complex, and arises from an equation that describes three stages of growth; early exponential growth where the rate is proportional to size, linear growth where resources are devoted to maintenance, and diminishing growth as a maintenance balance is approached (Verhulst 1838). The von Bertalanffy model arises from an equation that describes metabolic laws and the balance between anabolism and catabolism (von Bertalanffy 1957). The Richards model does not have the underlying biological basis of the previous models and arises on an empirical basis as a theoretical advancement that allows application to both exponential and sigmoid growth curves (Richards 1959). The point of inflection is defined as the theoretical time of maximum growth, and for monomolecular, Gompertz, logistic, and von Bertalanffy models, is fixed at 33.3 % (A∞ · [1/3]), 36.8% (A∞/e), 50.0% (A∞/2), and 29.6% (A∞ · [8/27]p) of asymptotic body size, 2013 T. Bartareau, D. Onorato, and D. Jansen 31 respectively. The point of inflection for the Richards model is flexible and occurs at any fraction of asymptotic body size. Growth data were fitted to each model using the Levenberg-Marquardt- Nash algorithm (Analytical Software 2008). The small-sample, bias-corrected form of the Akaike information criterion (AICc) was used to evaluate and compare models (Burnham and Anderson 2002). The Akaike weight (wi) of each model was calculated to evaluate the weight of evidence that i is the best model within the available set of models (Burnham and Anderson 2002). The best model had the lowest AICc value and the highest wi, recognizing that models ± 2 AICc are considered equal (Burnham and Anderson 2002). Residual sums of squares (RSS), pseudo R2, and residual standard deviation of data points about fitted models (RSD) were used to evaluate general goodness of fit and accuracy of each model to observed growth data (Sokal and Rohlf 1995). T-tests for independent samples (Sokal and Rolf 1995) were used to evaluate differences between model parameter estimates by gender. Statistical analyses were conducted using Microsoft Excel® (Microsoft Corporation, Redmond, WA) and Statistix® 9.0 (Analytical Software 2008), and we employed an alpha value of 0.05. All means are presented ± standard error. Results The body length and mass of Panthers aged 0.01 to 12 yrs differed by gender. Body length ranged from 39.0 to 192.5 cm for females and 44.0 to 219.0 cm for males. Body mass ranged from 0.43 to 51.03 kg for females and 0.45 to 72.6 kg for males. Body mass increased with length (Fig. 1.A), and the early growth rate was rapid, reaching a maximum at the point of inflection in the curve and then declining to zero at asymptotic body length (Fig. 1B) and mass (Fig. 1C). The power functions for females (a = 2.64 x 10-5 ± 1.1 x 10-4, b = 2.7 ± 0.8, n = 12, r2 = 0.916, P < 0.001) and males (a = 7.9 x 10-6 ± 2.1 x 10-5, b = 2.9 ± 0.5, n = 13, r2 = 0.975, P < 0.001) indicated that growth in body mass relative to length was nearly isometric and negative allometric. The power functions did not differ significantly by gender; females had a slightly larger rate of change in mass per unit length than males (t23 = 0.173, P = 0.864) and were slightly smaller per unit length (t23 = 0.274, P = 0.787). The Gompertz, logistic, monomolecular, and von Bertalanffy models were fitted without difficulty, and convergence criteria were met after 7 to 14 iterations (Table 1). Difficulties were encountered when fitting the Richards model, for which convergence criteria were met after 21 to 56 iterations (Table 1). Each of the five models fitted the growth data well for both genders and pseudo R2 were ≥98.7%. For both genders and body size measurements, the von Bertalanffy model performed the best with largest pseudo R2 and lowest RSS, RSD and AICc values (Table 1). The von Bertalanffy model accounted for ≥45.8% of model weight (wi). The Gompertz, monomolecular, Richards and logistic models were least supported by the data with wi ≤ 35.4%, ≤ 31.0%, ≤ 18.5%, and ≤ 10.1%, respectively (Table 1). 32 Southeastern Naturalist Vol. 12, No. 1 The growth data for both genders fit the von Bertalanffy model well in younger Panthers, but became more variable in specimens >1 yr of age (Fig. 1B, C). Individual variation in body length and mass growth data were greater than differences due to gender among panthers age ≤0.08 and 0.38 yr, respectively. The difference between estimated and actual body length were 6.1 ± 0.9 Figure 1. Body length and mass growth curve of wild female (□) and male (■) Puma concolor coryi (Florida Panther) as estimated from (A) two-parameter mass-length power function, and von Bertalanffy growth model for (B) body length (C) and mass by age. Fitted lines reflect growth curve for female (dashed line) and male (solid line). 2013 T. Bartareau, D. Onorato, and D. Jansen 33 cm (3.3% of asymptote) for females and 5.2 ± 1.1 cm (2.5%) for males. The difference between estimated and actual body mass were 1.1 ± 0.2 kg (2.9%) for females and 1.1 ± 0.2 kg (1.9%) for males. The estimated body length and mass at birth was 37.95 cm and 0.58 kg for females and 36.0 cm and 0.55 kg for males, respectively. For each growth model (Table 2), the asymptotic body length and mass values were greater in males than in females. The von Bertalanffy model estimated asymptotic body length and mass values for males were 9.4% longer (t23 = 3.41, P = 0.002) and 33.2% heavier (t359 = 18.32, P < 0.001) than that for females. The corresponding maturing index values were smaller in males than in females. The von Bertalanffy model estimated maturing index values for female body length and mass were 6.1% and 21.7% larger than for males, respectively, with significant gender differences in relative growth rate evident for mass (t359 = 4.14, P < 0.001) and not body length (t23 = 0.05, P = 0.961). Table 1. Assessment of five body length and mass growth models of wild Puma concolor coryi (Florida Panther) based on number of model parameters (P), number of necessary iterations for convergence (I), the relative model fit using residual sums of squares (RSS), pseudo R2 (R2), residual standard deviation of data points about fitted growth curve (RSD), minimum small-sample bias-corrected form of the Akaike’s information criteria value of model i in the candidate set (Δi), and weight of evidence that model i is the best of the available set (wi). Model P I RSS R2 RSD Δi wi Body length (cm) Female (n = 12) Bertalanffy 3 17 564.91 0.999 7.92 0.000 0.470 Monomolecular 3 11 565.91 0.997 7.94 1.252 0.251 Gompertz 3 9 631.60 0.995 8.38 2.065 0.167 Logistic 3 9 672.07 0.993 8.64 3.085 0.101 Richards 4 56 631.61 0.995 8.89 7.625 0.010 Male (n = 13) Bertalanffy 3 7 552.63 0.999 7.42 0.000 0.458 Monomolecular 3 14 553.83 0.998 7.43 0.785 0.310 Gompertz 3 11 657.88 0.997 8.11 2.265 0.148 Logistic 3 8 730.05 0.993 8.54 3.619 0.075 Richards 4 28 657.89 0.997 8.55 7.837 0.009 Body mass (kg) Female (n = 171) Bertalanffy 3 15 987.97 0.999 2.42 0.00 0.537 Gompertz 3 12 989.67 0.995 2.43 1.72 0.227 Richards 4 24 990.09 0.991 2.44 2.13 0.185 Logistic 3 12 1015.70 0.989 2.46 4.73 0.050 Monomolecular 3 9 1062.10 0.987 2.51 12.38 0.001 Male (n = 190) Bertalanffy 3 13 1644.20 0.999 2.97 0.00 0.523 Gompertz 3 8 1651.00 0.993 2.98 0.78 0.354 Richards 4 21 1653.05 0.991 2.98 2.89 0.123 Logistic 3 16 2016.00 0.989 3.28 38.74 0.000 Monomolecular 3 12 2021.60 0.987 3.29 39.27 0.000 34 Southeastern Naturalist Vol. 12, No. 1 Table 2. Estimated parameters of five growth models of wild Puma concolor coryi (Florida Panther). Estimates (± SE) are shown of asymptotic body length and mass (A∞), maturing index (K), integration constant (b), age at the inflection point ( I), fitting constant (T), and shape parameter (m). Model A∞ K (yr-1) b I (yr) T (yr) m Body length (cm) Female Bertalanffy 186.15 (4.15) 2.28 (0.39) - - -0.10 (0.03) - Monomolecular 186.15 (4.16) 2.28 (0.39) -0.10 (0.03) - - - Gompertz 185.98 (4.55) 3.09 (0.47) - 0.37 (0.06) - - Logistic 185.86 (4.35) 4.21 (0.57) - 1.11 (0.10) - - Richards 185.98 (4.28) 3.09 (5.83) -9.45 (9.37) - - 5.43x10-5 (3.46) Male Bertalanffy 205.47 (3.86) 2.14 (0.27) - - -0.09 (0.02) - Monomolecular 205.47 (3.87) 2.14 (0.27) -0.09 (0.02) - - - Gompertz 203.24 (3.66) 3.06 (0.34) - 0.46 (0.06) - - Logistic 201.95 (3.59) 4.22 (0.42) - 1.28 (0.11) - - Richards 203.24 (4.99) 3.06 (1.68) -9.35 (2.75) - - 5.44x10-5 (1.47) Body mass (kg) Female Bertalanffy 38.31 (0.47) 2.03 (0.09) - - -0.14 (0.02) - Gompertz 37.94 (0.45) 2.67 (0.12) - 1.38 (0.06) - - Richards 37.94 (0.48) 2.67 (0.47) -8.18 (3.03) - - 7.06x10-5 (0.21) Logistic 37.25 (0.43) 5.44 (0.29) - 3.64 (0.18) - - Monomolecular 39.11 (0.54) 1.18 (0.06) 0.02 (0.01) - - - Male Bertalanffy 57.34 (0.89) 1.59 (0.06) - - -0.15 (0.02) - Gompertz 56.08 (0.81) 2.11 (0.08) - 1.42 (0.05) - - Richards 56.08 (0.88) 2.11 (0.24) -9.16 (4.48) - - 2.55x10-5 (0.11) Logistic 53.62 (0.74) 4.19 (0.19) - 3.54 (0.14) - Monomolecular 60.35 (1.30) 0.86 (0.05) 0.02 (0.01) - - 2013 T. Bartareau, D. Onorato, and D. Jansen 35 The asymptotic body length and mass estimates of the von Bertalanffy and monomolecular models were higher and the maturing index lower than those estimated by all other models. The asymptotic body length and mass estimates for the logistic model were smaller and the maturing index larger than those estimated by other models. The asymptotic body length or mass and maturing index estimates for Gompertz and Richards models were nearly identical and fell between those of other models. The von Bertalanffy model placed the inflection point for body length and mass growth curves at age 0.05 yr and 0.4 yr in females and 0.07 yr and 0.5 yr in males, respectively. The estimated age to reach asymptotic body length was 4.6 yr for females and 4.9 yr for males. Growth in body mass continued for a longer duration than length, and females were estimated to reach the asymptotic value at age 4.9 yr, about 1.6 yr earlier than males. Discussion Historically, inference and estimation of Puma growth curves and their precision relied solely on the Richards model (Laundré and Hernández 2002, Maehr and Moore 1992), but other models may be more appropriate for some populations (Zullinger et al. 1984). Growth curves for Pumas can differ between genders and populations (Laundré and Hernández 2002, Maehr and Moore 1992), and assessing multiple models through an information-theoretic approach should delineate which model provides the best representation of observed growth data. This application of an information-theoretic-approach to five classical growth models for body length and mass at-age data from wild Panthers is, to our knowledge, the first such study for Pumas. Also, the data set of the current study is unique based on the large sample of Panther body-size measurements over a wide range of known ages. Our results suggest that when used for inferences on the Panther, the von Bertalanffy model provided the least-biased point estimates of growth in body length and mass as a function of age. The different models produced variable results when fitted to the growth data. In examining ease of convergence to obtain parameters as initial criterion to evaluate candidate models for goodness of fit, our analyses revealed problems of convergence for the Richards model resulting in more iterations required to fit the data compared to the Gompertz, logistic, monomolecular, and von Bertalanffy models. The Richards model is flexible, but it presents certain disadvantages such as a shape parameter that has no obvious biological interpretation (Ratkowsky 1983), and its parameters exhibit significant colinearity and are sometimes numerically unstable (Zeide 1993). The Richards model was most difficult for practical use in describing the growth curve of Panthers and, in this study, is an example of over-parameterization. Based on a pseudo R2 comparison alone, with a minimum and maximum value of 0.987 and 0.999, no model was appreciably better than the other. However, model selection according to RSS, RSD, and AICc revealed that the von Bertalanffy model had the lowest values, indicating the best fit to growth data for both genders relative to the other models. The monomolecular and Gompertz models provided a similar fit to von Bertalanffy body length and mass models, 36 Southeastern Naturalist Vol. 12, No. 1 respectively (ΔAICc < 2). The logistic and Richards models provided the least best fit relative to the other models (ΔAICc > 2). Akaike weights indicated that the Gompertz, logistic, monomolecular, and Richards growth models have considerably less support (wi ≤ 35.4%) than does the von Bertalanffy model (wi ≥ 45.8%). While not specifically tested, this finding is in agreement with Maehr and Moore (1992), who suggested that Gompertz and logistic forms of the Richards model were unsuitable for modeling body mass-at-age growth curves of Panthers. Our results were consistent with Laundré and Hernández (2002), who noted that the body mass growth curves of Pumas in their study were similar to the von Bertalanffy form of the Richards model. The difficulty in comparing results of this study with other studies lies in the different data sets that were examined. For instance, Maehr and Moore (1992) found that gender differences in body mass growth rates to be inconsistent because of the sparse data for 1- to 4-yr-old Panthers in their data set. Like Laundré and Hernández (2002), our body-mass data set contained ample specimens for this age span, and the model results indicated a gender difference in growth rates. Maehr and Moore (1992) also estimated unreasonably high birth mass due to a lack of growth data for Panthers aged ≤0.33 yr. In contrast, the presence of growth data for Pumas aged ≤0.02 yr in the data set of Laundré and Hernández (2002) gave reasonable model estimate of birth mass. We had data for Panthers aged 0.01 yr and estimated realistic birth body length and mass sizes when compared to those reported in the literature (Currier 1983, Robinette et al. 1961), indicating that our data set and choice of model was suitable for describing the early postnatal growth curve of Panthers. Growth in body dimension and mass for both genders followed a sigmoid curve, a form of progressive development that is prevalent among determinately growing animals (Ratkowsky 1983). The estimated age at inflection point for body length (≤0.07 yr) and mass (≤0.5 yr) models indicated that growth was more rapid during the early postnatal period than at juvenile or adult ages, and most of a Panther’s lifetime was spent near asymptotic size. The failure of estimates for the generalized Richards model to be more strongly correlated to data than those for the von Bertalanffy model is an indication of a rational effect of fixing the point of inflection at about 29.6% of asymptotic size in a Panther growth curve. We conclude from these results that the von Bertalanffy model is the best-fitting theoretical equation to our data set for estimating the body length and mass growth curve of Panthers from birth to age ≤12 yr . Animal growth can exhibit complex seasonal patterns that depend on the growth data selected. For instance, it can be difficult to separate continuing mass growth from non-monotonic, oscillating changes in mass due to accumulation and utilization of fat. Pumas can consume up to 10 kg of prey in a single feeding (Ackerman et al. 1986), and variation in body mass independent of age is expected (Jansen and Jenks 2010, Kohlmann and Green 1999). However, the difference between estimated and actual body mass of 1.1 ± 0.2 kg in this study is well within the range that might be expected from measurements of Panthers 2013 T. Bartareau, D. Onorato, and D. Jansen 37 made during a random capture. This difference could reflect variation in stomach contents such as the time since last feeding and the amount of food consumed (Ackerman et al. 1986) and fluctuation in mass of females when pregnant or rearing offspring (Jansen and Jenks 2010). The large data set with inclusion of size-increment growth data used to construct our growth models should reduce bias associated with limited sampling. Thus, we believe that our von Bertalanffy model parameter estimates reliably explain the observed growth data and accurately depict the gender-specific body length and mass growth curves of wild Panthers as a function of age. The results of the von Bertalanffy growth models indicated that male Panthers reached physical maturity at an older age than females, and significant gender differences in growth rates were evident for body mass but not length. Both genders continued growth in body mass for a longer duration than length. A nearly isometric relationship of body length and mass is indicated by the similar value in the exponent of the power curve for females (b = 2.7) and males (b = 2.9). The von Bertalanffy mass function is based on a cubic relationship, and the maturing index values for female and male body mass were 89.0% and 74.3% of those for length, indicating that any fraction of mass growth was reached later than the same fraction of length. The estimated asymptotic body length and mass of Panthers indicated malebiased sexual size dimorphism. Adult males were 19.32 cm (9.4%) longer and 19.0 kg (33.2%) heavier than females. Our results support findings from other studies that report male Pumas are about 10% longer and 30% heavier than females (Currier 1983). The asymptotic size estimates were not the largest observed body length or mass attained by any individual in the population, but instead they represent the mean maximum size attained in the population at maturity, as argued from metabolic laws. Possible explanations for this sexual size dimorphism may be that males grow faster, continue growing for a longer duration, or a combination of these developmental processes. The growth curves indicated that both genders grew at about the same rate after birth, but there was well-defined body length and mass sexual size dimorphism at age ≥0.09 and ≥0.39 yr, respectively. The fact that males ultimately grew to a larger asymptotic body length and mass than females of the same age revealed that a male must have a greater absolute rate of growth than female. Logan and Sweanor (2001) found that sexual size dimorphism in Puma body mass can develop as early as weaning by age 0.14 yr due to faster male growth. Panther kittens are weaned by age 0.3 yr (Maehr 1997), and independence and dispersal of offspring generally occurs at just over 1 year of age (Hostetler et al. 2012, Maehr et al. 2002). Therefore, the proximate cause of gender differences in the rate of body length and mass growth apparently begins to operate after offspring are weaned and continues through to family dissolution and adulthood. The gender differences in growth curves have biological and ecological implications because of the correlation of Puma age at first reproduction with growth (Robinette et al. 1961). Female Puma body mass is often attributed to 38 Southeastern Naturalist Vol. 12, No. 1 the accommodation of developing offspring, and variation in the age to reach an estimated minimum size at sexual maturity of 36.3 kg to some extent is related to differences in growth rates (Robinette et al. 1961). Our growth models estimated that female Panthers reached 36.3 kg at 1.8 yr old, an age coinciding with 1.75 yr, when individuals are known to first reach sexual maturity (Benson et al. 2011; Hostetler et al. 2012; Maehr 1997; Maehr et al. 1989, 1991). A female at age 1.8 yr is estimated to have reached 98.7% and 94.3% of asymptotic body length and mass, respectively. The first sexual encounters for male Panthers typically occurs at about 3 yrs old based on radio-collared panthers of known ages (Maehr 1997, Maehr et al. 1991), but genetics revealed that males may become breeders as early as 1.4 years old (Johnson et al. 2010; Florida Fish and Wildlife Conservation Commission, Naples, FL, unpubl. data). A male at age 1.4 yr is estimated to have reached 95.9% and 76.6% of asymptotic body length and mass, respectively. These results indicated that growth in body length of both genders was largely complete by age at sexual maturity, but males continue growth in mass for longer duration than females after the onset of sexual maturation. The modeling of Puma growth curves is a useful tool for the derivation of gender- specific body mass estimates at different ages (e.g., Laundré 2005). The social structuring of Puma populations makes growth information valuable in studying population dynamics because male reproductive success depends on the ability to grow large enough in size to acquire territory, thwart competitors, and mate successfully with females in estrus (Logan and Sweanor. 2001, Maehr 1997, Maehr et al. 1991). Growth curves are also important components of bioenergetic models (Brody 1945) and could be combined with activity data to estimate food and space requirements for the population (e.g., Ackerman et al. 1986, Laundré 2005). Describing food and space requirements of populations is essential for examining range quality and carrying capacity, and has importance in developing conservation and management policies for Pumas (e.g., Laundré 2005). Future data collection, especially with regard to body size and age at different developmental stages (e.g., birth, weaning, sexual maturity, first reproduction) would enhance our understanding of the ontogeny of sexual size dimorphism in this species. Acknowledgments We thank O.L. Bass, R.C. Belden, J.E. Benson, M. Criffield, M. Cunningham, J. Kellam, M. Lotz, A. Johnson, E.D. Land, D.S. Maehr, R.C. McBride, R.T. McBride, R.M. McBride, C.E. McBride, J.W. McCown, J.C. Roof, S. Schulze, and D.B. Shindle for their assistance in collecting the samples used in this study. The Florida Fish and Wildlife Conservation Commission and National Park Service funded panther research, and this paper is dedicated to that ongoing work. Additionally, we thank the citizens of Florida for their contributions to the Florida Panther Research and Management Trust Fund via the purchase of “Protect the Panther” license plates. Thanks to L. Pulliam for diligence in sourcing literature, B. Crowder, J. Gore, J. 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