Carlson and Baremore: Growth dynamics of Carcharhinus brevipmna 



285 



The Gompertz model estimated size-at-birth (61 cm 

 FL) within the range reported for spinner sharks. Size- 

 at-birth off the United States southeast and Gulf of 

 Mexico coasts has been reported to range from 50 to 

 65 cm FL depending on the study (Branstetter, 1987; 

 Castro, 1993; Carlson, unpubl. data). 



Observed size-at-age and longevity were different 

 between males and females (Table 4). For most ages, fe- 

 males were larger. The oldest animals aged were 17.5 + 

 years (female) and 13.5+ years (male). 



Discussion 



Considering our statistical criteria (e.g., lowest MSE, 

 high r 2 , and level of significance), logistic models pro- 

 vided the best fits to the size-at-age data. The von Berta- 

 lanffy growth models, on the other hand, gave the worst 

 fits. However, the criteria used to evaluate the models in 

 this study may not be adequate. Because statistical fits 

 have not been reported by other elasmobranch age and 

 growth studies, we were not able to compare our criteria 

 with other studies. Although not directly comparable, 

 goodness-of-fit criteria used to select the best nonlinear 

 gastric evacuation models have employed a combination 

 of r 2 , residual sum of squares, standard deviation, or 

 coefficient of variation of residuals (review in Cortes, 

 1997). Until a more rigorous criterion is developed for 



growth models, efforts should continue to identify a 

 best-fitting growth model. 



We feel the von Bertalanffy model is inappropriate 

 for describing the growth of male spinner shark. As- 

 ymptotic values indicated an unreasonable theoretical 

 maximum size of 421 cm FL — much larger than sizes 

 from recent fishery-dependent and fishery-independent 

 sources (176-220 cm FL; Grace and Henwood, 1997; 

 Morgan 3 ; Carlson, unpubl. data). Asymptotic values from 

 other models approach those actual values. Because of 

 the relationship between k and L„, the von Bertalanffy 

 growth coefficient was also much lower than expected. 

 The growth coefficient from the Gompertz model was 

 0.14/yr, similar to those reported for other large coastal 

 species in general (Cortes, 2000) and to those reported 

 by Allen and Wintner (2002) for spinner sharks from 

 South Africa. 



The poor statistical fit and unrealistic biological es- 

 timates of the von Bertalanffy growth model for male 

 spinner shark illustrates the importance of fitting alter- 

 native models to the data when estimates do not appear 

 to be biologically real. Although sample size was well 

 represented for most ages, the von Bertalanffy growth 

 model did not reach an asymptote until well beyond the 



3 Morgan, A. Personal commun. Program for Shark Research, 

 Florida Museum of Natural History, Univ. Florida, P.O. Box 

 117800, Gainesville, FL, 32611. 



