280 



Abstract— The age and growth dynam- 

 ics of the spinner shark (Carcharhinus 

 brevipinna) in the northwest Atlan- 

 tic Ocean off the southeast United 

 States and in the Gulf of Mexico were 

 examined and four growth models 

 were used to examine variation in 

 the ability to fit size-at-age data. The 

 von Bertalanffy growth model, an 

 alternative equation of the von Ber- 

 talanffy growth model with a size-at- 

 birth intercept, the Gompertz growth 

 model, and a logistic model were fitted 

 to sex-specific observed size-at-age 

 data. Considering the statistical cri- 

 teria (e.g., lowest mean square error 

 [MSE], high coefficient-of-determina- 

 tion, and greatest level of significance) 

 we desired for this study, the logistic 

 model provided the best overall fit 

 to the size-at-age data, whereas the 

 von Bertalanffy growth model gave 

 the worst. For "biological validity," 

 the von Bertalanffy model for female 

 sharks provided estimates similar to 

 those reported in other studies. How- 

 ever, the von Bertalanffy model was 

 deemed inappropriate for describing 

 the growth of male spinner sharks 

 because estimates of theoretical 

 maximum size (L„) indicated a size 

 much larger than that observed in the 

 field. However, the growth coefficient 

 (£ = 0.14/yr) from the Gompertz model 

 provided an estimate most similar to 

 that reported for other large coastal 

 species. The analysis of growth for 

 spinner shark in the present study 

 demonstrates the importance of fit- 

 ting alternative models when stan- 

 dard models fit the data poorly or 

 when growth estimates do not appear 

 to be realistic. 



Growth dynamics of the spinner shark 



(Carcharhinus brevipinna) 



off the United States southeast and 



Gulf of Mexico coasts: a comparison of methods 



John K. Carlson 



Ivy E. Baremore 



Southeast Fisheries Science Center 



National Marine Fisheries Service, NOAA 



3500 Delwood Beach Road 



Panama City, Florida 32408 



E-mail address (for J K Carlson): |ohn carlsoniSnoaa gov 



Manuscript submitted 3 May 2004 

 to the Scientific Editor's Office. 



Manuscript approved for publication 



29 December 2004 by the Scientific Editor. 



Fish. Bull. 10.3:280-291 (2005). 



Virtually every study concerned 

 with describing the growth of elas- 

 mobranchs uses the von Bertalanffy 

 growth equation (von Bertalanffy, 

 1938). despite criticism of the model 

 (Knight, 1968; Roff, 1980). A review 

 of the existing literature from 1962 

 to 2002 indicates that only about 12% 

 of the published papers concerned 

 with elasmobranch age and growth 

 provide or have examined an alter- 

 native model (I.E.B., unpubl. data). 

 Most studies on elasmobranch age and 

 growth have simply fitted the von Ber- 

 talanffy model to observed or back- 

 calculated size-at-age data without 

 much concern about goodness-of-fit. In 

 addition, appropriate age-structured 

 assessments require accurate mea- 

 sures of the growth coefficient ik) of 

 the population when calculating, for 

 example, indirect estimates of natural 

 mortality. A complete study on the age 

 and growth of a species may require 

 the application of multiple growth 

 models, especially when data do not 

 appear to fit a given model (e.g., when 

 there is no statistical significance or 

 when there is poor goodness-of-fit) or 

 when results do not appear to be bio- 

 logically realistic. 



The spinner shark (Carcharhinus 

 brevipinna) is a cosmopolitan species 

 occurring in warm-temperate areas of 

 the Atlantic Ocean, the Indian Ocean, 

 and the western Pacific Ocean (Com- 

 pagno, 1984). Off the United States 

 east and Gulf of Mexico coasts, the 

 spinner shark is managed under a 

 large coastal shark complex (NMFS, 

 1993). Sharks within this complex are 



considered to be relatively large, slow 

 growing, long lived, and are currently 

 overfished (Cortes et al. 1 ). 



Although Allen and Wintner (2002) 

 recently examined the age and growth 

 of the spinner shark off South Africa, 

 the only existing information on spin- 

 ner sharks from U.S. waters is from 

 Branstetter (1987), who examined 

 just 15 animals from the Gulf of Mex- 

 ico. The purpose of the present study 

 is to re-examine the age and growth 

 dynamics of the spinner shark off 

 the U.S. southeast and Gulf of Mex- 

 ico coasts. We compare and contrast 

 four growth models to determine the 

 model that best describes the growth 

 data of the spinner shark. 



Materials and methods 



Sharks (n = 273) were collected from 

 1995 to 2003 in the U.S. Exclusive 

 Economic Zone from Galveston, Texas 

 to Key West, Florida, in the Gulf of 

 Mexico and in the U.S. south Atlantic 

 Ocean from Charleston, South Caro- 

 lina, to West Palm Beach, Florida 

 (Fig. 1). Precaudal (PC), fork (FL) 

 or total (TL) length (cm) were mea- 

 sured, and sex and maturity state 

 were determined for each shark. Total 



1 Cortes, E„ L. Brooks, and G. Scott. 

 2002. Stock assessment of large coastal 

 sharks in the U.S. Atlantic and Gulf of 

 Mexico. Sustainable Fisheries Divi- 

 sion contribution SFD-02/03-177, 64 

 p. Southeast Fisheries Science Center, 

 3500 Delwood Beach Rd.. Panama City, 

 FL, 32408. 



