Carlson and Baremore: Growth dynamics of Carcharh/nus brevipmna 



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winter growth form approximately six months later 

 (i.e., 0.5 years) and 3) subsequent translucent bands 

 representing winter growth form at yearly intervals, 

 thereafter. Thus, ages (yr) were calculated by following 

 the algorithm of Carlson et al. (1999): age = birth mark 

 + number of translucent winter bands-1.5. If only the 

 birth mark was present, the age was 0+ years. All age 

 estimates from growth band counts were based on the 

 hypothesis of annual growth band deposition (Branstet- 

 ter, 1987). 



The von Bertalanffy growth model (von Bertalanffy, 

 1938) is described by using the equation 



L t =LJl- 



-k<t-t,,) 



where L, = mean fork length at time t; 



L r = theoretical asymptotic length; 

 k = growth coefficient; and 

 r = theoretical age at zero length. 



An alternative equation of the von Bertalanffy growth 

 model, with a size-at-birth intercept rather than the r 

 parameter (Van Dykhuizen and Mollet, 1992, Goosen 

 and Smale, 1997; Carlson et al., 2003) is described as 



L t = LJl-be~ 



where b 

 L 



(L^-L^IL^ and 

 - length at birth. 



Estimated median length at birth for spinner shark is 

 52 cm FL (Carlson, unpubl. data). 



We also used the modified form of the Gompertz 

 growth model (Ricker, 1975). The model is expressed 

 following Mollet et al. (2002) as 



L. 



-Lo(t 



G(l- 



where G 



ln(L /L 3 



For the Gompertz model, the estimated median asymp- 

 totic length for spinner shark is 220 and 200 cm FL for 

 females and males, respectively (Carlson, unpubl. data). 



A logistic model (Ricker, 1979) was also considered 

 in the form 



w =w ja + e 



-k(t-a) , 



where W t = mean weight (kg) at time r; 



W x = theoretical asymptotic weight; 

 k = (equivalent tog in Ricker, 1979) instanta- 

 neous rate of growth when w—*0; and 

 a = (equivalent to t Q in Ricker, 1979) time at 

 which the absolute rate of increase in weight 

 begins to decrease or the inflection point of 

 the curve. 



If weight was not available, length was converted to 

 weight by using the regression: weight= 0.0000209 x 

 FL 29524 (/2=226, r 2 =0.98, range: 1.1-66.1 kg). 



All growth model parameters were estimated with 

 Marquardt least-squares nonlinear regression. All mod- 

 els were implemented by using SAS statistical software 

 (SAS version 6.03, SAS Institute Inc., Cary, NO. The 

 goodness-of-fit of each model was assessed by examin- 

 ing residual mean square error (MSE), coefficient-of- 

 determination (r 2 ), F from analysis of variance, level 

 of significance (P<0.05), and standard residual analysis 

 (Neter et al., 1990). 



Results 



Morphometric relationships were developed to convert 

 length measurements. Linear regression formulae were 

 determined as PC=0.880(FL) + 1.503, «=163, r 2 = 0.88, 

 P<0.0001; and FL = 0.847(TL)-3.497, rc=260, r 2 = 0.99, 

 P<0.0001. 



Of the original 273 samples, 14 were deemed unread- 

 able and were discarded (Table 1). The index of average 

 percent error for the initial reading between authors 

 was 10.6%. When grouped by 10-cm length intervals, 

 agreement for combined sexes was reached for an aver- 

 age of 30.2% and 58.2% (±1 band) of band counts for 

 sharks less than 115 cm FL (Table 2). Above 115 cm 

 FL, agreement was reached for 33.5% and 74.0% (±1) 

 of band counts for samples initially read. Hoenig's et al. 

 (1995) test of symmetry indicated that there was bias 

 between readers (x 2 =98.33, df=40, P<0.001). 



Relative marginal increment analysis indicated that 

 bands form annually during winter months (Fig. 3). The 

 smallest relative increment was found in January and 

 the greatest in July. The relative marginal increment 

 ratio increased through spring months (March-May), 

 peaked in summer (June-August), and then declined to 

 fall. However, no statistical difference was found in MIR 



