Simpfendorfer: Growth rates of Carcharhinus obscurus 



813 



50 54 58 62 66 70 74 78 82 86 90 94 98 102 106 110 



Fork length! (cm) 



Figure 2 



Size at release for 2199 juvenile Carcharhinus obscurus tagged off southwestern 

 Australia, 



methods. Only recaptures with data that included the date 

 of recapture and accurate length at release and recapture 

 were used in the analyses. 



function to a size-frequency distribution of tagged individ- 

 uals that had an open umbilical scar (Fig. 3). From these 

 data the mean size at birth was 75.3 cm FL. 



Gulland and Holt (1959) The first method used for esti- 

 mating growth rates was that of constructing plots of 

 growth rate by average fork length (Gulland and Holt, 

 1959). The average fork length was calculated as the aver- 

 age of the fork length at release and recapture. Von Berta- 

 lanffy growth parameters were estimated by fitting a line 

 through the data. The slope of the line was equal to -K, 

 and the intercept with the x-axis was equal to L^. 



Fabens (1965) The Fabens (1965) method involved fit- 

 ting the nonlinear function: 



L^ = L + {L,_-L){l-e-''^''), (1) 



where L^ = the length at recapture; 

 L = the length at release; and 

 d = the period at liberty. 



This function was fitted to the data by using the nonlinear 

 estimation module in STATISTICA ( Statsoft, 1998 ). The value 

 of ^Q was estimated by solving the function for the value of T 



Lg + (L . 



-Ljd 



-KTy 



(2) 



where the value of Lq 



the mean size at birth; and 

 cm. 



The mean size at birth of C. obscurus from southwestern 

 Australia was estimated by fitting a normal probability 



Francis (1988) method This method uses a maximum 

 likelihood approach to fitting a growth function that 

 includes estimated growth rates ig^ and^^) at two selected 

 lengths (a=75 cm FL and /3=100 cm FL), the coefficient 

 of variation of gi'owth variability iv), measurement error 

 (assumed to be normally distributed with a mean, m, and 

 standard deviation, s ), and outlier probability (p ). The esti- 

 mated growth increment for an individual, /, is given by 



AL, 



Pg„-ag, 



g., - gu 



1- 1 + - 



a-p j 



where L, = the length at release; and 

 zlT, = the period at liberty. 



Francis ( 1988) suggested several methods of incorporating 

 growth variability into the model. 

 The likelihood function is 



where A 



A = y log[(l-p)A, +p/R], 



exp(-0.5(AL, - p, - m f I (a' + s")) 



[2n-|CT; +s-)J 

 R - the range of the observed growth increments; 



