814 



Fishery Bulletin 98(4) 



fi^ = the expected value of 



growth increment of the 



ith individual; and 

 a = the standard deviation of 



the growth VEiriability. 



In the present study ct, was as- 

 sumed to be proportional to pre- 

 dicted growth increment (i.e. ct, = 

 v?/,). 



The solver function in Micro- 

 soft Excel (Microsoft, 1999) was 

 used to maximize the likelihood 

 value of the model. Although the 

 growth model allowed the use of 

 six parameters, the number of 

 parameters used for each of the 

 groups was determined by using 

 the likelihood ratio test (LRT). 

 In its simplest form growth was 

 assumed to be linear (g^=g^^ and 

 to include s. The addition of more 

 parameters ( nonlinear growth |^,,* 

 gA, V, m. and p) was significant if 

 the likelihood increased by more 

 than 1.92 per parameter (Francis. 

 1988). The final model used for 

 each group was the one with the 

 least number of significant parameters. 



Bootstrapping was used to estimate 95% confidence 

 intervals for parameter estimates. New growth increment 

 values were generated by adding randomly selected points 

 from two normal distributions. The first distribution had a 

 mean of the predicted growth increment with a standard 

 deviation equal to \7/ and represented gi'owth and giowth 

 variability. The second distribution represented the mea- 

 surement error and had a mean of m and a standard devia- 

 tion of s. Five hundred bootstrapped data sets were created 

 by using each method and fitted by using the technique 

 described above. Ninety-five percent confidence intei-vals 

 were calculated from the 2.. 5th percentile and the 97.5th 

 percentile of the resulting parameter distributions. 



Length-at-age for neonate releases The use of length-at- 

 age data is normally associated with aging studies where 

 the age of an individual shark is estimated from the 

 number of bands on the vertebrae. Because most animals 

 tagged in the current study had open umbilical scars, it 

 was possible to estimate the age of each of the recaptured 

 animals directly from the time at liberty and the rate of 

 healing of the umbilical scar. There is limited information 

 available on the time that it takes for the umbilical scar 

 to close, but most estimates range from 4 to 6 weeks (Bass 

 et al., 1973). If it is assumed that a shark with an open 

 scar was tagged at an age of three weeks (the assumed 

 age at release), the age at recapture is the time at liberty 

 plus three weeks. Preliminary data analysis showed that 

 a linear growth function (L, = bL + a, where b is the 

 growth rate and a is a constant) provided a better fit to 

 the data than a von Bertalanffy function. Thus a linear 



68 70 72 74 76 

 Fork length (cm) 



80 82 84 85 88 90 



Figure 3 



Size-frequency distribution of 1537 neonate Carcharhmus obscurus from southwest- 

 ern Australia with open umbilical scars. The line represents a normal distribution with 

 a mean of 7.5.3 cm and a standard deviation of 3.75 cm. 



model was fitted to the length-at-age data. Growth rates 

 (6 values) were compared between males and females, 

 and between injected and noninjected animals, using the 

 homogeneity-of-slopes model within the visual general 

 linear model module of STATISTICA. Significant differ- 

 ences in growth rates existed when the interaction term 

 (agexsex or agexinjection status) was significant. If there 

 were significant differences in the growth rates for sexes 

 then differences in the growth rates between injected and 

 noninjected animals were assessed separately for males 

 and females, otherwise they were assessed for males and 

 females combined. 



Results 



A total of 473 recaptures of juvenile C. obscurus were 

 reported to September 1998. Recaptured animals were at 

 liberty between and 1716 days (4.7 years); seven were 

 at liberty for more than three years. Tag-recapture data 

 from all individuals with usable data were included in the 

 Francis (1988) method, whereas only those with times at 

 liberty greater than 60 days were used in the other meth- 

 ods of analysis. Individuals at liberty less than 60 days 

 were excluded because many individuals had growth rates 

 that were beyond those considered reasonable because of 

 the short period at liberty (Fig. 4). The size at recapture 

 ranged from 68.5 to 147 cm FL. There were 304 recaptured 

 sharks with usable data, and 274 recaptured sharks with 

 times at liberty gi-eater than 60 days. These recaptured 

 sharks included 153 males (137 at liberty >60 days), 143 

 females ( 130 at liberty >60 days), 118 individuals injected 



