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Fishery Bulletin 101 (3) 



were added to successively increase the model complexity. 

 Significant improvement in the model results were deter- 

 mined by using log likelihood ratio tests in accordance with 

 Francis {1988a). Bootstrapping was used to calculate the 

 95% confidence intervals for the final parameter estimates. 

 The modeling and bootstrapping were carried out by using 

 a Solver based spreadsheet in MS Excel (Microsoft Corp., 

 Redmond, WA) (Simpfendorfer^). The value oft^ cannot be 

 estimated from tagging data alone, it requires an estimate 

 of absolute size at age, such as size at birth, and was calcu- 

 lated with the VBGF by solving for t^ such that 



t„=l + {\/ K)[\n\L^-L,/ Lj] 



where L, = known length at age (size at birth); 



K = the von Bertalanffy growth constant; and 

 L^ = the theoretical maximum attainable length 

 from the VBGF. 



The <Q values were calculated based on an average size at 

 birth of 45 cm FL (Pratt, 1979) with t = 0. 



Longevity 



The oldest fish aged from the vertebral method provides 

 an initial estimate of longevity. However, this value is 

 likely to be underestimated in a fished population. Using 

 a teleost species, Taylor ( 1958) defined life span (A) as the 

 time required to attain 95% of the L^ with the following 

 equation: 



Therefore, we calculated the regressions based on the 

 ln(FL)-ln(VR) relationship 



Aj5 



log,(l-0.95) 



This equation can be used to determine life span based 

 on 99% of L^ by substituting 0.99 for 0.95 in the equation 

 (Taylor, 1958). Fabens (1965) calculated time of >99% ofL^ 

 using the equation 



> 99% = 5 



(ln2) 



Results 



Interpretation of vertebrae 



Vertebral samples from 411 blue sharks were used in our 

 study: 287 males, 119 females, and five of unknown sex. 

 These samples comprised free-living sharks ranging from 

 49 cm to 312 cm FL. In addition, vertebrae from seven late- 

 term embryos ranging from 36 cm to 43 cm FL were exam- 

 ined. Blue shark vertebrae did not have consistent prebirth 

 marks; thus, the first distinct opaque band was generally 

 considered the birth mark. The location of the birth band 

 coincided with a slight angle change (Fig. 1). 



The FL-VR relationship was slightly curvilinear and the 

 In-transformed data provided a better linear fit (Fig. 2), 



In(FL) = 0.89*ln(VR) + 3.10 



[r!=392r2=0.97]. 



■* Simpfendorfcr, C. 2000. Personal commun. Mote Marine 

 Laboratory, 1600 City Island Park, Sarasota, FL 33577. 



There was no significant difference between the sexes 

 (ANCOVA,P>0.10). 



Confirmation of the birth band was made by comparison 

 of the BR of all individuals to the VR of YOY and late-term 

 embryos ( Fig 2 ). The VR of seven late-term embryos ( mean 

 VR ±95% CI=2.04 ±0.25) was slightly less than the BR 

 value of the total sample (mean BR ±95% CI=2.70 ±0.03; 

 n=351); the mean VR of 11 early YOY was slightly higher 

 than the BR of the entire sample (49-58 cm FL; mean VR 

 ±95% CI =2.97 ±0.18) (Fig. 2). The location of the birth ring 

 between the VR of both the late-term embryos and the YOY 

 indicated that the birth ring was identified correctly. 



Validation 



OTC-injected recaptured blue sharks provided evidence 

 for the use of vertebral band pairs as age indicators. 

 Vertebrae from two OTC-injected sharks were returned 

 after 0.7 and 1.5 years at liberty (Table 1). OTC injection 

 produced strong fluorescent marks in the vertebral centra 

 of both these sharks (Fig. 3) and the number of annuli past 

 the OTC mark coincided with the number predicted from 

 time at liberty (Table 1 ). In OTC-injected recaptured shark 

 (B536), an opaque growth band was deposited just after 

 tagging in May (Fig. 3). In recaptured shark B 116452, an 

 opaque growth band was deposited just prior to tagging 

 in June (Fig. 3). These results suggest an annual spring 

 deposition of growth zones within the vertebrae. Thus, ver- 

 tebral annuli were validated in these two sharks, which 

 were up to 4* years of age; the older of these fish (B536) 

 corresponded to this age. Beyond this age, bands were 

 assumed to be annual on the basis of the similar nature 

 of band deposition. 



Comparison of counts between two readers indicated no 

 appreciable bias (Fig. 4). The coefficient of variation fiuc- 

 tuated around 15%. This level of precision was considered 

 acceptable; thus, counts generated by both readers and 

 preparation methods were combined for the analyses. The 

 reader maintained quality control by periodically recount- 

 ing earlier samples and by cross-checking the readings. 



Length-at-age data indicated that males and females 

 grow at roughly the same rate. The overlap in observed 

 size-at-age data, as well as the graphical representation 

 of the VBGF curves, indicated that there is little differ- 

 ence in growth for the sexes (Fig. 5). However, the LOW- 

 ESS (locally weighted regression smoothing) derived 

 curves as well as the VBGF parameters indicated that, 

 theoretically, females grow slower and to a larger overall 

 size than males (Table 2, Fig. 6). The LOWESS curves 

 clearly showed minor differences in growth beginning at 

 approximately seven years of age (Fig. 6), but this was 

 likely an artifact of low female sample size at older ages. 

 Subsequent analyses are presented for each sex and for 

 sexes combined for ease of comparison with previously 

 published studies. 



