Skomal and Natanson: Age and growth of Pnonace glauca 



629 



The relationship between VR and FL was 

 calculated to determine the best method for 

 back-calculation of size-at-age data and to 

 confirm the interpretation of the birth band. 

 Age was calculated for each fish based on a 

 birth date of June 1 (Pratt, 1979), corrected 

 for date of capture. Regressions were fitted 

 to the male and female size-at-age data and 

 an ANCOVA was used to test for difference 

 between the two relationships. The relation- 

 ship between FL and VR was best described 

 by a polynomial equation; therefore the 

 data were In-transformed before linear 

 regression. The Fraser-Lee equation of the 

 In-transformed data was derived for back 

 calculation: 



liUFLJ = b + (ln[FLJ+b) (InradiusJ (InradwsJ'K 



where a = age; 



b = intercept from the regression; and 

 c = capture. 



Validation 



To evaluate the periodicity of band pair 

 formation, vertebrae from OTC-injected and 

 measured tag-recaptured sharks were exam- 

 ined. Over 350 blue sharks of various sizes were measured, 

 tagged, and injected with a 25 mg/kg body weight dose of 

 OTC by scientific personnel aboard research and commer- 

 cial vessels in the North Atlantic. Upon recapture, vertebrae 

 were removed from injected specimens and stored in 70% 

 ethanol or were frozen. Vertebrae from these sharks were 

 processed, digitally photographed as previously described, 

 and examined for the OTC mark with reflected UV light. 

 The number of band pairs distal to the OTC mark was then 

 compared with the number of years at liberty and expressed 

 as the proportion of the previous complete growth zone. 



Data analysis 



Aging bias and precision of bands counts were examined by 

 using age-bias plots and the coefficient of variation (Cam- 

 pana et al., 1995). Reader 2 counted 98 sections previously 

 counted by reader 1 (Skomal, 1990). Pairwise comparisons 

 were generated from these data. 



Von Bertalanffy growth functions (VBGF) were fitted to 

 length-at-age data by using the following equation (von 

 Bertalanffy, 1938): 



Z., = Z..(l-e-''"-'"'), 



where L, = predicted length at time t; 

 L^= mean asymptotic length; 

 K = a. growth rate parameter (yrM; and 

 Iq = the theoretical age at which the fish would 



have been zero length. 



The VBGF was calculated by using the nonlinear regression 

 function in Statgraphics (Manugistics, Inc., Rockville, MD). 



Figure 1 



Photograph of a vertebral section from a male blue shark (Prionace glauca) 

 estimated to be 14 years old. 



Tagging data 



From 1963 through 1999, members of the NMFS Coopera- 

 tive Shark Tagging Program tagged 88,899 and recaptured 

 4967 blue sharks. Only those sharks reliably measured by 

 biologists or fishermen at both tagging and recapture were 

 used in the analyses. All measurements were converted to 

 FL by using the relationships of Kohler et al. (1995). 



The Gulland and Holt ( 1959) and Francis ( 1988a) models 

 were used to generate VBGFs from the tag-recapture data. 

 The Gulland and Holt ( 1959) method uses graphical inter- 

 pretation of the recapture data to produce estimates of L, 

 and K. Specifically, annualized growth rate (cm/yr ) was plot- 

 ted against average FL (cm) between tagging and recapture 

 to calculate linear regression coefficients. The slope of the 

 line is equal to -K and the x-axis intercept is equal to L^. 



The Francis ( 1988a) method (GROTAG) uses maximum 

 likelihood techniques to estimate growth parameters and 

 variability from tagging data. A coefficient of variation of 

 growth variability (v), measurement errors (m and s) and 

 outlier contamination (p) are estimated, as well as growth 

 rates at two user selected lengths (« and p). The reference 

 lengths, a and p, were chosen to lie within the range of 

 tagged individuals. The form of the von Bertalanffy equa- 

 tion becomes 



AZ.= 



Su-gp 



1-1 + 





The simplest model, a linear fit with minimal parameters 

 (o and s) was used initially and additional parameters 



