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Fishery Bulletin 103(2) 



Figure 2 



Sagittal section from a 3.5+ year-old spinner shark tCarcharhinus brevipinna) illustrating the band- 

 ing pattern and winter marks (annuli) used to assign age. 



Both authors randomly read vertebrae independently 

 without knowledge of sex or length of specimens. Verte- 

 bral age estimates for which the readers disagreed were 

 reread simultaneously by using a digital camera and 

 software (Pixera Studio version 2, Pixera Corporation, 

 Los Gatos, CA). If no agreement between readings was 

 reached, samples were discarded. 



Several methods were used to evaluate precision and 

 bias among age determinations following the recom- 

 mendations in Cailliet and Goldman (2004). Percent 

 agreement (PA=number agreed/number read)x 100 and 

 percent agreement plus or minus one year were cal- 

 culated for 10 cm (e.g. 76-85 cm FL) length intervals 

 to evaluate precision (Goldman, 2002). The index of 

 average percent error (APE: Beamish and Fournier, 

 1981) was calculated to compare the average deviation 

 of readings from the means of all readings for each 

 vertebral section: 



IAPE^-% 



■M 



R 



-v— 



where n = number of sharks aged; 

 r = number of readings; 



Xy = i th age estimation of j th shark at / th reading; 



and 

 x = mean age calculated for the j' th shark. 



Chi-square tests of symmetry following Hoenig et al. 

 (1995) were used to determine if differences between 

 readers were systematic or due to random error. 



Several models were fitted to sex-specific observed 

 size-at-age data to estimate the growth dynamics in 

 spinner shark. Although back-calculated size-at-age 

 length data would increase sample sizes for some ages 

 (Cailliet, 1990), multiple back-calculated lengths-at-age 

 are not independent samples and violate statistical as- 

 sumptions in estimating parameters for a growth model 

 (Vaughan and Burton, 1994). Vaughan and Burton (1994) 

 pointed out that estimates of the model parameters 

 may be biased because multiple back-calculated lengths 

 cause an inaccurate number of degrees of freedom. 

 Thus, we used data only from observed size-at-age. 



In developing theoretical growth models, we assumed 

 that 1) the birth mark is the band associated with a 

 pronounced change in angle in the intermedialia, and 

 we assigned an arbitrary birth date of 1 June, the ap- 

 proximate mid-point date when neonates were present 

 in field collections, 2) translucent bands representing 



