Sulikowski et al.: Age and growth of Amblyro/a rodiata 



163 



Marginal increment analyses 



The annual periodicity of band pair formation 

 was investigated using marginal increment 

 analyses (MIA). Because the annuli in older 

 adult specimens were compressed, marginal 

 increments were calculated from randomly 

 selected juvenile specimens (Simpfendorfer, 

 1993; Sulikowski et al., 2003). For MIA. the 

 distance of the final opaque band and the 

 penultimate opaque band, from the centrum 

 edge, was measured with a compound micro- 

 scope and optical micrometer. The marginal 

 increment was calculated as the ratio of the 

 distance between the final and penultimate 

 bands (Branstetter and Musick, 1984; Cail- 

 liet, 1990; Simpfendorfer, 1993; Simpfendorfer 

 et al., 2000; Sulikowski et al., 2003). Average 

 increments were plotted by month of capture 

 to identify trends in band formation, and a 

 Kruskal-Wallis one-way analysis of variance 

 on ranks was used to test for differences in 

 marginal increment by month (Simpfendorfer 

 et al., 2000; Sulikowski et al., 2003). 



Growth estimates 



A von Bertalanffy growth function (VBGF) 

 was fitted to the data with the following equa- 

 tion (von Bertalanffy, 1938): 



L t =LJl -e 



-kit - t„\ 



V), 



where /, = total length at time t (age in 

 years); 

 L = theoretical asymptotic length; 

 k = Brody growth constant; and 

 t = theoretical age at zero length. 



Figure 1 



Longitudinal cross-section of a vertebral centrum from a 97-cm-TL 

 female Amblyraja radiata estimated to be 12 years. BM = birth 

 mark; Black dots represent age in years. 



The VBGF was calculated by using FISH- 

 PARM, a computer program for parameter 

 estimation of nonlinear models with Marquardt's (1963) 

 algorithm for least-square estimation of nonlinear 

 parameters (Prager et al., 1987). 



Results 



Morphological measurements 



Out of the 320 specimens collected, a total of 224 were 

 used for our study (Table 1). Males (rc=103) ranged 

 between 29 and 103 cm TL, 18-75 mm DW, and 0.125- 

 10.5 kg body weight (data not shown), whereas females 

 (n=121) ranged between 31 and 105 cm TL, 18-74 cm 

 DW, and 0.170-11.4 kg body weight (data not shown). 

 Total length, disk width, and body weight were strongly 

 correlated in males, females, and when data from the 

 sexes were combined (all coefficient of determination [r 2 ] 

 values were greater than 0.87). 



Vertebral analyses 



Comparison of counts between two readers indicated 

 no appreciable bias in the counting process (Fig. 2) and 

 the coefficient of variation for all sampled vertebrae was 

 2.8% This level of precision is considered acceptable 

 (Campana, 2001) and counts generated by both readers 

 were combined (averaged) for the analyses (Skomal and 

 Natanson, 2003). 



The relationship between TL and centrum diameter 

 was linear (r 2 =0.93; P<0.05) and there were no signifi- 

 cant differences in this relationship (ANCOVA, P<0.05) 

 between males and females. Because no significant 

 difference existed between TL and centrum diameter 

 between the sexes, these data were combined (Fig. 3). 



A total of 120 skates (10 per month) were used for 

 marginal increment analyses. Marginal increments 

 were significantly different between months (Kruskal- 

 Wallis P<0.001); there was a distinct trend of increasing 



