850 



Fishery Bulletin 98(4) 



Figure 1 



The six areas in the Gulf of Alaska sampled for giant Pacific sea scallops during the 

 Viking Queen survey, 1968. 



scallop, Pecten maximits (Gibson, 1956; Mason, 1957), and 

 shows reasonably good agreement with "true" (isotopi- 

 cally predicted) ages when growth rings are clearly visible 

 (Dare and Deith, 1989). Application of the method to Pati- 

 nopecten caiainus has been verified by Haynes and Hitz 

 (19711. 



Terminal shell heights (size of shell to the last annulus; 

 hereafter called "shell heights") were used to fit a growth 

 model for each sample (Table 1). No attempt was made to 

 determine the sex of the scallops because of indications 

 that growth differences between sexes were insignificant.' 

 After our sampling, scientists of the ADF&G provided sex 

 and age data for scallops taken in August 1970 northwest 

 of Kodiak Island. The von Bertalanffy growth model was 

 fitted to these data, and growth differences between sexes 

 were tested as described in the following section. 



Estimation and fitting of von Bertalanffy curves 



Mean shell heights by age were plotted for sea scallops 

 in each sample (Fig. 2). Growth decreased steadily with 

 age, suggesting that sigmoid gi-owth was not present or 

 that the shell heights used were beyond the point of inflec- 

 tion; thus the von Bertalanffy growth model was consid- 

 ered appropriate for our study. In this model, length of the 

 i''' individual at age / is 



l„ = L[l-e"'"""'] + e,; e, ~ N(0,a'). 



Kimura (1980) showed that maximum likelihood esti- 

 mation for the von Bertalanffy curve is equivalent to 



^ ADF&G. 

 and Game 



1970. Unpubl, obsenations. 

 Kodiak. AK 99615. 



Alaska Dept. Fish 



finding least-square estimates of model parameters (see 

 also Cerrato, 1990). Least-square estimates for the three 

 parameters were obtained by nonlinear regression meth- 

 ods. Analysis of residuals showed that the von Bertalanffy 

 model provided an adequate fit for all samples. The pre- 

 cision (variance) of parameter estimates varied with age 

 composition of the sample. For example, samples with few 

 young scallops showed relatively large variances for the 

 parameters K and fg, whereas samples with few old scal- 

 lops resulted in imprecise estimates of asymptotic length 

 (Table 2). However, the residual mean square error (MSE), 

 denoting variability about fitted growth equations, did not 

 vary widely among samples. 



Comparison of growth curves for different areas 



No significant difference (P>0.15) in growth between sexes 

 was detected in the ADF&G samples, supporting the pre- 

 survey decision not to determine the sex of the scallops. 

 Growth of scallops from the six areas was compared by 

 likelihood ratio tests by using two probability models: 

 model 1 specified equality of the von Bertalanffy para- 

 meters of each area; model 2 allowed separate parameters 

 for each area (Kimura, 1980). The first model consisted 

 of pooling the data over all areas, yielding one growth 

 equation; the second model allowed separate growth equa- 

 tions for each area. Because there was no a priori hypoth- 

 esis concerning growth differences between the areas, 15 

 simultaneous tests were performed to evaluate pairwise 

 differences in growth. These tests were equivalent to test- 

 ing /.' independent hypotheses at a significance level of a. 

 Applying Bonferonni's inequality (Miller, 1966) to the 15 

 tests resulted in an experimental-wise significance level 

 < k X a. We chose a to equal 0.003, giving an experimen- 

 tal-wise significance level of 0.045. Likelihood ratio tests 



