664 



Fishery Bulletin 98(4) 



Maturation curves 



Maturation by length and by age were estimated for fe- 

 male (/!=934) and male (« = 1232) Dover sole with logistic 

 regression (McCullagh and Nelder, 1989). Significance of 

 fish length or age as a predictor of fraction mature was 

 tested with the likelihood-ratio chi-square test. Standard 

 errors for model parameters were estimated by using the 

 nonparametric bootstrap method with 1000 replicates. 



Geographic differences in maturation rates were also 

 evaluated for male and female samples by using logistic 

 regression. Step-wise model selection was used to deter- 

 mine the best model of length or age and the factors 

 INPFC area and sex, and all possible higher order interac- 

 tions between these terms. The full model with all possible 

 interactions was 



6j=B. Because lognormal errors were assumed, the retrans- 

 formed intercept needs to be adjusted to give an accurate 

 predictive equation for mean weight, and the adjusted inter- 

 cept was computed as A=exp(fe|,)exp((CT-- crQ-)/2), where d- 

 is the residual variance from the regression and a^ is the 

 variance of 6q (Hayes et al., 1995). Nonparametric boot- 

 strapping with 1000 replicates was used to estimate stan- 

 dard errors of parameters and to provide nominal estimates 

 of parameter bias (Efron andTibshirani, 1993). 



Geogi'aphic variation and sexual dimorphism in the 

 length-weight relationship for Dover sole were investi- 

 gated by a step-wise procedure among generalized linear 

 models relating the log-transformed length-weight obser- 

 vations to the factors INPFC area and sex, and all pos- 

 sible higher order interactions between these terms. The 

 full model with all possible interactions was 



log =(A,+i3..+ft.+B^,) + 



^-^1 (3) 



(/i,+/3,,+/j„+yg,,,)X, 



where k = the probability of being sexually 



mature; 

 /3^ , Pg , and ji^^^ = coefficients of area, sex, and their 



interaction; and 

 /3,.4 , /3jt; , and /3j^^^. = coefficients of first- and second-order 



interactions between area, sex, and 



the variable length (or age), denoted 



byX 



Akaike's information criterion (AIC) was used to compare 

 competing nested models in a step-wise manner (Hastie 

 and Pregibon, 1993 1. We also evaluated whether overdisper- 

 sion due to cluster sampling was present (McCullagh and 

 Nelder, 1989). If the ratio of observed to expected sampling 

 variation (0) for the estimated model was less than 1, we 

 concluded that overdispersion was not present. Nonpara- 

 metric bootstrapping based on 1000 replicates was used to 

 estimate standard errors for parameter estimates. 



Length-weight curves 



We estimated length-weight relationships for pooled-sex, 

 male (7i=1549), and female (w = 1470) samples based on the 



oil nrvi ofr"ir> omi oti/rr* 





(5) 



allometric equation 



W=AL>xp(f,), 



(4) 



where W, andL, = theobserved total weight (gi-ams) and 

 total length (centimeters) of the /''' fish; 

 A and B = parameters; and 



f, = independent and identically distrib- 

 uted normal error terms with zero 

 mean and constant variance. 



A natural logarithmic transformation was applied to length 

 and weight measurements and linear regi-ossion was 

 applied to estimate parameters, denoted as 6Q=logA and 



where p. Pg , and P^g 

 Pal  PsL ' and P^gL 



coefficients of area, sex, and their 

 interaction; 



coefficients of first- and second- 

 order interactions between area, 

 sex, and the natural logarithm 

 of length; and 

 f , = a normally distributed error 

 with zero mean and constant 

 variance. 



As in the maturity analyses, the AIC criterion was used 

 to choose among competing models in a step-wise manner 

 (Hastie and Pregibon, 1993). Estimates of standard errors 

 of parameters and nominal estimates of parameter bias 

 were computed with the nonparametric bootstrap with 

 1000 replicates. Bootstrap estimates of residual variance 

 and (Tf,2 = Var|6Ql=Var(logA-i-/J^-t-j3i;+/3^g] were used to com- 

 pute the adjusted intercept. 



Results 



Length-at-age samples 



Female and male age and total length distributions dif- 

 fered across areas. On average, females were 1 to 2 years 

 older than males (Table 2). Mean ages of males and 

 females were significantly different for all areas combined 

 and within the Vancouver, Columbia, and Eureka areas 

 (P<0.05). Mean ages were lowest in the Vancouver area 

 and highest in the Eureka area. The youngest males were 

 2 years old and had lengths of 19, 22, and 25 cm, whereas 

 the oldest male was 42 years old and 41 cm long. The 

 youngest female was 2 years old and 21 cm long, whereas 

 the oldest female was 48 years old and 51 cm long. Maxi- 

 mum observed ages of females were greater than those 

 of males in all areas except the Vancouver area where 

 the fewest samples were collected. Females were 4 to 5 

 cm longer than males on average (Table 2). Mean female 



