FISHERY BULLETIN: VOL. 75, NO. 2 



the linear regression program previously 

 employed. If it is assumed that the estimates of 

 Z .5o are normally distributed, then the quantity 



2i 



«2 

 02 



Vvar(£) + Var(!) 



is distributed as Z and can be used to test the 

 hypothesis that there is no difference in l 050 be- 

 tween areas. TheZ values obtained for both males 

 and females (Table 14) indicate that the observed 

 differences in length at maturity are highly sig- 

 nificant, since P(Z>3.0067) = 0.0013 and 

 P(Z>9.9277) « under the hypothesis being 

 tested. 



Age-maturity relation 



Age at maturity was estimated by two methods. 

 The first series of estimates was developed by 

 using the logistic equation: 



P t = 



1 



1 + exp 



C-^ n ) 



where P t = proportion mature at age t 



*o.50 = age whenP, = 0.50 = age at maturity 

 cr = constant. 



The parameters for this equation were estimated 

 in the same manner described in the length- 

 maturity section, through weighted linear regres- 

 sion analysis of the data in Tables 11-13. The re- 

 sulting estimates of £ .5o and cr are shown in Table 

 14, and the predicted relationships betweenP, and 

 t are shown by the solid lines (QCS stock) and 

 dashed lines (WVI stock) in Figure 20. The £ .5o 

 estimates obtained in this way are estimates of the 

 age when males mate for the first time and when 

 females release their first brood of embryos. TheZ 

 statistic shows that between-stock differences in 

 age at first brood release were statistically sig- 

 nificant, since P(Z>5. 8533) ~ 0. 



A second series of estimates for the age at 

 maturity it' 050 ) was obtained by utilizing the Z .50 

 values obtained in the previous section, and von 

 Bertalanffy growth parameters from Table 3. The 

 equation used was: 



390 



FIGURE 20.— Age-maturity relation for QCS and WVI stocks 

 of Pacific ocean perch, by sex. 



Resulting estimates for males (Table 14) are 

 probably quite accurate, since both l 50 and the 

 age-length relations in Table 3 were based on data 

 collected during June-December (near the mating 

 season). The t' 05Q estimates for females are biased, 

 however, since a significant amount of growth oc- 

 curs between the period when / .5o was estimated 

 (February- June) and the period when the age- 

 length data were collected (July for the WVI stock, 

 September-December for the QCS). The bias is 

 relatively small for the WVI stock, but in Queen 

 Charlotte Sound most of the annual growth prob- 

 ably occurs during the intervening time period. 

 The £'0.50 value obtained for QCS females con- 

 sequently underestimates age at first brood re- 

 lease by almost a year. 



The results from both methods used to estimate 

 age at maturity (Table 14) indicate that both 

 males and females mature at an earlier age off 

 Washington and southwest Vancouver Island 

 than they do in Queen Charlotte Sound. When 

 biases in t' 050 are considered, it appears that WVI 

 females release their first brood when 9-10 yr old, 

 while those in Queen Charlotte Sound are 11 yr 

 old. Estimates of age at first mating for males were 

 not subject to the same bias as those for females 

 and can be taken directly from Table 14. These 

 results suggest that males first mate at age 6 



