FISHERY BULLETIN: VOL. 75. NO. 2 



lOO-i 



-Cl 



10- 



A WVI 

 • QCS 



7.4l57-0.3465x 



-[ — l — I — I — l — i — I — i — l — l — I — I I l I 

 10 15 20 



Age 



FIGURE 14. — Relative abundance of age groups 5-19 during 

 1967-73, for the QCS and WVI stocks of Pacific ocean perch. 



u = exploitation rate 



V, = proportion of population vulnerable 

 at age i 



N ( = total number of fish in the ith age- 

 group. 



expressed as percent frequency 

 X = age in years. 



The slope of this line (0.35) was used to repre- 

 sent Z for fully recruited age-groups. This was 

 then separated intoF and M by assuming a known 

 value for M. 



Estimation of V, schedules began by assuming 

 that the vulnerability coefficient for 16 yr olds 

 (V 16 ) was 1.0. Using the QCS data, and M = 0.12 

 for example: 



Uu 



u. 



1.31 = 



V 



15 



16 



1.0 exp -(0.23 V 15 + 0.12) 



By iteration, it was determined that V 15 = 0.94 

 and this value was used to determine V 14 from: 



U u 



U u 



1.14 



V M 



0.94 exp -(0.23 V 14 + 0.12) 



Again this was solved iteratively, giving V 14 = 

 0.79. Proceeding backwards, the vulnerability 

 coefficients for Queen Charlotte Sound were esti- 

 mated for all age-groups 10 and older. The calcula- 

 tions could not be carried past age 10, since 

 younger age-groups may be subject to substantial 

 rates of discard by fishermen. 



Estimates of the V, schedules for both the QCS 

 and WVI stocks are shown in Table 6. Calculations 



Similarly, C i+ \ = uV l + 1 N l + i = «V ( --iiV,exp -(V, 

 F + M) if we assume that V,- remains constant 

 throughout the year, and: 



U 



C, 



U i+1 C i+1 V,,iexp -iV,F + M) 



This equation can be solved iteratively for V, if we 

 have estimates of F (fishing mortality). M (nat- 

 ural mortality), V; +1 , and the ratio UJU,+i. 



The estimates of Z (total instantaneous mortal- 

 ity) andF were derived directly from the data in 

 Figure 14. Trends in the relative abundance of 

 15-19 yr olds were quite similar in the QCS and 

 WVI stocks, and Z was estimated by fitting a 

 common regression line to the data for both stocks. 

 The resulting regression equation for 15-19 yr olds 

 was: 



log Y - 7.4157 - 0.3456X, 



where Y = relative abundance during 1967-73, 

 382 



TABLE 6. — Proportion of Pacific ocean perch population vulner- 

 able to fishing, by age-group and stock. 



were carried out for M — 0.15, F = 0.20 as well 

 as for M = 0.12, but this had little effect on the 

 estimates of vulnerability. The geometric means 

 of the vulnerability coefficients obtained by as- 

 suming different values of M have been plotted 

 graphically in Figure 15 and suggests that the 

 proportion recruited to the fishery is a linear func- 

 tion of age. There is no obvious reason why this 

 should be so, however, and no attempt was made 

 to fit a straight line (or lines) to these data, or to 

 extend the relationship to fish less than 10 yr old. 

 The geometric means of the V, estimates were 

 used directly in all later work. 



