ABRAMSON and TOMLINSON: APPLICATION OF YIELD MODELS 



Table 9. — Recruits vs. spawners and population biomass. 



^ R.,„ = Recruits in millions on May 1 of year i+2. 

 2 S. = Spawners in thousands of pounds during Seotember of 



year i. 



* P. = Population in thousands of pounds during September of 

 year i-f-1- 



* Estimated from June. 



relationship (Figure 8). Model II, which con- 

 siders the effect of the population competing 

 with the prerecruits, did not account for the vari- 

 ation in recruitment either. Consequently, a 

 realistic spawner-recruit relationship could not 

 be determined from the available data. 



Yield per Recruit 



Because a well-defined spawner-recruit rela- 

 tionship could not be determined the use of a 

 self-generating model of the dynamic pool type, 

 such as Walters (1969), is not feasible. We can, 

 however, utilize the age-structured catch data to 

 examine this type of model under the assump- 

 tion that recruitment is constant. 



We feel that the greatest confidence can be 

 placed in the estimates of instantaneous fishing 

 mortality (Fa) for 1961 through 1967 (Table 5) . 

 For this reason, these values were combined to 

 yield average monthly values (Fu) . The aver- 

 ages were computed as simple arithmetic means 

 to give vectors of average fishing mortality by 

 month and age for April through October (Table 

 10), and allow for computations of yield per re- 

 cruit. Yield per million recruits was computed 

 by step-wise integration (Ricker, 1958; Paulik 

 and Baylifl[", 1967). For a season of / months, 

 a year class would be exposed to fishing for 

 n = SI months and protected for 3(12 — I) 

 months. This would give a total lifetime after 



5 06 



SPAWNING FEMALES (Millions of Pounds) 



Figure 8. — Number of recruits on May 1 of year i+2 

 produced by spawning biomass of September, year i. 

 Smooth curve represents Model I of the text. 



recruitment of L = 36 months. The yield can 

 be expressed as 



L 3 12 



Y = X y^^ = XX ^^^^'' ^ ^ 12(t-l) +3 



k = l 



i = l 3 = 1 



where 



Wij — average weight taken from the empir- 

 ical growth curve, 



Cii — L^ Eij = number caught in month j of 

 year i, 



Eij = Fij(l — e~^k)/Zk = monthly exploita- 

 tion rate in month j of year i 



Z^ = (Fij + M) = total monthly instan- 

 taneous mortality 

 (note that Z was previously used 



Table 10. — Mean monthly instantaneous fishing mortal- 

 ity coefficients, F^j, by age group. 



1037 



