FISHERY BULLETIN: VOL. 75, NO. 3 



to simulate this phenomenon, the following 

 quarterly growth adjustment factors were used: 

 K, = K 2 = 0.0 and K 3 = K 4 = 2.0. 



Estimation of c 12 of the recruitment-tempera- 

 ture factor (TV, Equation (16)) depends on the form 

 of the recruitment relationship that is assumed. 

 The parameter c 12 was estimated for both the 

 linear and density independent recruitment func- 

 tions (Equations (17) and (18)) using estimates 

 of annual recruitment reported by Sissenwine 

 (1974). During 1949-53, recruitment averaged 

 6.82 million fish (recruits to the stock of market- 

 able fish, about 3 yr and older) with a spawning 

 stock size proportioned to an average relative 

 abundance of 1.4 tons/day and an average annual 

 temperature of 11.08°C. On the other hand, for 

 1960-63, recruitment averaged 49.7 million fish 

 with a relative abundance and annual average 

 temperature of 2.9 tons/day and 9.65°C, respec- 

 tively. 



For the density independent recruitment func- 

 tion, fluctuations in recruitment result directly 

 from fluctuations in T g . An increase in recruit- 

 ment and in T g by a factor of 7.3 while the tem- 

 perature anomaly changes from 0.905 to -0.525 

 provides an estimate of c 12 = -0.89 by solving the 

 following expression: 



7.3{l + c 12 (0.905)} = 1 + c 12 (-0.525). 



If egg production is assumed proportional to stock 

 size or relative abundance, then for the linear 

 recruitment function, the increase in recruitment 

 by a factor of 7.3 would reflect an increase in 

 spawning stock size by a factor of 2.05 (=2.9/1.4) 

 and an increase of T g by a factor of 3.56 (=7.3/ 

 2.05). Therefore, solving the following expression: 



3.56{l + c 12 (0.905)} = 1 + c 12 ( -0.525) 



C12 = -0.68 for the linear recruitment function. 



Since little is known about the survival of 

 yellowtail flounder eggs and their eventual re- 

 cruitment to age-group 1, c 13 of the recruitment 

 function was estimated by fitting the model to 

 data (see Verification). The parameter c 13 was 

 estimated as 5.8 x 10 6 (fish per egg) for the linear 

 recruitment model and as 60.0 x 10 6 (fish) for the 

 density independent recruitment model. 



Both estimates appear realistic as indicated by 

 the following discussion. The average recruitment 

 to the stock of marketable fish reported by Sissen- 

 wine (1974) was 22.8 x 10 6 fish. Assuming an 



instantaneous natural mortality of 0.4 for age- 

 group 1 and a natural mortality of 0.2 with a total 

 gear mortality of 0.5 (F + D) for age-group 2, 

 recruitment to age-group 1 may be crudely esti- 

 mated by multiplying recruitment to the market- 

 able stock by 3.0. Thus, average annual recruit- 

 ment to age-group 1 could be estimated as 68.4 

 x 10 G fish which is similar to the estimate of c 13 

 for the density independent model. For the linear 

 recruitment model, c 13 is the proportion of eggs 

 that survive to be recruited to age-group 1 under 

 average temperature conditions. Using the aver- 

 age catch per effort for 1943-66 ([/ = 2.5 x 10 6 

 g/day), the sex ratio (c 11 = 0.5), the catchability 

 coefficient (q = 1.68 x 10~ 4 ), and an estimate of 

 average weight and fecundity (of females) of the 

 nominal stock (W = 451 g, Fe = 700,000 eggs), 

 c 13 could be crudely estimated as 5.9 x 10~ 6 using 

 c 13 = (R  W  q)/(Uc 11  Fe). For the winter 

 flounder, Pseudopleuronectes americanus, Saila's 

 (1961) work indicated about 18 recruits to age- 

 group 1 per million eggs (actually reported 18 

 recruits/100,000 hatched eggs assuming 10% 

 hatching success). The value used here is some- 

 what lower, but the fecundity of the yellowtail 

 flounder is higher than for the winter flounder. 



In order to avoid the possibility of recruitment 

 becoming negative for extremely high tempera- 

 tures, the additional constraint that recruitment 

 never falls below 5 million fish was incorporated 

 into the model. 



The initial length and number of individuals of 

 each age-size compartment had to be specified 

 prior to simulating the fishery. Royce et al. (1959) 

 reported the mean length of age-groups 2-6 for 

 the first quarter of 1943. These values were 

 assumed as the initial length of size category 4 

 of the appropriate age-groups. For the initial 

 lengths of the other age-groups, reasonable but 

 arbitrary values were selected. The average ini- 

 tial size of each age-group is listed in Table 4. The 

 lengths of size categories 1, 2, 3, 5, 6, and 7 were 

 determined by multiplying the length of size 

 category 4 by 0.856, 0.908, 0.950, 1.050, 1.092, 

 and 1.144, respectively. These factors correspond 

 to the ratio of the maximum length of each size 

 category to the maximum length of size category 

 4. 



The onset of the collection of fishing effort data 

 was 1943; therefore, the model was used to simu- 

 late the fishery from that date. The relative abun- 

 dance of the yellowtail flounder during the first 

 quarter of 1943 was 5,742 fish/day (Royce et al. 



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