SISSENWINE: COMPARTMENTALIZED SIMULATION MODEL 



TABLE 4. — Initial (1 January 1943) mean total length in milli- 

 meters of each age-group for yellowtail flounder model. The 

 lengths of age-groups 2-6 were reported by Royce et al. ( 1959). 



Age-group 



Mean length (mm) 



Age-group Mean length (mm) 



160 

 271 

 324 

 353 

 372 



6 



7 



8 



9 



10 



401 

 425 

 440 

 450 

 460 



1959). Dividing this by q, the mean population 

 size during this quarter was estimated as 34.2 x 

 10 6 fish. Because there is little growth and, there- 

 fore, little recruitment during the first quarter 

 (since fish are recruited as they grow to the size 

 vulnerable to fishing gear), the population was 

 assumed to undergo exponential decay during this 

 time interval. The effort expended during the 

 first quarter of 1943 was 2,038 days (Royce et al. 

 1959), resulting in a total maturity Z = 1.47 

 (Z = M + qf where /"is the rate of fishery in days 

 per year). Accordingly, the size of the landable 

 stock at the beginning of 1943 was estimated as 

 about 41.1 x 10 6 fish (using Equation 1.38 of 

 Ricker (1975) modified for an interval of one- 

 quarter of a year). 



Royce et al. (1959) also reported the age compo- 

 sition for the first quarter of 1943. The catch pri- 

 marily comprised fish greater than 3 yr of age. 

 The number offish captured per day for age-group 

 3 and older is shown in Table 5. Based on the 



TABLE 5. — Catch per day and relative abundance adjusted for 

 fishing vulnerability of age-group 3 and older yellowtail flounder 

 for the first quarter of 1943. These age-groups represented 95% 

 of the catch. 



Adjusted 

 Age-group Catch/day relative abundance 



1,793 



1.596 



1,008 



504 



476 



3.984 



1,995 



1,061 



504 



476 



length composition assumed for each age-group 

 and Equation (9), the relative level of fishing 

 mortality suffered by fish of age 3, 4, 5, and older 

 was calculated as 0.45, 0.80, 0.95, and 1.00, re- 

 spectively. By dividing the catch per day of each 

 age-group by the appropriate factor, the relative 

 abundance adjusted for fishing vulnerability was 

 obtained (also Table 5). These values represent 

 the relative abundance of each age-group in the 

 population. Using Table 5, 



N 5 . 

 N e . 

 N 7 . 

 N 8 . 



N 9 



N 10 . 



0.55 7V 4 

 0.48 2V 5 , 

 0.50 N 6 

 0.50 7V 7 

 0.50 N 8 . 

 0.50 JV 9 . 



0.280 2V 3 . 

 0.130 2V 3 . 

 0.065 N 3 

 0.033 N 3 _ 

 0.016 N 3 _ 

 0.008 N 3m 



where the subscript . indicates the summation over 

 all size categories, and the survival of fish older 

 than 7 yr was assumed to be 0.50. The size of the 

 marketable population was estimated by sum- 

 ming N, times the relative fishing vulnerability 

 of age-group i. This expression was set equal to 

 41.1 x 10 6 fish and solved for N 3 _ (=32.0 x 10 6 

 fish). Estimates of initial conditions for other 

 age-groups were obtained using the equations in 

 this paragraph. Age-group 2 was assumed to be 

 twice age-group 3 as indicated by a natural mor- 

 tality of 0.2 and a discard mortality of about 0.5. 

 Based on a natural mortality of 0.40 age-group 1 

 was assumed to be 1.5 times age-group 2. The 

 initial conditions of each age-group for the begin- 

 ning of 1943 based on the above discussion are 

 shown in Table 6. The population was distributed 

 among the size categories according to the appro- 

 priate values of G,. 



TABLE 6. — Initial size of each age-group of yellowtail flounder 

 population assumed at the beginning of 1943. 



Age-group Number in thousands Age-group Number in thousands 



95,000 

 64,000 

 32,000 

 16,000 

 8,800 



6 

 7 

 8 

 9 

 10 



4,200 



2,100 



1.100 



530 



260 



N d = 0.50 JV, 



VERIFICATION 



The primary mode of verification of the model 

 was to compare predicted annual levels of catch 

 with published values. Lux's (1969a) record of 

 catch and fishing effort for 1943-66 is in conflict 

 for several years with data reported by Brown and 

 Hennemuth (see footnote 2) in an unpublished 

 form. These conflicts are minor, except for the 

 1966 catch where the difference is about 40%. 

 Since this year is at the end of the published record 

 and could easily be ignored, 1943-65 were initially 

 used for verification. After c 13 was fit to the data, 

 the model was then compared with data through 

 1972. 



Before comparing the model with the published 

 data, it was necessary to select a time step or 



473 



