SISSENWINE: COMPARTMENTALIZED SIMULATION MODEL 



P. = 



f y 3 for « P 3 ■■= c 9 + c 10 L = ; 1 

 for P, 



1 for P, 



< 

 > 1. 



(15) 



Equation (15) assumes maturation is a linear 

 function of length in the transition zone between 

 the length below which the entire population is 

 immature and the length above which the entire 

 population is mature. Assuming that the propor- 

 tion of females in the population is constant, c 11; 

 then the egg production of each age-size com- 

 partment is the product of Njj, Fe (L IJ ),P 4 , andcn. 

 The total egg production of the population (P e ) is 

 obtained by summing over all age-size compart- 

 ments. 



Recruitment 



The possibilities that recruitment is a linear 

 function of egg production and that recruitment 

 is independent of egg production, under average 

 environmental conditions, were considered. There 

 is evidence (Sissenwine 1974) that recruitment 

 of the Southern New England yellowtail flounder 

 is also related to temperature. In fact, most of the 

 variability in estimated recruitment for 1944-65 

 was explained by anomalies in air temperature, 

 ignoring egg production. In order to simulate the 

 influence of temperature, a recruitment tempera- 

 ture factor (T r ) was defined as follows: 



T r = 1 + c 



12 



(T - T). 



(16) 



The number of recruitments as affected by tem- 

 perature is calculated by multiplying the level of 

 recruitment expected at average temperature 

 conditions by T ',.. 



The total recruitment (R) of a year class (at 

 age 1) is calculated by 



R 



-13 



Pe 



or 



R 



Cl3 



T r . 



(18) 



The parameter c 13 has a different value in each 

 equation. Equation (17) is applicable when re- 

 cruitment is linearly related to P e for average tem- 

 perature conditions. Equation (18) is applicable 

 when recruitment is independent of P e . Equations 

 (17) and (18) will be referred to as the linear and 

 density independent recruitment functions, re- 



spectively. The model described in this paper 

 incorporating either Equation (17) or (18) will be 

 referred to as the linear or density independent 

 models, respectively. Recruits are assigned to size 

 categories of age-group 1 by multiplying R by 

 the appropriate value of G r 



Parameter Estimation 



Estimates of the parameters of the model were 

 taken from the literature or based on published 

 or unpublished data sources. The parameter val- 

 ues used in all the simulations reported in this 

 paper (unless otherwise stated) are shown in 

 Table 2 along with citations of the source of the 

 estimate. Special attention is given below to the 

 estimation of some parameters and initial condi- 

 tions. These estimates of parameters and initial 

 conditions required some subjectivity. 



The natural mortality rate of the yellowtail 

 flounder has yet to be precisely estimated. Lux 

 ( 1969a) estimated that the upper limit on natural 

 mortality of adult yellowtail flounder is 0.20. 

 Beverton and Holt (1957) estimated the natural 

 mortality of a similar species (North Sea plaice) 

 as 0.10. Values of instantaneous natural mortal- 

 ity of 0.10 and 0.20 have been used in the litera- 

 ture in the past, An instantaneous natural mor- 

 tality rate of 0.10 was assumed for age-groups 

 3 and older fish in the model. Instantaneous nat- 

 ural mortality rates of 0.4 and 0.2 were applied 

 to age-groups 1 and 2, respectively. Based on a 

 generalized simulation model, Walters (1969) 

 concluded that natural mortality rates, especially 

 in older fish, could vary widely without affecting 

 harvesting strategies. 



Brown and Hennemuth (see footnote 2) reported 

 the size-group structure of fish captured and 

 landed by yellowtail flounder fishermen during 

 1963. According to these data, few fish less than 



250 mm). 



(17) 250 mm long were captured (L 



gm\i\ 



The modal value of Brown and Hennemuth's 

 capture curve is about 330 mm. The modal value 

 usually coincides closely with the length of com- 

 plete functional recruitment. Therefore, gear 

 efficiency was assumed to reach its maximum at 

 this length (L gmax = 330 mm). All yellowtail 

 flounder less than 300 mm long were discarded 

 at sea (L mmin = 300 mm) and almost all fish cap- 

 tured of greater than 350 mm were landed (L mmax 

 = 350 mm). Of course, market conditions will 

 change with time and there are now reports of 

 some fish less than 300 mm being landed. 



469 



