SISSENWINE: COMPARTMENTALIZED SIMULATION MODEL 



TABLE 1. — List of variables of yellowtail flounder, Limanda 

 ferruginea, model. 



Variable 



Description 



m 



Yn 

 Yw 

 Pe 



w 

 Fe 



Z 

 D 

 F 

 M 

 G 

 f 

 t 



P1 



P 2 



pa 



T 

 k 

 Tr 



Number of fish in size category y of age-group / 



Length of fish in size category/ of age-group / 



Yield of fishery in number of fish 



Yield of fishery in weight of fish 



Annual egg production of stock 



Weight of fish as function of length 



Fecundity of fish as function of length 



Instantaneous total mortality rate 



Instantaneous discard mortality rate 



Instantaneous fishing mortality rate (excluding discard mortality) 



Instantaneous natural mortality rate 



Instantaneous gear mortality rate (G F • D) 



Instantaneous rate of fishing 



Time 



Relative gear effectiveness as function of length 



Probability of landing a captured fish as function of length 



Probability of a fish being mature as function of length 



Index of temperature 



Growth rate coefficient of von Bertalanffy equation 



Recruitment-temperature factor as function of temperature 



Growth-temperature factor as function of temperature 



Annual recruitment to age 1 



diNjj) 

 dt 



= -(F + D + M) • Ntj 



(1) 



where F, D, and M are the instantaneous fishing, 

 discard, and natural mortality rates, respectively, 

 and t is time in years. Total mortality of fish 

 greater than 10 yr old was assumed. Very few 

 fish reach this advanced age. Lux (1964) reported 

 that fish discarded at sea suffered a high mortality 

 rate. In the model, all discarded fish were assumed 

 lost. The yield rate, in number offish and biomass, 

 contributed by each compartment is 



d(Yn) 

 dt 



= F  N 



ij 



(2) 



and 



d(Yw) 

 dt 



= F  N 



i,j 



W(L U ) 



ij' 



(3) 



where W(L) is a function relating the weight of 

 a fish to its length. This function assumes the 

 usual form, 



W(L) = Cl • V 



(4) 



The letter c with a numerical subscript is used 

 throughout the paper to denote constants. The 

 total yield rate is obtained by summing d(Yn)ldt 

 and d(Yw)/dt for all age-size compartments. 



The mortality rate inflicted by fishermen 

 (F + D) on the yellowtail flounder population is 



assumed to be proportional to the instantaneous 

 annual rate of fishing if) for fish which are fully 

 vulnerable. This mortality is called the gear 

 mortality (G), 



G =F +D =q  f 



(5) 



where q is the catchability coefficient. The num- 

 ber of days fished annually is determined exter- 

 nally to the model and acts as a driving variable. 

 Natural mortality was assumed to decrease with 

 age until maturation and then remain constant 

 through the rest of the life span. 



In order to approximate the seasonality of 

 fishing, the instantaneous rate of fishing is esti- 

 mated by multiplying the total number of days 

 fished annually by quarterly effort adjustment 

 factors (c 3 , c 4 , c 5 , andc 6 ) where the average value 

 of these factors is 1. 



Yellowtail flounder first become available to 

 trawl gear on the Southern New England ground 

 in about 1 yr (Brown and Hennemuth see footnote 

 2), but they are not captured commercially until 

 they have grown to the minimum size retained 

 by the fishermen's nets, L gmin . Some fish continue 

 to escape the nets because of their small size until 

 they have grown to the length at which the gear 

 obtains its maximum effectiveness, L 



gmax- 



It is 



assumed that the relative effectiveness of the gear 

 from fish with a length between L gmin and L gmax 

 can be calculated by linear interpolation. Accord- 

 ingly, the relative effectiveness of the gear, P lt 

 is defined as follows: 



Pi 



(Li L/g m [ n )/(Lig max 



for L gmin =s L ^ L 



for L < L gmin 



1 for L > L gmax 



J-'grnin' 

 gmax 



(6) 



where L is the length for which Pj is applied. 



Since not all of the fish captured are large 

 enough to be marketed (for economic and techno- 

 logical reasons), the probability of landing a cap- 

 tured fish (P 2 ) as a function of its length must 

 be calculated. Let L mmin be the minimum length 

 landed by the fishermen and L mmax be the length 

 at which all fish are landed. Note that the deter- 

 mination of the marketability of each fish is made 

 by the fishermen on the decks of their vessels. 

 Therefore, a gradual transition from total un- 

 acceptability to total acceptability as L increases 

 is expected. Again applying linear interpolation, 



467 



