FISHERY BULLETIN: VOL. 75, NO. 3 



(1969a), Brown and Hennemuth (see footnote 2), 

 and Penttila and Brown. 5 



Some of the research cited above is recorded 

 only in unpublished documents. Any information 

 extracted from these reports must be considered 

 as preliminary. Accordingly, the work reported in 

 this paper was primarily based on the published 

 literature. 



Catch data used in this paper include both 

 domestic and foreign landings of yellowtail 

 flounder but exclude the industrial catch. All 

 effort data are expressed in standard days fished 

 as defined by Lux (1964). 



DESCRIPTION OF 

 THE MODEL STRUCTURE 



A diagram representing the compartments and 

 activities of the system is shown in Figure 1. Since 

 yellowtail flounder greater than 10 yr of age are 

 seldom encountered, fish were divided into 10 age- 

 groups. Certainly, the length of individuals 

 within each age-group is not uniform. Therefore, 

 each age-group was subdivided into seven size 

 categories in which all fish were assumed to be 

 of a uniform length. The number of size categories 

 was limited to seven in order to minimize com- 

 puter cost. The level (number of fich) of each of 

 the 70 age-size compartments is denoted by N lt j 

 where i indicates the age-group and j the size 

 category. Another attribute of each compartment 

 is its mean length, denoted by L, 7 with i and j 

 defined in the same manner. 



The yield of the fishery in weight (Y w ) and 

 number offish ( Y n ) landed annually are attributes 

 of the yield compartment. Total fecundity of the 

 population during each spawning season is P e 

 (number of eggs in the egg compartment). 



The important activities affecting the system 

 are: 1) fishing which results in a continuous trans- 

 fer of fish from age-size compartments to the 

 yield compartment and results in some non- 

 productive mortality (discard mortality) since not 

 all fish captured are actually landed (Brown and 

 Hennemuth see footnote 2); 2) natural mortality 

 which results in a continuous decay of each age- 

 size compartment and loss offish from the system; 

 3) aging which results in a discrete advancement 



RECRUITMENT 



5 Penttila, J. A., and B. E. Brown. 1972. Total mortality rates 

 for two groups of yellowtail flounder estimates from survey 

 cruise data from ICNAF Subarea 5. Int. Comm. Northwest Atl. 

 Fish., Res. Doc. 72/22, Ser. No. 2713, 14 p. 



DISCRETE DURING MAY OF YEAR 

 CONTIN UOUS 



FIGURE 1. — Compartments representing a fish population. 

 Three dots (...) indicate additional compartments. The age- 

 group is indicated by i and the size category by j. N,,, is the 

 number of fish in thejth size category of age-group i, and L,,, is 

 the mean length of the fish of the same compartment. Each com- 

 partment (only shown for (i,j)) undergoes continuous loss due to 

 fishing, discard, and natural mortality. Losses due to fishing 

 mortality are added to the yield compartment. At the beginning 

 (or end) of each year, aging occurs, advancing each compart- 

 ment to the next higher age-group, retaining the same value of 

 j. Recruitment to age-group 1 also occurs at the beginning of 

 each year as a function of the previous year's egg production. 

 Spawning occurs during May of each year (only shown for (i,j)) 

 with egg production a function of the number and size of fish in 

 each compartment. 



offish to the next higher age-group (retaining the 

 same value of j) at the beginning of each year; 

 4) spawning which is the discrete production of 

 eggs (P e ) during May (Bigelow and Schroeder 

 1953) of each year; 5) recruitment which is 

 represented as the discrete addition of individuals 

 to the youngest age-group of the model at the 

 beginning of each year according to the magni- 

 tude of P e during the previous year; and 6) 

 growth which results in a continuous increase 

 in Ltj. 



The dynamic system briefly described above 

 was simulated by a FORTRAN program using 

 finite difference approximation. Details of each 

 activity regulating the system are presented 

 below. The variables used in the model are defined 

 in Table 1. 



Fishing, Discard, and 

 Natural Mortality 



Each age-size compartment is subject to mor- 

 tality at a rate proportional to the number of 

 fish of the compartment; that is, 



466 



