FISHERY BULLETIN: VOL. 74, NO. 1 



lation. The succeeding 10 subroutine call state- 

 ments are imbedded within a double "do-loop" 

 which is indexed by month and year. This double 

 loop is the principal timing mechanism of the 

 program. Hence, each of these 10 subroutines is 

 executed once a month in the order indicated and 

 either simulates a component of the system, their 

 interactions, or else produces output. 



Subroutines PROCS, HARVS, and REGLS 

 make programmed monthly decisions for the sys- 

 tem's respective processors, harvesters, and regu- 

 lators. PROCS and HARVS simulate monthly 

 decisions concerning the processing capacity 

 committed, the number of days spent harvesting, 

 the number of harvesting units committed, and 

 the gear efficiency per unit. Moreover, since pro- 

 cessors have only limited storage capacity for raw 

 materials, HARVS adjusts allowable vessel ca- 

 pacities as if processors were establishing boat 

 quotas (a situation presently occurring in the re- 

 duction fishery); this prevents overfishing and the 

 consequent dumping of excess catches. REGLS 

 compares these decisions to standards (regula- 

 tions) supplied by the user or determined by the 

 subroutine. If regulations are "broken," the sub- 

 routine makes appropriate adjustments to the 

 values of those parameters associated with im- 

 proper decisions. 



STOCKS is a user supplied subroutine which 

 simulates the biomass dynamics of the exploited 

 resource on a monthly basis. The northern an- 

 chovy subroutine is an age-structured model 

 which accounts for the processes of growth, mor- 

 tality, graduation, and reproduction for each of 

 the seven age-groups (ages 0-6) comprising the 

 population. The basic mathematical theory for 

 age-structured models is treated by Ricker (1958) 

 and Beverton and Holt (1957). This basic theory 

 has been modified to account for age-dependent 

 exploitation and variable recruitment processes 

 in the northern anchovy population. Similar 

 age-structured models have been developed in re- 

 cent years for other species by Tillman (1968), 

 Walters (1969), Fox (1973), and Francis (1974). 



Described further in an ensuing section, 

 STOCKS feeds catch values to HRVST, the sub- 

 routine which then simulates the monthly har- 

 vesting process. HRVST determines the catch of 

 each stock by a harvester, his harvest propor- 

 tional costs, and the cumulative catch taken from 

 each stock. 



RMARKT then simulates the sale of the har- 

 vesters' catches to the processors, and PRCES 



transforms these newly purchased raw materials 

 into finished goods which are added to the proces- 

 sors' inventories. Subroutine CMARKT then 

 simulates the sale of these products on the open 

 market to final consumers. The quantities de- 

 manded are determined from a user supplied de- 

 mand curve and a sales price set by the processor. 

 STATS then computes and outputs financial 

 statements for the processors and harvesters. It 

 also provides physical reports describing through 

 key variables the activities of the harvester, pro- 

 cessor, stock, and market sectors. Subroutine 

 SMSTAT then provides user desired cumulative 

 physical reports. Although all reports may be 

 provided at monthly intervals, printout typically 

 is suppressed until the year's end. 



The Biological Sector 



Some Important Assumptions 



Development of the biological model for north- 

 ern anchovy depends critically upon two assump- 

 tions. One concerns the stock structure of this 

 population and the other, its stock-recruit be- 

 havior. The following discussion briefly exam- 

 ines how reasonable these assumptions are and 

 hopefully provides some justification for their 

 application. 



Mais (1974) and Tillman (1975) review the evi- 

 dence which generally supports the hypothesis 

 that three distinct stocks exist within the north- 

 ern anchovy's total geographic range. The 

 simplifying assumption has been made that the 

 reduction fleet fishes exclusively upon that stock 

 which resides in the southern California- 

 northern Baja California region of the California 

 Current system. Results of tagging studies indi- 

 cate that some mixing of adult members of adja- 

 cent stocks might conceivably occur due to sea- 

 sonal north-south migrations (Haugen et al. 

 1969). However, Mais (1974) cites evidence from 

 comparisons of length-frequency and age-length 

 distributions which, in his opinion, indicates that 

 very little, if any, mixing occurs. Moreover, he 

 concludes that anchovies in this region should be 

 treated as a single biological unit for manage- 

 ment (and therefore modelling) purposes. 



Several studies (Cushing 1971; Tillman and 

 Paulik 1971; Murphy 1973) suggest that recruit- 

 ment in clupeid and engraulid populations is a 

 density-dependent process. Moreover, these 

 authors imply that the asymptotic stock-recruit 



120 



