TILLMAN and STADELMAN: SIMULATION MODEL OF ANCHOVY FISHERY 



relationship of Beverton and Holt ( 1957) is gen- 

 erally applicable to populations which have an 

 extended spawning season, whose adults are 

 cannibalistic upon their own young, and whose 

 annual recruitment variations are relatively 

 small. Results from surveys for pelagic eggs and 

 larvae conducted off California indicate that the 

 northern anchovy spawns over virtually the entire 

 year (Ahlstrom 1966). Baxter (1967) stated that 

 this species is a filtering and biting feeder which 

 consumes its own eggs and larvae. Moreover, 

 Murphy (1966) noted that this species has never 

 had spectacularly good nor spectacularly bad 

 year classes and that this may have been a factor 

 in the relatively slow replacement of the Pacific 

 sardine, Sardinops sagax, by anchovies following 

 the collapse of the sardine fishery. Conse- 

 quently, since the northern anchovy apparently 

 fits the required life-style, an asymptotic stock- 

 recruit model does not seem too unreasonable 

 an assumption, although it is an admittedly cir- 

 cumstantial and speculative one at this time. 



General Description of STOCKS 



STOCKS' main job is to solve the catch equa- 

 tion and pass the result to subroutine HRVST. 

 The following description briefly summarizes the 

 sequence of operations which occur each month 

 and some of the parameter values required to 

 determine the catch in weight for each age group. 

 The details of parameter estimation are given 

 by Tillman (1972). 



Following the combined adjustments of 

 PROCS, HARVS, and REGLS, STOCKS first re- 

 ceives the allowed values of the following vari- 

 ables: level of fishing effort (number of vessels), 

 vessel capacity (metric tons (MT)/boatday), 

 fraction of the month fished, and fishing power of 

 a vessel (Table 1 gives values of relative fishing 

 power for various-sized vessels for which eco- 

 nomic performance data are available). These 

 four variables are used to calculate equivalent 



Table l. — Efficiencies and relative fishing powers of hypothet- 

 ical vessels operating on northern anchovy. From Till- 

 man (1972). 



standard effort, in terms of boats fishing the 

 entire month instead of a fraction of it, and the 

 total harvesting capacity of the reduction fleet. 



Next the age structure is updated by account- 

 ing for the process of graduation. Since the 

 great bulk of spawning activity occurs during 

 January-May, most anchovies have their birth 

 dates during these 5 mo. Table 2 gives the pro- 

 portion of each age-group that is expected to 

 graduate at the start of the months indicated. 

 Recruits due to enter in the current month are 

 added to the first age-group, and fish leaving the 

 last age-group disappear. Within each age- 

 group, size of the individual is computed as a 

 weighted average of the sizes of newly entered 

 and residual fish. From these adjusted weights 

 and numbers at age, the biomass of the popula- 

 tion is computed. 



Contribution to spawning then is calculated 

 for the current month. The number of females 

 eligible to spawn is determined by the propor- 

 tion of females in the population (Table 3), by a 

 maturity at age schedule (Table 4), and by a 

 schedule of the incidence of monthly spawning 

 activity (Table 5). The egg production of these 

 spawning females is computed by a fecundity at 

 age schedule (Table 6). The results of this proce- 

 dure are additions to the number of eggs de- 

 posited on the stock's spawning ground. 



Instantaneous total mortality rates then are 



Table 2. — Probabilities of graduating from one age group into 

 the next for northern anchovy. From Tillman (1972). 



Table 3. — Estimates of fraction of females by number in the 

 tottd northern anchovy population. 



Source 



Estimate 



Source 



Estimate 



Clark and Phillips (1952) 0.57 



(Vliller et al. (1955) 0.56 



Miller and Wolf (1958) 0.52 



l^acGregor (1968) 0.56 



Collins (1969) 

 Collins (1971) 

 Average 



0.60 

 0.58 

 0.56 



Table 4. — Maturity at age schedule of northern anchovy. From 

 Tillman (1972). 



MOO-MT (metric ton) vessel is standard. 



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