FISHERY BULLETINt VOL. 70, NO. 3 



and research vessel biomass estimates for 1965 

 through 1968. These data were used in applying 

 a stock production model and a dynamic pool 

 model. The general characteristics of these two 

 models were discussed by Schaefer and Beverton 

 (1963) under the designations of "Schaefer Ap- 

 proach" and "Beverton-Holt Approach," re- 

 spectively. 



STOCK PRODUCTION MODEL 



From an operational viewpoint stock produc- 

 tion models possess the advantage of requiring 

 only catch and effort data, which are usually 

 available at relatively little expense, for their 

 fitting. Another desirable characteristic is the 

 inclusion of density dependent effects, even 

 though they are treated grossly and population 

 response to density is assumed to be instanta- 

 neous. Pella and Tomlinson (1969) discuss the 

 assumptions implicit in the model. The most 

 notable fisheries application of this type model 

 was to yellowfin tuna of the eastern Pacific by 

 Schaefer (1954, 1957), who developed a method 

 for fitting the model to a population in a non- 

 equilibrium state, 



Pella (1967) examined a number of methods 

 for estimating parameters of the Schaefer model 

 and concluded that a surface searching tech- 

 nique for minimizing the summed, squared de- 

 viations between observed catches and catches 

 predicted by an integrated form of the Schaefer 

 model was generally most satisfactory. 



Pella and Tomlinson (1969) generalized the 

 Schaefer model to allow asymmetry in the inte- 

 grated form and gave the population growth rate 

 as 



dt 



= HP^it)-KP(t)-qfit)Pit), (1) 



where H, K, m, and q are constants. P{t) rep- 

 resents the population size at time t, f(t) is the 

 fishing intensity at t, q is the catchability co- 

 efficient, and m determines the amount of asym- 

 metry in the equilibrium yield curve. In the 

 Schaefer model, m = 2 and the equilibrium curve 

 is a parabola. The integral of (1) from time 

 to t with / constant is 



•(K + q/)(l-m)t 1-m 



J (2) 



X e- 



and Pella and Tomlinson (1969) used a numer- 

 ical approximation of 



C{t) = 



/: 



qf{t)P{t)dt 



(3) 



for computer calculation of expected catch over 

 the interval. Pella (1967) gives the integrated 

 form of (3) for the Schaefer model 



A computer program, GENPROD, (Pella and 

 Tomlinson, 1969) for fitting the generalized 

 model to catch and effort data uses the criterion 

 of least squares between observed and predicted 

 catches. Fox (1971) discusses least squares for 

 estimating parameters in (2) and suggests al- 

 ternatives which may be preferable to that used 

 by GENPROD. 



CATCH AND EFFORT DATA 



Catch and effort data have been collected since 

 the beginning of the fishery in 1952, but data 

 from the first 2 years of the fishery are not used 

 in this study because there was little effort and 

 low catch-per-effort values indicated that fish- 

 ermen had not fully acquired the skills needed 

 for successfully catching shrimp. California 

 landings were obtained from market receipts, 

 and effort by California vessels was obtained 

 from compulsory logbooks carried by all Cali- 

 fornia trawlers. Oregon landings and effort 

 were supplied by the Oregon Fish Commission 

 (Jack Robinson, Oregon Fish Commission, per- 

 sonal communication). 



California vessels were restricted to use of 

 beam trawls until otter trawls became legal in 

 1963. Oregon vessels have used otter trawls 

 since their entry into the fishery in 1960. A 

 correction factor was used to convert California 

 beam trawl effort to otter trawl effort for 1954 

 to 1962. 



Fishing power of beam trawls relative to otter 

 trawls was estimated from 40 pairs of catch- 

 per-hour statistics. These paired statistics con- 

 sisted of the average weekly catch-per-hour for 



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