ABRAMSON and TOMLINSON: APPLICATION OF YIELD MODELS 



each gear within a 10-fm depth interval bounded 

 by a 10-min by 10-min block area. The data 

 were collected during 1960 through 1962 when 

 Oregon vessels were using otter trawls and Cal- 

 ifornia vessels were still restricted to beam 

 trawls. California Department of Fish and 

 Game trawler logbooks and information supplied 

 by the Oregon Fish Commission were the sources 

 of the records (Tom Jow, California Department 

 of Fish and Game, personal communication). 



With otter trawl taken as the standard gear, 

 the relative log fishing power of beam trawls 

 was computed by Robson's (1966) method ex- 

 cept the two gear types were used in a manner 

 analogous to his treatment of individual ves- 

 sels. If the logarithm of catch-per-hour is nor- 

 mally distributed and the other assumptions of 

 Robson's model hold, then his method produces 

 Bi, an unbiased estimate of relative log fishing 

 power, (3i, for the tth gear. However, exp (Bi) 

 is a biased estimate of exp (/?,). An unbiased 

 estimator for exp {{30 is given by Laurent 

 (1963) as 



00 



exp (A) = rexp(5i)iri + v^ _t^ 



i = i 

 (n—k—1)' [v(Bi)V 

 (n—k—1) (n—k+l) ... (n—k + 2j—S)]' 



(4) 



X 



where v (Bi) is an unbiased estimate of the var- 

 iance of Bi with n — k — 1 degrees of freedom. 

 Robson's method provides v{Bi) and our com- 

 puter program for calculating fishing power 

 carries the series expansion in (4) to 15 terms. 

 This computer program is described by Berude 

 and Abramson (1972) and a FORTRAN listing 

 is contained in Abramson (1971). 



The estimated fishing power of beam trawls 

 relative to otter trawls in the shrimp fishery 

 was 0.71; all beam trawl effort used in this 

 study was adjusted by that factor. 



FITTING THE PRODUCTION MODEL 



Usable catch and effort data covered a period 

 of 16 years, each divided into open and closed 

 seasons. Each season was treated as a sep- 



arate interval in the fitting procedure and thus 

 population estimates were obtained at 32 points 

 in time. Table 1 shows catch, adjusted effort, 

 and time for the series of seasons used to fit 

 the generalized production model. 



When initially fitting GENPROD to the data 

 the parameters representing optimum effort 

 (Fopt), catchability coefficient (q), maximum 

 catch-per-effort (C/max), and the ratio of initial 

 population to maximum population (r) were un- 

 restricted. Pella and Tomlinson (1969) give 

 these parameters as transformations of those in 

 ( 2 ) . The equation was fitted with the parameter 

 m taking values from 1.4 to 2.6 by increments 

 of 0.2. Results showed that number or distri- 

 bution of data points was not sufficient to de- 

 termine the value of m with any degree of pre- 

 cision and that very small population estimates 

 accompanied by excessively large q values were 

 being obtained. 



The first problem was handled by setting m 

 = 2, since the symmetric or Schaefer model 

 seemed best in face of the uncertainty. The 

 catchability coefficient was fixed at a value which 

 minimized the sum of the squared deviations be- 

 tween GENPROD'S estimates of Pit) and re- 

 search vessel cruise estimates of population bio- 

 mass at seven time points when both were avail- 

 able. The research vessel biomass estimates 

 were obtained from surveys conducted in the 

 spring and fall of 1965, 1966, and 1967 and the 

 fall of 1968 (Gotshall, in press). Gotshall's 

 catch in weight per standard haul was expanded 

 on an areal basis to provide estimates for the 

 entire survey area; as mentioned previously, 

 these are negatively biased. Based on this pro- 

 cedure, q = 8.5 X 10 ~^ was the best value. The 

 final fit of the Schaefer model was made with 

 GENPROD's computing parameters KK and AT 

 set equal to 5 and 10, respectively. KK is re- 

 lated to the fineness of the surface searching 

 procedure, and N involves the accuracy of the 

 numerical integration used to estimate expected 

 catch. These computing parameters are ex- 

 plained fully in Pella and Tomlinson (1969). 



GENPROD estimated a maximum equilibrium 

 catch (Cmax) of 2.46 million pounds, an effort 

 level required to obtain this catch under equi- 

 librium conditions (Fopt) of 6,049 otter trawl 



1023 



