METHODOLOGICAL PROBLEMS IN 

 SAMPLING COMMERCIAL ROCKFISH LANDINGS 



A. R. Sen 1 



ABSTRACT 



The present sample survey plan, for the estimation of age and species composition of California rockfish 

 landings, which is stratified two-stage with port-month group as a stratum, poses serious operational 

 problems in data collection. A revised plan is suggested which is workable. Formulas have been developed 

 for estimating total catch and its error by species-sex-age groups; optimum sampling and subsampling 

 fractions have been obtained for a given cost function and the precision of the estimator is compared 

 with two other estimators. The method developed has been extended to cover situations other than rockfish. 

 The paper also deals with double-sampling for specified cost for the estimation of age composition 

 of a species, which is important to predict the status of a stock in future years, the inherent problems 

 in data collection in commercial fisheries, and the measurement errors involved in the survey. 



Estimates of the total catch (in terms of number) 

 by species-sex-age and by area of landing and dur- 

 ing a given time for commercial rockfish caught in 

 California north of point Arguello are currently 

 based on a probability sample of landings. The com- 

 mercially important species of rockfish taken by 

 California's fishery with mixed species are widow 

 rockfish, Sebastes entomelas; bocaccio, Sebastes 

 paucispinis; and chilipepper, Sebastes goodei. 



A study was undertaken during 1983 under agree- 

 ment between the present author, the Humboldt 

 State University Foundation, and the Tiburon 

 Laboratory of the National Marine Fisheries Ser- 

 vice, NOAA, to determine if the present sampling 

 plan for the estimation of species and age-composi- 

 tion of California rockfish landings is workable. The 

 study revealed that the current plan is not opera- 

 tionally feasible. A revised plan is proposed which 

 is workable and would provide efficient estimates 

 of the parameters based on existing catch data 

 within the usual limitations of budget and person- 

 nel and under the assumptions made in the plan. 

 Formulas have been developed for the ratio 

 estimators of mean and total catch and their errors. 

 Optimum sampling and subsampling fractions have 

 been obtained for a given cost function and the preci- 

 sion of the estimator is compared with two other 

 estimators. 



For most theoretical population work and for 

 management purposes, the knowledge of the age 



'Department of Mathematics and Statistics, Queen's University, 

 Kingston, Ontario, Canada K7L 3N6; present address: 67 Ranch- 

 Ridge Way N.W., Calgary, Alberta, Canada T3G 1Z8. 



composition is important to predict the status of the 

 stock in future years. Fridricksson (1934) developed 

 the age-length key method for determing age com- 

 position from a large number of length measure- 

 ments. Fridricksson's approach was improved by 

 Ketchen (1950) who provided more accurate results 

 for age groups at the extremities of the distribution. 

 Kutkuhn (1963) mentioned the limitations of the age- 

 length key approach except in situations where price 

 differentials may demand sorting of landings by size 

 criterion. Westrheim and Ricker (1978) pointed out 

 that the age-length key approach will almost always 

 give biased estimates. Clark (1981) and more recent- 

 ly Bartoo and Parker (1983) dealt with methods for 

 control or elimination of bias. Following the method 

 of Tanaka (1953) in which stratification occurs after 

 subsampling for age, Kutkuhn (1963) estimated 

 absolute age composition of California salmon land- 

 ings by port-month groups. He showed that the sam- 

 pling procedure is not effective unless the age sam- 

 ple is at least five times costlier than the length 

 sample. 



Mackett (1963) found double sampling more effi- 

 cient than simple random sampling with fixed sam- 

 pling costs for estimating relative age composition 

 of Pacific albacore landings. 



Southward (1976) found that a sample of otoliths 

 proportional to the length frequency of sampled fish 

 from each port was preferable to fixed sample size 

 procedure for estimating age composition of Pacific 

 halibut. Kimura (1977) arrived at the same conclu- 

 sion as Southward by following a somewhat dif- 

 ferent approach. 



We will present some of the important considera- 



Manuscript accepted August 1985. 



FISHERY BULLETIN: VOL. 84, NO. 2, 1986. 



409 



