AN APPLICATION OF YIELD MODELS TO A CALIFORNIA 



OCEAN SHRIMP POPULATION 



Norman J. Abramson' and Patrick K. Tomlinson^ 



ABSTRACT 



Two types of yield models were utilized to analyze fishery data from California's northern- 

 most bed of ocean shrimp, Pandalus jordani. The Schaefer form of stock production 

 model was applied to catch and effort data for the years 1954 through 1969. Age-struc- 

 tured catch data for 1955 through 1968 were analyzed by the Murphy method to obtain 

 mortality rates and biomass estimates. Catchability coefficients and a growth curve 

 were also estimated. Attempts to fit spawner-recruit models to estimates obtained from 

 the age-structured catch data were inconclusive; so, age specific mortality and growth 

 estimates were only used to fit a yield-per-recruit model. 



After comparing the results from the two models, the Schaefer model was deemed 

 most suitable for managing this fishery. The model estimated the maximum sustain- 

 able yield at 2.46 million pounds. A strategy for managing the fishery under a quota 

 system was proposed. 



The fishery for ocean shrimp, Pandalus jordani, 

 in California has a unique importance despite 

 the fact that it does not rank high among the 

 State's fisheries in terms of pounds landed or 

 value of the landings. This unique importance 

 exists since the fishery developed after discovery 

 of the shrimp beds by the California Department 

 of Fish and Game's exploratory fishing and be- 

 cause it has been under continuous quota control 

 by the California Fish and Game Commission 

 since the fishery's inception in 1952 (Dahlstrom 

 1961, 1970). It is also the only California com- 

 mercial fishery whose catch is fully regulated 

 under a quota system. 



This paper is limited to a discussion of the 

 population and fishery which range along the 

 coast from the mouth of the Mad River in Cal- 

 ifornia to the Rogue River in Oregon. This 

 fishery consists primarily of regulated Califor- 

 nia vessels, but there is a small Oregon fleet not 

 covered by California's regulations while fishing 



^ California Department of Fish and Game, Opera- 

 tions Research Branch, Long Beach, Calif.; present 

 address: National Marine Fisheries Service, Tiburon 

 Fisheries Laboratory, P.O. Box 98, Tiburon, CA 94920. 



- California Department of Fish and Game, Opera- 

 tions Research Branch, La Jolla, Calif.; present ad- 

 dress: Inter- American Tropical Tuna Commission, P.O. 

 Box 271, La Jolla, CA 92037. 



north of the California border. Three smaller 

 populations which occur farther south in Cali- 

 fornia are not considered here. 



Initially, quotas were set arbitrarily at one- 

 fourth the estimated biomass on the bed. Bio- 

 mass was originally estimated from an exam- 

 ination of commercial catch data and later from 

 research vessel cruise data. In later years, quota 

 recommendations were at least partially directed 

 toward allowing what was deemed an appropri- 

 ate spawning stock to remain at the end of the 

 season. Spawning stock values were based on 

 estimated preseason year class abundance and 

 estimated survival over the fishing season. 



Estimating procedures which assume commer- 

 cial or research fishing gear catches all shrimp 

 in the water column above the swept path must 

 inherently be negatively biased since escape- 

 ment over, around, and through the gear occurs. 

 The methods just discussed are of this type. A 

 more complete account of the basis for quota 

 recommendations prior to 1969 is found in Dahl- 

 strom (1961, 1970), Dahlstrom and Gotshall 

 (1969), and Gotshall (in press). 



Over the history of this fishery substantial 

 amounts of data have been collected. Of rel- 

 evance to this paper are catch and effort data, 

 estimated age and sex composition of landings, 



Manuscript accepted March 1972. 



FISHERY BULLETIN: VOL. 70, NO. 3, 1972. 



1021 



