PRELIMINARY ANALYSIS OF THE CATCH CURVE OF THE PACIFIC 



SARDINE, Sardinops caerulea Girard 



By SiGEiTi Hayasi, ' Nankai Regional Fisheries Research Laboratory, Kochi, Japan 



ABSTRACT 



This is a report on a method of estimating age- 

 dependent changes in rates of natural mortality and 

 the age- and season-dependent changes in rates of 

 availability of the Pacific sardine. It includes estimates 

 of the virtual average catch curve and relative year class 

 strengths and deviations of individual curves from these 

 estimates. The calculations are carried out with each of 

 three sets of data: total California catch, catch per unit 

 of effort in central California, and catch per unit of 

 effort in southern California. 



The average catch curve allows an estimate to be 

 made of the increase in the natural mortality rate 

 during fully recruited ages. The deviations of individual 

 curves are assumed to represent the annual changes in 



rate of availability of each year class under a certain 

 condition. The deviations of different age groups in the 

 same years are compared to give a general idea of age- 

 dependent change in the rate of availability in a year. 

 Availability is also examined in regard to ocean tem- 

 peratures preceding the fishing season. 



A detailed model is proposed to estimate parameters 

 relevant to the sardine population on the basis of the 

 above examination as well as on the basis of earlier 

 estimates of rates of natural mortality and availability. 

 Consideration of the detailed model indicates the 

 necessity for several sources of information to establish 

 methods for predicting the sardine catch. 



A fisherman's income depends on the size and 

 behavior of stocks of fish entering his fishing 

 grounds as well as on the efficiency of his gear. A 

 fishery biologist must predict the size of the fish 

 stocks available to the commercial fisheries. 

 Taylor's ^ multiple regression equation, based on 

 temperature and salinity in the year of spawning 

 and on body length at the end of the first year of 

 life, predicts the virtual stock size of a Pacific 

 sardme year class. Availability of this fish, how- 

 ever, varies from season to season (Widrig, 1954), 

 thus complicating the problem of prediction. To 

 be useful to the fishermen, therefore, forecasts are 

 needed for particular seasons and they must be 

 based on yearly changes in availability in addition 

 to year-class strength. 



Widrig (1954) used relative rate of availability 

 of the Pacific sardine to estimate population sizes 

 and Yamanaka ' developed a method for estimat- 

 ing the absolute value of the rate. Both authors 

 started from the formida: 



Z=M-log {re~'^+{l-r)] 



(1) 



' This manuscript was prepared during tlie author's visit at the Bureau 

 of Commercial Fisheries Biological Laboratory, La Jolla, Calif., November 

 1959 to October 1960. 



2 Taylor, Clyde C. Some factors associated with year class size of the Pacific 

 sardine. Bureau of Commercial Fisheries Biological Laboratory, La Jolla, 

 Cahf. (Manuscript). 



Published May 1968. 



where Z and M denote instantaneous coefficients 

 of total and natural mortalities as defined by Holt, 

 GuUand, Taylor, and Kurita (1959). Other sym- 

 bols are defined as:/=amount of effort, Q=efR- 

 ciency of unit effort, and r=rate of availability. 



Widrig (1954) and Yamanaka ' assumed that 

 tlie rates of natural mortality and availability are 

 constant for four age groups (III- to Vl-year-old 

 fish). Introducing age-dependent changes in these 

 rates into the calculations complicates the prob- 

 lem. Because the above authors did not do so, it is 

 necessary to check the assumptions of equation 

 (1) from another point of view. 



In this paper I am interested in three matters. 

 First I determine, through a simple examination 

 of the catch data, if there is evidence of age- 

 dependent changes in natural mortality and in 

 availability. I also compare the various estimates 

 of availability and their relation to an environ- 

 mental factor, ocean temperature. Then I present 

 a method to estimate the parameters on more 

 probable assumptions resulting from these 

 examinations. 



GENERAL STATEMENT 



In the first examination of the age data, I made 



3 Yamanaka, Ichiro. Some notes on the natural mortality and availability 

 of the California sardine. Nankai Regional Fisheries Research Laboratory, 

 Kochi, Japan (Manuscript). 



FISHERY BULLETIN: VOLUME 66, NO. 3 



587 



