Therefore, 



A,,=log C,,-E (log C,,) 



+ (log /-o-Clog /-i+log r,.-log r) } + {log E,^ 



-(log£:,-+log£;,-logE)} (8) 



Among the variables in formula (8), we can deter- 

 mine combined effects of yearly changes in 

 mortality coefficients and availability rate. Be- 

 cause 2;A,j = 0, the deviations of the same year 

 class should be negatively correlated when the 

 changes in rates of availability and exploitation 

 are less important than change in mortality 

 coefficients in determining the catch curves. On 

 the other hand, significant positive correlation 

 between deviations of any two age groups taken 

 in the same seasons indicates that deviations in 

 availability and exploitation are important. 



A similar meaning attaches to any measure that 

 is proportional to the available stock size, such as 

 catch per unit of effort; here the change in rate uf 

 exploitation is disregarded. It should be noted 

 that the deviations are affected by the year-class 

 average of logarithms of availability and are not, 

 then, a measure of relative availability on the 

 same base. 



TOTAL CALIFORNIA CATCH 



Age composition of the California sardine has 

 been reported for 26 seasons, 1932-33 through 

 1957-58 by Eckles (1954), Wolf (1961), Felin and 

 Phillips (1948), Mosher, Felin, and Phillips (1949), 

 Felin, Phillips, and Daugherty (1949), Felin, 

 Daugherty, and Pinkas (1950, 1951), Felin, Anas, 

 Daugherty, and Pinkas (1952), Felin, MacGregor, 

 Daugherty, and Miller (1953, 1954, 1955), Felin, 

 Wolf, Daugherty, and MiUer (1958), Wolf, 

 MacGregor, Daugherty, and Miller (1958), and 

 Daugherty and Wolf (1960). When catch is 

 plotted against age on a semilog scale for each year 

 ?lass, the catch curves are fairly smooth for fish 

 alder than age II of most year classes, but are 

 rary irregular for some year classes — especially 

 bhose spawned in 1947 through 1949 (fig. 1). 

 rhese irregular curves may be due to changes in 

 ivailability and exploitation. The catch curves of 

 some year classes indicate moderate irregularity. 

 For instance, year classes 1930 through 1933 

 night have been highly available in the 1936-37 

 season. 



Figure 1. — Catch curves of Pacific sardine, year classes 

 1926 through 1954. Vertical scale equals log of millions 

 of fish; distance between zero points for each year class 

 equals 1.0 (i.e., 10,000,000 fish). 



The age- and year-class mean of log 0^ for the 

 22 year classes from 1930 to 1951 are, nevertheless, 

 regarded as sufficiently significant to give a reliable 

 standard catch curve and estimates of year-class 



iNALYSIS OF CATCH CURVE OF PACIFIC SARDINE 



589 



