natural mortality coefficient fluctuated around a 

 mean and that the rate of availability fluctuated 

 around a logarithmic mean for the 23 seasons 

 from 1932-33 to 1954-55. Because the level of 

 availability changed between the early and later 

 years of the investigation, he di\'ided the period 

 into two parts; one from 1932-33 to 1945-46, and 

 the other from 1945-46 to 1954-55. The present 

 report examines only Ms final estimates based 

 on the divided data. Because these authors first 

 estimated the rate of availability in logarithms, 

 my analysis of the rate is usually made with 

 logarithmic rather than actual values. 



As estimated by Yamanaka (footnote 3), the 

 increase in vu-tual total mortaUty coefficients 

 with age is comparable to decrease in availability 

 of older fish. As expected from his assumption, 

 availabiHty should decrease with age if total 

 mortality increases. Therefore, I conclude that 

 the virtual coefficient of total mortality of the 

 Pacific sardine increased with age for the period 

 investigated. 



The age-dependent change in the virtual 

 coefficient of total mortaUty may be partly 

 attributed to incomplete recruitment * in addition 

 to a real change in natural mortaUty, insofar as 

 it is estimated from the age composition of the 

 commercial catch. Although no conclusive evi- 

 dence is obtained, it seems to me that the increase 

 in natural mortaUty with age is real rather than 

 caused by incomplete recruitment for the fish 

 at and older than the three ages discussed, since 

 the fishery has exploited fish as young as age I 

 and sometimes age zero. If this increase in natural 

 mortaUty with age is real, the natural mortality 

 coefficient of these fish is considered to increase 

 linearly with age (table 1). A Unear increase of 

 the coefficient with age was postulated by 

 Beverton and Holt (1957, pp. 69-71) for thi-ee 

 species: two herrings, Clupea harengus harengus 

 and C. harengus pallasi, investigated by Hodgson 

 (1932) and Tester (unpublished, cited by Ricker, 

 1948) and the whitefish, Coregonus clupeaformis, of 

 Lake Opeongo studied by Ricker (1949). A Unear 

 increase with age may not always hold, however, 

 as was shown for the same species, or ecologically 

 related ones, surveyed on other occasions: namely 

 the whitefish of Shakespeare Island Lake, the 



' Age of complete recruitment of a partially available population is defined 

 as the age at which all the fish are potentially "catchable" by the fishery 

 even if, actually, some of them do not always enter the fishing ground. When 

 rates of availability are estimated for all the age groups appearing in the catch, 

 the age of complete recruitment is determined by comparison of the average 

 rate for each age. 



sauger, Stizostedion canadense, of Lake Opeongo 

 (Ricker, 1949), and the herring, C. harengus pallasi 

 (Tester, 1955). 



It is noteworthy that total mortality coefficients 

 are higher in southern California than in central 

 California — also the increments, which average 

 about 0.30 in southern California but 0.15 in 

 central California, as previously shown. This 

 difference is partly attributed to differential dis- 

 tribution of the fish by age; older fish migrate 

 farther north. It should be noted, however, that 

 Yamanaka (footnote 3) estimated the natural 

 mortality coefficient of the sardines to be higher 

 in the more recent years, when the southern sub- 

 popidation predominated, than in earlier years 

 for the entire range of the fishery in California. 

 Thus, both his and my results agree that the 

 mortality rate is higher in the southern subpopula- 

 tion than in the northern one. 



It has been shown thus far that the rate of 

 availability differed between age groups exploited 

 in the same fishing season but that it was close 

 for two adjacent age groups. A comparable result 

 is obtained from the analysis of the availability 

 rates as estimated by Yamanaka (footnote 3). 

 As to the age-dependent change in availability, it 

 has already been suggested that some species of 

 fish school together by size or by age, including, 

 among others, the hening, C. harengus (Hjort, 

 1926, p. 8); the sardine, Sardinops melanosticta 

 (Yamanaka, 1955, p. 51) ; the anchovdes, Engraulis 

 mordax (Miller, 1955, p. 30), and Cetengraulis 

 mysiicetus (Howard and Landa, 1958, p. 394) ; 

 the yeUowfin tuna, Thunnus alhacares (Schaefer, 

 1948, p. 199); and the skipjack tuna, Katsuwonus 

 pelamis (Brock, 1954, p. 99). 



As an approach to predicting catch, the tempera- 

 tin-e data at Scripps pier just before the fishing 

 season were regarded as having been correlated 

 with the preliminary estimates of availability. 

 The correlation coefficients between temperatures 

 and the logarithms of each series of estimates by 

 Widrig (1954), based on assumed values of the 

 natural mortality coefficients of 0, 0.2, and 0.4, 

 are 0.256, 0.305, and 0.300, respectively. Smce 

 Yamanaka (footnote 3) estimated the natural 

 mortality coefficient to be 0.35 for all the seasons, 

 or 0.25 "for 1932-33 through 1945-46 and 0.65 

 for 1945-46 through 1954-55, the most probable 

 rate of Widrig's estimates of availability, based on 

 the assumed natural mortality coefficient of 0.4, 

 is best correlated with temperature. In Yama- 

 naka's estimates, the correlation coefficient with 



ANALYSIS OF CATOH CURVE OF PACIFIC SARDINE 



593 



