mortality rate with age than was found for total 

 catch (table 1): 



The deviations from the expected catch for some 

 year classes did not always indicate significant 

 negative correlation; the coefficients range between 

 —0.661 and 0.478. On the other hand, the devia- 

 tions in tiie same season were always positively 

 correlated; the coefficients vary between 0.2cS0 

 and 0.850. It is again found that the closer the 

 ages, tlie higher the correlation coefficients. The 

 multiple correlation coefficient for the tliree major 

 age groups is 0.877. 



In the southern California catch, the curves 

 were irregular for the year classes that occurred 

 after 1947. The following analysis of variance of 

 the means of logarithms of tlie catch per unit of 

 effort in southern California for the year classes 

 1930-48 shows that age and year class are signifi- 

 cant sources of variation : 



■Significant at a prot)al)ility of less than 0.1 percent. 



The standard catch curve is fairly smooth after 

 age III; age-dependent changes in mortality are 

 minor. The four year classes that were produced 

 in 1945-48, however, may differ in survival rate 

 as well as in stock size (table 2). The correlation 

 coefficient between deviations of the same year 

 class fluctuates l)roadly between —0.495 and 

 0.138. The correlations between deviations in tlie 

 same season are always positive, 0.223 to 0.890, 

 and are iiigher for two adjacent age groups; the 

 multiple correlation coefficient for age groups 111 

 to V was as high as 0.910. 



The mean deviations for age groups III through 

 V in central and southern California fluctuate 

 similarly; the correlation coefficient between them 

 was 0.810. Compared with the different regional 

 fluctuations in calcli per unit of effort of all the 



T.vBLE 2. — Mean sardine catch {In), total mortality co- 

 efficients, and change in mortality by age for the year 

 classes 1930-48 and 1930-44 in southern California | 



Age 0) 



Mean catch (In) 



Mortality 

 coefficient (Z,) 



Z,>,-Z, 



1930-48 1930-44 1930-48 1930-44 1930-48 1930-44 



Millions MiUioni 



offish offish 



II 907.6 888.5 



III . 701.9 680.2 



IV 251.1 283.6 



V 71.1 85.2 



VI 18.8 14.3 



age groups, this similarity may suggest that 

 some younger and older age groups than those in 

 question showed different changes in availability 

 between tliese two regions. 



The temperature anomaly at Scripps pier does 

 not correlate well with the deviations in catch, 

 but is slightly higher witli those in central Cali- 

 fornia (0.560) than with those in southern Cali- 

 fornia (0.495). 



DYNAMICS OF THE PACIFIC SARDINE 

 FISHERY 



This discussion deals with the age-dependent 

 changes in rates of natural mortality and a\ nil- 

 ability derived from information obtained tlius 

 far. A detailed model is presented for estiiuating 

 the ])arameters inherent in the jjopulation dy- 

 namics of the Pacific sardine. 



AH three sets of data analyzed above indicate 

 three characters of catch curves of the sardine: 

 (a) the increase of the virtual total mortality 

 coefficient with age; (b) the close relation ])clween 

 virtual indices of availability of two adjacent 

 age groups; and (c) the dependence of the avail- 

 ability on temperature in the months just before 

 the fishing season. To examine tiie reliability of 

 tliese findings, similar analyses are repeated with 

 estimates of tliese |)arameters as ])resented by 

 Widrig (1954) and Yamanaka (footnote 3). 



Previous authors a.ssumed that the natural 

 mortaUty coefficient was constant over the four 

 age groups III through VI. In Widrig's study 

 (1954) three api)ropnate values of tlie coeflicients 

 were assumed, and the rate of availability in a 

 season was showTi in relative rate to tliat of the 

 1936-37 season for each of these assumed coef- 

 ficients. Yamanaka (footnote 3) assumed that the 



592 



U.S. FISH AXU WILDLIFE SKRVICE 



