temperature is 0.686 — hijjher than that calculated 

 by me or by Widrig (1954). 



The correlation coefficient based on the rate of 

 availability is 0.757 and, thus, higher than that 

 based on the logarithmic values. 



Siunmarizing these examinations of the age 

 composition of the sai'dine catch by Widrig ( 1954), 

 Yamanaka (footnote ',i) and the present study, I 

 may be able to assume the following characteristics 

 of the available sardine stocks: 



a. The natural mortality differs by age and by 

 subpopulation and i)robably by year class; 

 therefore, T recommend that the rate be estimated 

 for each age group with the data taken in the short- 

 est period of years for which the analysis can be 

 made and for each fishing ground in which the 

 stock is more homogeneous. 



b. The availability also differs by age of the 

 fish. It is indicated, however, that the rates of 

 two successive age groups are similar. This fact 

 also indicates that the i)aranieters shoidd be 

 estimated for each age group separately. 



c. Availability seems to be correlated with 

 temperature. This possibility should be studied 

 in relation to temporal and areal patterns of the 

 envii'onment, as well as the general levels of 

 availability. For instance, Craig (1960) demon- 

 strated that the herring catch was related to 

 increase in temperature and strength and direc- 

 tion of winds in early summer, even though the 

 catch was not highly correlated with each of 

 these factors. Factors sru'h as these, regarded 

 important in Japan, include temperature dis- 

 tribution, intensity of cold water masses (up- 

 welling), and current strength and direction 

 (Shimomura, 1954). 



A more detailed model is ])resented on the 

 basis of age specific mortality and availability 

 characteristics. Because rates of availability of 

 two adjacent age groups in any year may be 

 assumed to be almost the same, the virtual 

 survival rate, S'at, obtained from age and catch 

 data is expressed as: 



S;,=exp(Z;,)=(Ar„+,.,+,)/(Ar„,r„,) 



= {r„,6-^<««'+(l -/•„,) }e^«'/V,+,. ,+,//•„, (9) 

 then 



Z',,=M„ -log {r„,e-^.««. + (!-/•„) } 



+ (logr„,-logr„+,.,+,) (9') 



where a and t denote age of fish and season, 

 594 



respectively. It is assumed that /•„, and Qa, are 

 equal to ra.,+, and Q„. ,+i respectively. 



The mean of virtual mortality coefficients for 

 7i seasons is the sum of means of the first and 

 second terms, and (log r„.i— log r„.„+i)/n. Then, 

 if Q remains constant for a long jjcriod of years 

 so that the last term diminishes to zero, the means 

 of the parameters including Q, M, and /- are esti- 

 mated as shown by Yamanaka (footnote 3). 

 The value of Q, however, siiould be regarded as 

 variable during rather sliurt ])eri()ds of years, 

 partly depending on gear improvement, such as 

 the several gear im|)rovements in the sardine 

 fishery in California. In addition, Q may vary 

 because of biological and economic reasons even 

 if the same type of fishing gear is used. Tlie 

 major factors relating to this quantity may be 

 classified in the following three groups: 



a. The first and most essential factor afl'ecting 

 Q depends on such variables as fish size, gear type, 

 and speed of liaulmg. This factor and the mechan- 

 ical selectivity discussed below, defined as 7 in 

 the following discussion, determined the efficiency 

 of a fishery for a particular size of fish distributed 

 in a certain way. 



b. The second factor, selectivity, is related to 

 both the fish and the fishery. Two general cate- 

 gories of selectivity sliould be distinguished. The 

 first is a mechanical selectivity, such as the size 

 and number of fish retained by the gear, and is 

 determined by the relation between sizes of mesh 

 or hook and fish; the second is an economic 

 selectivity, controlled by market ])erformance by 

 size or species. The former type of selectivity is 

 included in the first category (a above) of factors 

 controlling Q. The mean of the latter selec- 

 tivity factor is included in the rates of natural 

 nu)rtality. The deviation from mean is included 

 in availability. 



c. The third factor, volume of the water in 

 which the available |)art of the stock is distributed, 

 also causes change in Q even though the rate of 

 availability is constant. The same gear should be 

 more eft'ective or the same fishermen should locate 

 the schools more readily when the fish are distrib- 

 uted in smaller vohmies of water than in larger 

 ones. Changes in ])atchiness and depth of distri- 

 bution may not be as important as the size of the 

 waters when tlie discussion concerns a whole 

 season during which total eff"ects may be nearly 

 constant. Since sardines may remain in a particular 

 stratum, the volume of water may be a])])roxi- 

 mated by the area of fishing ground. A, that is 



U.S. FISH AND WILDLIFE SKRVICK 



