198 



Fishery Bulletin 102(1) 



Materials and methods 



Biological data 



Biological data have been compiled since 1964 for purse- 

 seine, set-net, dip-net catches, and other catches by national 

 fisheries research institutes and local government fisher- 

 ies experimental stations in Japan. Fork length (FL) was 

 measured for one thousand to 100 thousand fish per year 

 and body weight (BW) and gonad weight were measured for 

 10-100Tf of these fish. The monthly FL compositions and 

 the relationships of FL to BW were established for each 

 year with this data set. Year-specific age-length keys from 

 1970 to 1994 were adopted from the reports of cooperative 

 research on Pacific mackerel by local government agencies 

 in Chiba, Kanagawa, Shizuoka, and Tokyo. 2 Between 1995 

 and 1997, age-length keys were developed by national 

 fisheries research institutes and local government fisher- 

 ies experimental stations. 



For calculating the mean FL for ages 0, 1, 2, 3, 4, 5. and 6 

 years and older, we used data from the purse-seine fishery 

 of northeastern Japan during September-December for 

 28 years, from 1970 to 1997. The catch of this fishery in 

 these four months constituted 26-80% ( the 28-year mean is 

 about 639c ) of the total annual catch of the Pacific stock of 

 chub mackerel. Catch in number at FL class i (cm) of each 

 month were calculated by 



n.,=C. 



(1) 



I* 



where n a i = catch in number at FL class i (cm) (= 1, . . . , 

 k, . . 50) of month a {= Sep., Oct., Nov., Dec.]; 

 d a t = frequency at FL class i of month a; 

 w a ( = a mean weight of each FL class derived from 

 the FL-BW relationship; and 

 C a = a total catch of month a. 



We then summed n a , of 4 months to derive the annual 

 catch in number at FL class i: 



where n t j = the annual catch in number at FL class i at 

 age J; and 

 r :j = the proportion of agej at FL class i ( r t + r, 1 + 



•••• + '-,*= 1»- 



From n lt , we calculated the mean and variance of FL at 

 age./': 



I" » 

 l.,=^\ 



(4) 



and 



I",X,-// 



Va /•(/,) = - 



2Xi 



(5) 



where L = mean FL at age./'; and 



/,■ i = mean FL at FL class i at age j. 



Sea surface temperature 



Time-series data for sea surface temperature (SST tem- 

 peratures averaged over 10 days for 1° latitude x 1° longi- 

 tude blocks over the northwestern North Pacific between 

 0-53°N and 110-180°E since 1950) were provided by the 

 Oceanographical Division of the Japan Meteorological 

 Agency. The SST data for each block was averaged for 

 periods of three months (i.e. January-March, April^June, 

 July-September, and October-December). The relationship 

 between the SST of each block and FL at age were exam- 

 ined from 1970 to 1997. 



Autocorrelation 



For correlation analysis, effective sample sizes («') were 

 calculated for all time series data to take autocorrelation 

 into account, n* was computed by the formula (Pyper and 

 Peterman, 1998): 



"i = X "°" 



(2) 



a Sep 



where /;, = the annual catch in number at FL class i. 



Using the age-length key, we converted n t to catch at FL 

 class i at age j: 



(3) 



J_-i 1 



5/jaC/XrO"). 



(6) 



where r x> Xj) and r^Xj) are the autocorrelations of X and Y 

 at lagj, defined here with the additional weighting factor 

 proposed by Pyper and Peterman ( 1998): 



^(X t -XKX l+j -X) 



r„U) = 



"-./ 



£«■,-*) 



(7) 



2 Age-length keys. In Kanto Kinkai no Masaba ni tuite, Ap- 

 pendix 1, vol. 30, 30 p. [In Japanese. Available from Kanagawa 

 Prefectual Fisheries Research Institute. Jyogashima, Misaki. 

 Miura. Kanagawa 238-0237. .Iapan.1 



Growth model 



We used the modified von Bertalanffy growth model to 

 incorporate the effects of population density and sea sur- 



