LAURS and WETHERALL: GROWTH RATES OF NORTH PACIFIC ALBACORE 



"outliers" it identified was consistent with the 

 number expected due to chance alone, because the 

 procedure has no sensible stopping rule, and 

 because even with length at release fixed, the 

 expected relationship between growth increment 

 and time out is nonlinear. 



Grouping of Data 



The selected data were cross-classified by loca- 

 tion of tagging and location of recapture (Table 2). 

 Nearly 66*^ of the 436 tagged fish were released 

 inshore, and of these 74% were released south of 

 lat. 40° N, the remainder north of this latitude. 

 Eighty-four percent of recaptured fish released 

 inshore south of lat. 40° N were recovered in the 

 same area, 5% were recovered inshore north of 

 lat. 40° N, 1.4% were taken in the offshore area 

 east of long. 180°, and 8.4% were recovered in the 

 western Pacific. Of the recovered fish tagged and 

 released inshore north of lat. 40° N, only 8.2% were 

 recaptured inshore south of lat. 40° N, 1.4% were 

 taken east of long. 180° in the offshore area, 27.4% 

 were recovered in the area of tagging and 63% 

 were recovered in the western Pacific. Of the re- 

 covered fish tagged offshore, 70.5% were re- 

 captured either inshore north of lat. 40° N or west 

 of long. 180°, and only 27.5% were recovered in the 

 southern inshore area. 



For purposes of constructing and testing 

 hypotheses about differences in growth rates, 

 tag returns were grouped into three categories 

 depending on recapture location: 1) Group A 

 includes all fish recaptured inshore south of lat. 

 40° N, except those released inshore north of lat. 



^Fish released (recaptured) east of long. 130° W in the area 

 south of lat. 49° N, or east of long. 135° W between lat. 49° and 54° 

 N were considered to be released ( recaptured) inshore. Demarca- 

 tion of the inshore area boundary is based on analysis of tag 

 recoveries discussed in Laurs and Lynn (1977). 



Table 2. — Classification of selected tag data by locations of 

 release and recapture. 



40° N (221 fish). 2) Group B consists of tag 

 recoveries made inshore north of lat. 40° N, 

 excluding those released inshore south of lat. 

 40° N (75 fish). 3) Group C consists of all tag 

 recoveries made west of the 180° meridian (114 

 fish). The three groups together comprise 410 

 recaptures. Excluded are 6 fish tagged inshore 

 north of lat. 40° N and recovered south of this line 

 the following year or later; 11 fish released south 

 of lat. 40° N and recaptured in the northern 

 inshore area (1 the same season, 10 in following 

 years); 6 fish recaptured offshore east of long 180°; 

 and 3 fish whose recapture locations are unknown. 



Growth Models 



We used observations of growth increment, 

 length at tagging, and time at liberty to estimate 

 the growth rate, K, and the asymptotic length, L^c, 

 of the standard deterministic von Bertalanffy 

 model. In addition, we considered an extension of 

 the von Bertalanffy model which allows the 

 growth rate to vary with age in a simple manner. 

 In general terms, we assumed that the expected 

 growth increment for thejth fish in the ith group 

 (i = 1, . . . , m; J = 1, 2,. . . , n,), given the initial 

 length and time out, could be stated as 



£(AL..) = J G{u) (L^ - L{u)) du. 



where E{^ Lij) = expected growth increment of 

 jth tagged fish in ith. group 

 during itij, Uj + ^ij) 

 = L(tij + Xj) -L(tij) 

 tij - age of jih. fish in ith group at 



time of release 

 Ay = time at liberty for jih. fish in 

 ith group 

 Liu) = length at age u 



Ly. = asymptotic length 

 G(u) = unspecified age-dependent 

 growth rate. 



If we set G(u) =K = constant, we have the 

 standard von Bertalanffy model, and 



E{AL.j) = (L^-L,..)[l-exp(-/CA.p], 



where L, = L(tfA. 



We call this Model 1. (We omit subscripts on 



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