LAURS and WETHERALL; GROWTH RATES OF NORTH PACIFIC ALBACORE 



Loc determined, the other parameters may be 

 estimated by the least squares method using the 

 general model: 



where 



Y, = -ln( 



L -Lj 

 L -Li 



ir 



^u * % 



Yij = - m 



— — ^ 1 = f G{u) du + ey 



and specified a fixed value for L^- Then we 

 developed and applied a weighted zero-intercept 

 covariance analysis to test hypotheses of the 

 form: 



where we assume that eij are independent errors 

 with zero means and variances cr^y. 



This approach handily accommodates any well- 

 behaved form of G(w). In the case of Model 1, the 

 problem of estimating/iC reduces to a simple linear 

 regression: 



H:Ki =K 



2 — • 



= K 



Yij = KA.J + e,. 



(1) 



When a reasonably accurate estimate of Lx can 

 be made by sampling the catches, this sequential 

 estimation procedure for Model 1 has the advan- 

 tage that the range of observations on Li.. and Aij 

 is not so critical. 



With Model 2, the sequential method may be 

 applied to estimate K, a, and fB using the 

 equation: 



on the basis of F-statistics. Statistical weights 

 were computed on the assumption that crlj — Aij, 

 as suggested by Figure 2. 



RESULTS 



Standard Model 



Joint estimates of K and Ly^ for Groups A, B, 

 and C, based on the BGC 4 program, are shown in 

 Table 3. We consider the estimates inaccurate, 

 owing to sampling biases discussed earlier. In 

 particular, we think the unexpectedly low L^ esti- 

 mates (and correspondingly high K estimates) are 



Y,j = KA,j -I- Un 



(l+a)/[l+aexp(-^Ay)] 



\+e,j. (2) 



The desirability of fitting this nonlinear model 

 to any particular set of data may be judged by 

 examining the residuals around the least squares 

 fit of Model 1 (Equation (D). As is evident from 

 Figure 2, the detection of nonlinearity in this 

 manner requires that observations be available 

 uniformly over a broad range of At;. 



Covariance Analysis 



One of our chief objectives was to determine 

 whether growth rates differed between groups of 

 fish, based on estimates of parameters of the 

 standard von Bertalanffy model. Since BGC 4 

 estimates of K and L^ are highly correlated, 

 particularly when few large fish are in the 

 sample, and since probability statements con- 

 cerning intergroup comparisons of both K and L 

 were not possible, we used the sequential esti- 

 mation procedure. For the ith group of fish we 

 assumed 



£{¥.,) = K,A 



U 



i "y. 



(3) 



due to the absence of very large albacore in the 

 release and recovery samples. Of the 410 selected 

 tag returns, 141 exceeded 80 cm fork length at 

 recapture, but only 42 were >85 cm and just 11 

 were >90 cm. The average fork length of tagged 

 albacore at time of release was 63.7 cm (range 45- 

 89 cm), and at recovery, 75.7 cm (range 51-103 

 cm). 



Because of the difficulties with BGC 4 

 estimates, we based intergroup comparisons on 

 estimates ofK from the sequential estimation pro- 

 cedure. A preliminary F-test showed no sig- 

 nificant difference in K between fish whose 

 lengths at recovery were measured and those 

 whose lengths were estimated from the inverted 

 weight-length relationship. Further sequential 

 analyses (as well as the earlier BGC 4 estimates) 

 were therefore based on all data, regardless of how 

 recovery length was determined. 



Ly-_ was fixed at 125 cm, a reasonable choice 

 well supported by available length-frequency 

 data. Although Otsu and Sumida (1970) reported 

 an albacore measuring 132.7 cm from the 



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