Hampton Natural mortality and movement rates of Thunnus maccoyn 



603 



Consequently, in the second fit to the data, M was 

 assumed to be equal for the three fisheries (constrained 

 M), thus reducing the number of parameters from ten 

 to eight. A likelihood ratio test (Kendall and Stuart 

 1979) was conducted with the constrained-M fit defined 

 as the null hypothesis and the unconstrained-M fit as 

 the alternative hypothesis (assuming R = 1.0). The test 

 indicated that the unconstrained-M fit was significantly 

 better than the constrained-M fit (P<0.01). However, 

 the constrained-M fit resulted in much smaller standard 

 errors for the critical parameters (Table 8); q 3 has a 

 coefficient of variation (CV) of 15%, with all other 

 parameters having CVs of less than 10%. The correla- 

 tion among the parameters is also much more accep- 

 table (Table 9), although M is still correlated to a degree 

 with q 3 and T 13 , as are the qs with their respective in- 

 coming and outgoing movement parameters. 



There are substantial changes in some 

 of the parameter estimates obtained from 

 the constrained-M fit. The overall esti- 

 mate of M is 0.23/year, which is similar 

 to the estimate of M 3 obtained from the 

 unconstrained-M fit, but is much smaller 

 than the M] and M 2 estimates. There is 

 little change in q! , c^, T 12 , or T 2] ; how- 

 ever, T 13 and T 23 are much larger in the 

 constrained-M fit. These higher values 

 compensate for the reduced M] and M 2 

 estimates (now assumed equal to M 3 ) in 

 order to maintain the observed high rate 

 of attrition of tagged fish in the NSW and 

 SA fisheries. With the higher movement 

 rates into the Japanese fishery, q 3 is 

 smaller in the constrained-M fit so that 

 the observed rate of return of tags from that fishery 

 is still well described by the model. The estimate of M 

 is insensitive to reductions in reporting rate to about 

 0.7, while the other parameter estimates behave 

 similarly to those of the unconstrained-M fit. 



Plots of observed numbers of returns and the num- 

 bers expected on the basis of the constrained-M fit for 

 each of the release-recapture categories do not reveal 

 any glaring deficiencies in the model (Fig. 2). Plotting 

 expected numbers of returns using the unconstrained- 

 M fit produced an essentially identical result. 



Analysis B The results of the unconstrained-M fits 

 to the results of experiments 2 and 4 are given in Table 

 10. The estimate of M : is substantially smaller (0.28/ 

 year) than that obtained from analysis A. To maintain 

 the observed rate of attrition of tagged fish in the NSW 



