Hampton. Natural mortality and movement rates of Thunnus maccoyn 



605 



fishery, a compensatory increase in T 12 is observed. 

 The estimate of M 2 is again relatively high (1.16/year) 

 while the estimate of M 3 compares closely with that 

 obtained from the unconstrained-M fit in analysis A. 

 Recall that releases into fishery 2 (SA/WA) for anal- 

 ysis B were made some distance away from the com- 

 mercial fishery operating at the time. This could ex- 

 plain the much lower estimate of q 2 , and as a result, 

 fishing mortality (~0.04/year). Similarly, the smaller 

 estimates of movement from WA/SA into the NSW and 

 Japanese fisheries is likely to be due to the fish being 

 released further away from those fisheries. 



The standard errors of the estimates that were ob- 

 tained for the unconstrained-M fit are somewhat less 

 than the equivalent values for analysis A, but are 

 nonetheless far too high for the estimates to be con- 

 sidered reliable. The correlation matrix (Table 11) 

 reveals a similar pattern of correlation among the 

 parameters as was observed for analysis A. 



It was not possible to obtain estimates of standard 

 errors for reporting rates less than 0.8 because of a 

 boundary condition with respect to the M] estimate, 

 which approached zero for low reporting rates (the Hes- 

 sian matrix could not be inverted because it was not 

 positive definite). This also indicates that the parameter 

 estimates obtained from this data set for reporting 

 rates less than 0.8 are not the maximum likelihood 

 estimates and therefore cannot be considered reliable. 



A constrained-M fit resulted in much smaller stan- 

 dard errors, changes in parameter estimates consistent 

 with analysis A (Table 12) and much lower correlation 

 among parameters (Table 13). A likelihood ratio test 

 (assuming R = 1.0) again indicated that the uncon- 

 strained-M fit is significantly better than the con- 

 strained-M fit (P<0.01). However acceptance of the 

 more complex model cannot be justified in view of the 

 large standard errors and correlations among the 



parameter estimates. Plots of 

 observed and expected num- 

 bers of returns (Fig. 3) indi- 

 cate a good fit of the con- 

 strained-M model to the data. 



Simulation results 



Simulated data sets were ana- 

 lysed in order to test the per- 

 formance of the HSH and SE 

 models. The simulations were 

 designed to produce data sets 

 identical in their character- 

 istics to experiment 2 and 3 

 (analysis A), with the excep- 

 tion that tag shedding and 

 non-reporting were not con- 

 sidered. Two sets of simulations were performed: type 

 1 simulations used the results of the analysis A un- 

 constrained-M fit as input parameters; type 2 simula- 

 tions used the results of the analysis A constrained-M 

 fit as input parameters. Thirty data sets were produced 

 for each simulation. Type 1 simulated data were ana- 

 lysed by the SE model using both unconstrained-M and 

 constrained-M fits. Type 2 simulated data were ana- 

 lysed using the SE model constrained-M fits and the 

 HSH model in order to provide a basic comparison bet- 

 ween the two models. 



Parameter estimate means and their standard devia- 

 tions for type 1 simulations are given in Table 14 for 

 the unconstrained-M fits and Table 15 for the con- 

 strained-M fits. These results indicate that (i) the un- 

 constrained-M fit provides unbiased estimates of all 

 parameters, and (ii) the constrained-M fit to simulated 

 data behaves in an identical fashion to similar fits to 

 real data in terms of the changes in the estimates of 

 q 3 , T 13 , and T 23 . Moreover, the accurate recovery of 

 parameters input to the simulation model demonstrates 

 the soundness of the SE method as applied to southern 

 bluefin tuna tagging data. 



Table 16 provides a direct comparison of parameter 

 estimates obtained by fitting the HSH and SE models 

 to type 2 simulated data. The results indicate that the 

 HSH model considerably overestimates M. The mean 

 estimates from simulated experiments 2 and 3 and the 

 mean estimate based on pooled data are almost iden- 

 tical (0.42-0.43/year) and are nearly double the value 

 of M input to the simulation model. The SE model, on 

 the other hand, is able to accurately retrieve the param- 

 eters input to the simulation model. This result casts 

 considerable doubt on the estimates of M for southern 

 bluefin tuna obtained using the HSH model. 



The reason for the biased estimates of M obtained 

 using the HSH model appears to lie in the very low 



