Adam et al,; Dynamics of Thunnus obesus and T albacares in Hawaii's pelagic fisheries 



219 



which is the area other than the bounded compartments, 

 would represent the entire Pacific-wide fishery. 



Results 



The maximum likelihood method of estimating parameters 

 allows one to statistically select among nested models those 

 models that best fit the data on the basis of the likelihood 

 ratio test (Brownlee, 1965; Hilborn and Mangel, 1997). The 

 size-specific attrition model is a special case and is nested 

 within the general model with constant mortality rates. By 

 setting the size-specific attrition to be the same for all the 

 sizes, the model reverts to the general case. Thus, with only 

 a minor change, the model can be made to estimate attri- 

 tion over a single size class or a single F for more than one 

 site by describing alternative models of the data. 



The parameters of the tag shedding model were esti- 

 mated at a = 0.94 ±0.035 and A = 0.000243 ±0.000452 per 

 day. Because the standard deviation of the estimate of A 

 was greater than the estimate, A was assumed to be zero 

 in the analysis. Estimates of a and the point estimate of A 

 were consistent with what has been estimated elsewhere 

 with the same methods of tag release (Table 2, Adam and 

 Kirkwood, 2001). 



Several variants of the attrition model were evaluated 

 including attrition estimated over a single size class and 

 common fishing mortality rates among the offshore sites, 

 (buoy 1, buoy 2, buoy 3, and Cross Seamount). The number 

 of parameters to be estimated may be conveniently used to 

 identify these structurally different models. For example, 

 MJ<'.^ jT,., is the model in which M is estimated over three 

 size classes, F over three size class and by five sites and 

 with 13 transfer coefficients for the observed exchanges. 



For both species, the model in which the attrition is 

 partitioned over size classes demonstrated significant 

 improvement (P>0.999 using a likelihood ratio test) over 

 the reduced models: M3F3 5T'j3 versus M^F^^^Ty^ for bigeye 

 tuna and M.^F^^T^- versus Mi^i gTn for yellowfin tuna. 

 Similarly, the models with site-specific fishing mortalities 

 described the data significantly better (P>0.999) than mod- 

 els where a common fishing mortality was estimated for all 

 offshore sites. The observed and predicted tag returns by 

 time-at-liberty and by initial size classes of releases pro- 

 vide good descriptions of the data. The graphs for the Cross 

 Seamount fishery are shown in Figures 2 and 3. Agreement 

 between observed and predicted number of tags by site is 

 reasonably good, particularly for sites where large num- 

 bers of recoveries were made (Tables 2 and 3). 



The transfer coefficient estimates for movements between 

 the various sites ranged from virtually zero to 0.05/day (Ta- 

 bles 4 and 5 ). For bigeye tuna, the transfer rate estimates 

 from buoy 2, buoy 3, and the Cross Seamount to the longline 

 fishery were higher than the transfer rates from those same 

 sites to inshore areas (Tables 3 and 4 ). For yellowfin tuna, the 

 pattern was similar except for the additional high transfer 

 estimate from buoy 1 to the longline area. These differences 

 between the transfer rates (from offshore sites to inshore 

 site versus offshore sites to longline area) in both species 

 were statistically significant (taken to mean that the 95% CI 

 ranges did not overlap) showing the importance of emigra- 

 tion into the longline fishery compared with emigration into 

 the inshore area. Yellowfin tuna transfer rate from inshore to 

 the Cross Seamount was virtually zero but transfer from in- 

 shore to the longline area was very low (0.00703/day ). There 

 was no observed transfer of bigeye tuna to the longline fish- 

 ery from the inshore areas and a very low transfer rate was 

 estimated to the Cross Seamount (0.00375/day). 



