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



217 



ian Islands. Additional details on the tagging program and 

 the fisheries are given in Itano and Holland (2000). As of 

 June 2001, 1131 (14.9%) bigeye and 983 (18.5%) yellowfin 

 tuna were recovered. A summary of releases and recap- 

 tures with usable information given in Table 1. 



The method used to analyze the data is an extension of a 

 tag attrition model commonly used in the analysis of tuna 

 tagging data (e.g., Kleiber et al, 1987, Hampton, 1991a). 

 We developed a site- and size-specific model to describe 

 the dynamics of the tagged population in the study area 

 by combining Sibert et al.'s (2000) site-specific model with 

 Hampton's (2000) size-specific model. This size- and site- 

 specific tag attrition model can be written as 



di 





(1.1) 



where T,, = ^"^ = 0; and at f=0, N^,= aN^,. 



L(/,,n= L„-/J + 



1-e 



(-K>i-t„i] 



+ L 



dC„ _ 

 dt 



I"., a,., A. 



at f = 0; C,, = 0. 



(1.2) 



(1.3) 



The subscripts ; and 7 ii, j=i;2..,tU indicate release and 

 recapture sites and k is the release cohort stratified over 



three size classes (see below). Note "site" is used in this 

 paper to refer to a release or recapture "compartment" 

 from the modeling perspective. Equation (1.1) partitions 

 the rate of attrition (loss of tags) into fishing mortality F, 

 natural mortality M, tag shedding A. and the transfer rates 

 T, (emigration from site / toj). It may also include immi- 

 gration of returnees that occurred in previous time step(s). 

 Note that T^, are not defined in the model and are set to 

 zero. Tag shedding parameters A and a were estimated 

 by an independent tag-shedding analysis (see below). F 

 and M are defined as functions of release size /^ and time- 

 elapsed since release up to the middle of the current time 

 interval i. Because there is no direct way of observing the 

 size of released cohorts as they grow in the model, we 

 used a growth model to track their growth in the model. 

 We assumed that individuals in tagged population grow 

 according to the von Bertlanffy growth model (Eg. 1.2), 

 which has the parameters t^, K, and L„. The parameters 

 of the growth model (K, and LJ may be estimated from 

 the same data set by using the growth increment and 

 time-at-liberty data (Hampton, 1991bl. We attempted 

 estimating the model parameters using our data set from 

 various approaches (James, 1991; Kirkwood and Somers, 

 1984; Wang and Thomas, 1995). Regrettably none of the 

 approaches provided satisfactory estimates of the growth 

 parameters to cover the full size range of the fish that 

 would be required for the attrition model. The usable 

 growth data and the size range available in the data 

 set were simply not sufficient for estimating the growth 

 parameters. Instead we used the parameter estimates for 

 bigeye and yellowfin tuna from the tropical Central Pacific 

 estimated by (Hampton, 2000). The third part of the model 

 (Eq. 1.3) describes the recapture rate of the tagged fish 

 (C^,), which is assumed to be proportional to the numbers 

 available (A^^, ) in the time period — the proportionality con- 

 stant being the fishing mortality rate. 



For the purposes of this model, a release cohort is defined 

 as the number of releases of a given size class stratified by 

 site. One-centimeter initial size classes were used result- 

 ing in 252 cohorts (29-133 cm fork length, |FL| ) for bigeye 

 and 247 cohorts (20-140 cm FL) for yellowfin tuna for all 

 the sites. The recoveries from each cohort were stratified 

 by the recovery sites over 10-day time-at-liberty intervals. 

 Further stratification of releases by calendar date was not 

 practical because of the small numbers of releases and 

 subsequent recaptures in each 1 cm x date x site stratum. 

 Instead, we assumed that all releases occurred at time zero. 

 This assumption in tag releases inevitably led us to assume 

 that fishing effort was constant during the recovery period 

 (1995-2000). This is a common assumption (e.g. Hampton, 

 2000) and justified if the fishery operated at a more or less 

 constant level during the recovery period. Although the 

 crude catch and effort I fishing days) data that we have 

 show seasonality in the catch rates, we felt it was reason- 

 able to assume the fishing effort exerted on the fishery 

 remained constant throughout the experiment 



We assumed zero lagging-induced mortality and that 

 nearly all (95%) recoveries were reported, at least from 

 the local fisheries. Close communication and a high level 

 of cooperation between the fishing and fish processing 



