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Fishery Bulletin 101(2) 



community of Hawaii and the HTTP were maintained to 

 ensure high levels of reporting. There were 191 releases of 

 bigeye (2.5% of release) lacking size of fish or geographic 

 position of released fish (or both), which are necessary in- 

 formation for the analysis. For yellowfin tuna this figure 

 was 79 (1.5% of release). The number of tag returns with 

 no usable information, i.e. accurate recapture fork length 

 or recapture position (or both) were few (2.9% for bigeye 

 and 1.1% for yellowfin tuna). We had to assume a value for 

 a, because this parameter cannot be estimated accurately 

 from tagging data. The components included in a were 

 the proportions recoveries with no useful information, 

 proportion of tags lost immediately following release (the 

 so called type-I shedding, see below) and the nonreporting 

 of recoveries. Using the proportions in these categories, we 

 obtained values of a as 0.85 for bigeye and 0.87 for yellow- 

 fin tuna, which were fixed in the model fits. 



In order to reduce the number of parameters, attrition was 

 estimated over size classes instead of the one-centimeter 

 release cohorts. First a vector indexed from the smallest to 

 the largest possible size was used to assign the one-centime- 

 ter size classes of the cohort as it "grew" in the model over 

 time. A second vector with the same number of elements 

 indexed with the desired size-class numbers can then be 

 mapped onto the previous vector to estimate attrition over 

 size classes. The attrition rates were estimated over three 

 size classes for each species. For yellowfin tuna the size 

 classes were 20-45, 46-55, and >56 cm FL and for bigeye 

 tuna the size classes were 29-55, 56-70, and >71 cm FL. 

 There was no reason for selecting these size classes but 

 these ranges produced strata with sufficient numbers of 

 recaptures to give model stability and convergence. 



The number of parameters to be estimated can be fur- 

 ther reduced by only estimating transfer coefficients for 

 empirically observed transfers. It is possible to estimate 

 coefficients for all possible transfers. However, we found 

 that estimated coefficients for nonobserved transfers are 

 not well determined by the data. Therefore in the interest 

 of parsimony and model stability, we estimated transfer 

 coefficients for the observed transfers only and assumed 

 transfer coefficients for unobserved transfers to be zero. 



Attrition from cohorts was followed independently for 

 140 ten-day time periods (approximately 47 months). A 

 semi-implicit finite difference approximation was used to 

 obtain numerical solutions of Equation 1.1. The estimates 

 of the parameters were the values, which maximized the 

 Poisson likelihood function: 



L=p(c,jc„,i=nf]n 





where C 



kit 



the observed recoveries; and 



(2) 



Ckit ~ ^^^ predicted recoveries from the model. 



The maximum likelihood estimates of the parameters were 

 obtained by minimizing the negative log of the likelihood 

 function (Kq. 2) with ADModel Builder nonlinear optimiza- 

 tion package (Otter Research Ltd., 2000). 



Tag shedding 



Tag shedding was estimated independently from a double 

 tagging experiment conducted simultaneously with the 

 main experiment with identical methods and procedures. 

 The first tag was inserted on the left side and the second 

 tag on the right side. Of the total 200 fish (bigeye and yel- 

 lowfin tuna) double tagged and released, 57 were recovered; 

 49 with two tags and eight with one tag. The model used 

 to estimate tag shedding was a simple exponential decay 

 model with constant type-II shedding rate (Kirkwood and 

 Walker, 1984; Hampton, 1997).Theprobabihty of retaining 

 a tag Qit) over time is given by 



Q{t) = ae-^ where < a < 1, (3) 



where a = the type-I retention proportion; and 

 A = the constant type-II shedding rate. 



Using the assumptions and method described in Adam and 

 Kirkwood (2001), we obtained the maximum likelihood 

 estimates of the parameters by comparing the observed 

 and predicted returns using exact dates of recovery. 



Site selection 



One of the primary goals of conducting the HTTP was to 

 estimate the transfer rates between various fishery compo- 

 nents, such as the Cross Seamount and the inshore fishing 

 areas, and the Cross Seamount and offshore longline fish- 

 ery. For the type of "bulk transfer" model described here, a 

 site can be any arbitrary area with reasonable numbers of 

 releases or recoveries (or both). The sites used in our study 

 were carefully selected to represent individual fishery com- 

 ponents from a management perspective. A total of six such 

 compartments were identified and are shown in Figure 1. 

 There were no releases of bigeye tuna from buoy 1 and 

 only two recoveries of bigeye tuna were made from buoy 1 

 from the releases made elsewhere. For these reasons, these 

 two recoveries were assigned to "other" area. This protocol 

 resulted in five sites for bigeye and six sites for yellowfin 

 tuna (see Table 1). 



The NOAA weather-monitoring buoys 1, 2, and 3, act 

 as de facto fish aggregating devices that concentrate large 

 schools of bigeye and yellowfin tuna, making them highly 

 vulnerable to the handline fishery (Itano and Holland, 

 2000). From a management point of view, the fishery 

 around these offshore FADs is essentially similar to the 

 Cross Seamount fishery and is exploited by the same 

 vessels. The primary method of fishing at these areas is 

 handlining. The inshore fishing areas contain a network 

 of some 50 moored FADs that, when combined, can be 

 considered one of the most frequently visited inshore fish- 

 ing areas used by a diverse small-boat fleet (Itano and 

 Holland, 2000). Fishing methods around inshore FADs 

 include surface trolling, live baiting,jigging, and handline. 

 The "other" area specified in the model is essentially the 

 longline fishing ground more than 50 nmi offshore from 

 the inshore sites. P'roni the model's perspective, this area, 



