Bertignac et al.: Estimates of exploitation rates for Thunnus alalunga from tagging data 



423 



130E 



150E 



170E 



170W 



150W 



130W 



now 



i \ 



• • • 



• • • 



01 

 o 



Z 



o 



130E 



150E 



170E 



170W 



150W 



130W 



110W 



Figure 3 



Geographical distribution of North Pacific albacore releases, 1971-89 



Population dynamics model for tagged albacore 



We used a tag-attrition model (e.g., Seber, 1973; 

 Kleiber et al., 1987) to describe the dynamics of 

 tagged albacore (hereafter referred to simply as 

 "tags"). The model may be represented by 



':,/ =«,(l-a)i37exp 



ijf 



Z,^,./+^+ 



w 



l-exp(-X,i^,/-^-V/)j. (1 



where 



'jf 



a - 

 P = 



Y = 



the estimated number of tags from re- 

 lease group ( recaptured by fleet f in 

 time period J and returned with com- 

 plete information (recapture time and 

 fleet); 



the number of tags released in release 

 group ;; 



the proportion of type- 1 tag losses; 

 the proportion of recaptured tags that 

 are returned; 



the proportion of returned tags having 

 complete information; 

 the instantaneous rate of fishing mor- 

 tality on release group ; in time period 

 j by fleet f; 



M 



J 

 k 



= the instantaneous rate of natural 



mortality; 

 = the instantaneous rate of type-2 tag 



loss; 

 - an index for release group; 

 = an index for time period; 

 = an index for time periods prior to^; and 

 = an index for fleet. 



Data stratification 



In order to allow seasonal variability in tag returns 

 to be modeled, tag releases and returns were grouped 

 by the quarter (Jan-Mar, Apr-Jun, Jul-Sep, and 

 Oct-Dec) and year of release and recapture. This 

 resulted in 48 release groups (Table 2). Small num- 

 bers of releases in 1994 and 1995, from which no re- 

 captures have so far been reported, were not included 

 in the analysis. We defined five fleets: 1) U.S. baitboat; 

 2) Japanese baitboat; 3) U.S. and Canadian troll (re- 

 ferred to as the troll fleet); 4) Japanese, Korean, and 

 Taiwanese longline (referred to as the longline fleet); 

 and 5) others (consisting of recapture sources not oth- 

 erwise defined). This definition was designed to group 

 fleets having similar characteristics (fishing methods, 

 seasonal distributions of effort, and sizes of albacore 

 caught). The observed tag returns, r^^ were thus 

 grouped by tag release group ii), quarter and year of 

 recapture (j), and recapture fleet if). Tag returns to 

 the end of 1992 were considered in the analysis. 



