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



425 



130E 



150E 



170E 



170W 



150W 



130W 



110W 



T 



o 



o 



CO 



o 



n 



yjy 



• • • 



• • • • # • 



• ••••• 



J L 



J L 



tn 

 o 



Z 



o 



o 



2 



130E 



150E 



170E 



170W 



150W 



130W 



now 



Figure 5 



Geographical distribution of North Pacific albacore recoveries, 1971—92 



Additionally, we tested constraints on Qji that speci- 

 fied how catchability might vary over longer 

 (multiyear) time periods. Let T,/ be a matrix that, 

 for each f, maps time period / into a series of 

 multiyear periods within which the seasonal pattern 

 of catchability for that fleet may be assumed to be 

 constant. We tested two schemes for T,^: a constant 

 pattern of catchability over time for all fleets and 

 catchability patterns for all fleets specific to four time 

 periods (1=1971 Q4 to 1974 Q4, 2=1975 Ql to 1979 

 Q4, 3=1980 Ql to 1984 Q4, and 4=1985 Ql to 1992 

 Q4). Incorporating the notation for seasonal and 

 multiyear effects, Equation 2 may then be rewritten 

 as 



F,- 



^s„tEjc 



l3j 



Quarterly effort statistics for fleets 1 and 3 were ob- 

 tained from NMFS databases. Statistics for fleets 2 

 and 4 were obtained from Secretariat of the Pacific 

 Community databases. An arbitrary, constant level 

 of effort was assumed for fleet 5. Effort data were 

 compiled for the period from 1971 Q4 to 1992 Q4 to 

 correspond to the period of the tagging experiment. 



Changes in availability of the tagged population 



The model as described thus far implies that the 

 availability of the tagged population to the various 

 fisheries remains constant for the duration of the 

 experiment. There are two reasons why this assump- 



tion may not be satisfied, necessitating some adjust- 

 ment to the model. First, the spatial distribution of 

 the tagged population of any release set in relation 

 to the spatial distribution of fishing effort by the re- 

 capture fleets was not constant over time. In par- 

 ticular, because most releases occurred in the east- 

 ern Pacific, the tagged population would have been 

 initially more available to the U.S. baitboat and troll 

 fleets and less available to the Japanese baitboat and 

 longline fleets, which have a more westerly distribu- 

 tion. Over time, as the tagged population dispersed, 

 the effects of such differential spatial availability 

 would be expected to dissipate. Second, the availabil- 

 ity of the tagged population to the recapture fleets 

 would also be affected by the size distribution of the 

 tagged population. Tagged fish at release were gen- 

 erally of a size similar to sizes of fish captured by 

 the surface fisheries but were considerably smaller 

 than those captured by the longline fishery. There- 

 fore, the availability of the tagged population at re- 

 lease would not be limited initially by size for the 

 surface fisheries but would be reduced for the longline 

 fishery. As the tagged fish grew, their availability to 

 the longline fishery would become less restricted by 

 their size, but their availability to the surface fish- 

 eries might be reduced as they "grew out" of the size 

 range typically exploited by those fisheries. Because 

 our model has neither spatial nor size structure, the 

 effects of size and spatial distributions cannot be 

 explicitly incorporated. However, we developed an 

 approximate means to allow for such effects in ag- 



