Harley and Suter: Potential use of time-area closures to reduce the catches of Thunnus obesus in eastern Pacific Ocean 



53 



Note that the index is scaled to be between and 1, 

 and the larger values within this range were associ- 

 ated with greater bigeye-skipjack ratios. To obtain an 

 overview of the hotspots over the 1995-2002 period we 

 summed the annual indices 



(=2002 

 (=1995 



^j= I ^,r 



(3) 



We defined hotspots as those time-area regions where 

 the summed index was in the top 20% of the values. 



Closed-area model 



The basic model is summarized in four steps: 



The new catch for each time-area closure was es- 

 timated as the new effort multiplied by the original 

 CPUE: 



"i.j,tlx,y ~ ^iJMx.y '^ i.j.t 



and 



'-'ij.tlx.y " '^i.jfix.: 



u 



i.J.t  



(8) 



(9) 



because it was assumed that CPUE in an area will not 

 change when additional effort is added with closure. 



The summary statistic for each simulated closure 

 was the percentage change in bigeye and skipjack tuna 

 catches, compared to the catches observed in the ab- 

 sence of a closure. 



1 Choose an area to close in a given time period. 



2 Re-allocate effort from the chosen area during the 

 period of the closure to other areas in proportion to 

 the effort in each area. Leave the effort outside the 

 closure period unchanged. 



3 Calculate the new catch of each species expected in 

 each area based on the new effort and catch per unit 

 of effort (CPUE) for each species in each area. 



4 Compare new annual catches to original catches. 



The possible consequences of these assumptions and 

 alternative modeling approaches are detailed in the 

 discussion. 



The data used for the closed-area analysis were simi- 

 lar to those used in the hotspot analysis. The definitions 

 of catches remained the same (e.g., B, ^,1, although the 

 spatial strata reflected by j differed, depending on the 

 closure considered. 



We incorporated effort in terms of the number of sets, 

 £, ,, and defined the CPUE of bigeye and skipjack tuna 

 in tons per set, 



'■■■ 





"'.j.i 



and 



Uf 



;j.t 



"'■j.i 



"ij,( 



(5) 



We allocated effort from a time-area closure (/=.<• and 

 j=y) to the remaining areas in that time period on the 

 basis of proportion of effort in each area (P,jt) (exclud- 

 ing the closed area) e.g., 



E, 



^'.j.i 



i,j,tit=x,j^y 





(6) 



For each time-area closure we determined the new 

 effort allocation, E, ,,i,„, as 



E. 



ij.t\x,y ' 







E,,j,t+E^y, Pij^t/x.y 



■'i.j.t 



where i = x andj = y 

 where i = x andj ^ y. in. 

 where i = x 



Z^i.j'^i.j.' 



(10) 



and 



AS. 



la,j^,.J.t\x.y Z^.j^l.j.t 



xlOO. 



(11) 



We repeated the calculations for the catch and effort 

 data in each year (1995-2002) to consider the potential 

 variability in the effect of a closure due to interannual 

 variation in the spatial distribution of fish and fishing 

 effort. 



In addition to the model described above, we also 

 considered a "two set-type" model in which FOB and 

 UNA sets were redistributed separately (i.e., we did not 

 allow switching between set types). Although this model 

 gave very similar results, it was probably less realistic; 

 therefore the results are not presented here. 



Simulated closures 



We compared the performance of two closed areas for 

 each quarter and year. The first closed area corresponded 

 to the hotspots (those 5°x5° areas for a quarter for which 

 0^ I was in the top 20%) associated with each quarter. 

 A closure of the hotspots should be optimal in the sense 

 of reducing bigeye tuna catch with minimal impact on 

 skipjack tuna catch but may not be practical from a 

 management perspective because the 5°x5° areas are 

 not continuous. The second closed area approximated the 

 hotspot closure, but it was a more practical, continuous 

 region. It extended from 5°N-10°S, to 90°-120°W. The 

 total area of this closure was the same as the total area 

 of the hotspot regions. We refer to this as the practical 

 closure. In each case, effort during the closure period 

 was redistributed between two areas, one north and one 

 south of the equator, in proportion to the effort in each 

 open area. Summaries of the effort and CPUE data, 

 stratified by the areas that we used in the practical 

 closure analysis, are provided in Table 2. 



