754 



Fishery Bulletin 97(4), 1999 



l3((,y,mJ\E) = li(i,») + [p{y),p{iu)] + li{f) + (HE), 



where / indexes fleet, and each constant takes the 

 corresponding value, depending on the specific length 

 class ( ' ), time, year (_v) or month (m I, fleet if), and 

 the specific density-dependent effect {E}. 



Discussion 



The catchability model incorporates several sources 

 of variation, such as individual size, time variations, 

 and density-dependent effects, for which we assumed 

 fishing effort is the most important variable affect- 

 ing fish density, and the participation of several fish- 

 ing fieets which differ in gear, catching power, and 

 effort allocation. 



The additive-catchability model, as applied to the 

 red grouper, performed well and allows us to iden- 

 tify some aspects of fish behavior that influence 

 catchability. For example, reproductive aggregation 

 increases vulnerability offish. Of particular impor- 

 tance are the relative constancy of catchability and 

 its variance for immature individuals, and the in- 

 creasing vulnerability of adult fish with size, espe- 

 cially during reproductive aggregation. This is re- 

 lated to the reproductive behavior of the population. 

 Young fish remain close to the coast, with east-west 

 seasonal displacements, whereas adults move across 

 the continental shelf and aggregate during winter 

 for reproduction. This means that juveniles and 



adults respond differently to fieets. The model also 

 identified the differential accessibility of specific size 

 ranges to different fieets. This is important because, 

 in a fully exploited fish resource such as the red grou- 

 per, controls on fishing mortality must enhance sur- 

 vival of spawners and recruits. Figure 6 summarizes 

 the relation between fishing effort, maturity, and 

 seasonal changes in catchability for the red grouper 

 fishery. During reproductive aggregation, identified 

 by the maturity index, vulnerability increases and 

 vessels spend less fishing effort to obtain a given level 

 of yields. After reproduction, groupers disperse along 

 the continental shelf and fleets must increase fish- 



