Arreguin-Sanchez and Pitcher: Catchability estimates for the Epinephelus mono fishery 



753 



higher, and at least two prob- 

 able tendencies were empiri- 

 cally identified (Fig. 4B), both 

 of them as a consequence of 

 changes in the catch quota as- 

 signed to the Cuban fleet. For 

 further computations, the den- 

 sity-dependent effect was as- 

 sumed to be similar for both 

 fleets because of the absence of 

 more detailed information to 

 support quantitative analysis. 

 This assumption is reasonable 

 because both fleets average 

 more than 60*^ overlap in a 

 year, but almost 100'7( during 

 reproductive aggregation. 



Because of the evident differ- 

 ences in behavior between juve- 

 nile and reproductive fish, the 

 density-dependent effect of the 

 amount of fishing was also ap- 

 plied within each length class, 

 as in Equation 9. Parameters of 

 the model are given in Table 6. 

 Variation of the slope ji(E) with 

 length class is shown in Figure 

 5. Once again, immature fish 

 behaved differently from adults. 

 The density-dependent effects 

 for immature fish were con- 

 stant, whereas the same effect 

 increased with size for sizes >50 

 cm TL. It is clear that the den- 

 sity-dependent effect during ag- 

 gregation promotes a greater catcha- 

 bility, and because the older adult 

 fish tend to remain longer in deeper 

 waters (Shapiro, 1987), the density- 

 dependent effect will increase with 

 size (age). 



The additive catchability model for 

 the red grouper fishery 



Once several sources of variation 

 were estimated, a model (Eq. 12) was 

 obtained by adding partial effects to 

 the slope of Equation 13, as follows: 



m 



20 



22 



24 



26 



28 



mid-size fleet 

 30 



32 



m 



0.09 

 0.04 

 -0.01 



-0.06 



B 



86 "•«^- 



/■■■as 



••-78 



i85 



I /-y- - . 



76 



81 



• 82 



'• 

 ♦■75. 



Cuban fleet 

 13 15 



"  - .• 80 



9 11 



Fishing effort (10' days) 



Figure 4 



Estimation of density-dependent effects on catchability-at-length pattern for (A) 

 the Mexican midsize fleet and (B) Cuban fleet of the red grouper fishery (Eq. 111. 

 General trends suggest density-dependent effects by fleets are of the same magni- 

 tude (see text for interpretation!. 



q(i,t,f,E}: 



where 



0.00004256 



-{3.896* /J(',ly.ml./\£)i} 



1+e 



P(E) 



2 - 



20 



30 



40 



50 



60 70 



80 90 



Total Length (cm) 



Figure 5 



Ti'end in density-dependent effects on q within each length class with size. 



