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



755 



ing intensity because vulnerability offish will 

 decrease. 



For the density-dependent catchability, the 

 model describes fish behavior reasonably well. 

 The red grouper is a gregarious and territorial 

 fish. Stock density is reflected straightfor- 

 wardly in yields. If fish densities decrease, q 

 will decrease, and vice versa. This response to 

 the amount of fishing is reflected by the model. 



For the catchability model, note that al- 

 though a transition matrix is very helpful for 

 the estimation process, the form of the 

 catchability-at-length function must be inter- 

 preted with good understanding of the biology 

 of the exploited fish resource and of the fish- 

 ery. Fish biology probably is the most important 

 aspect because the effect of other sources of varia- 

 tion are added to the slope of this function. 



The resulting catchability model can be eas- 

 ily incorporated into estimations of fishing 

 mortality and population size; i.e. for the mid- 

 size fleet at time /, fishing mortality can be 

 expressed by 



Jan 



-0 05 00 0,05 

 Catcfiability deviation 



0.05 015 



Fishing effort index 



t- -  -A 



1 2 

 H/latunty index 



Figure 6 



Schematic representation of the main q features of the red grou- 

 per fishery on the Campeche Bank: l Al seasonal catchability varia- 

 tion represented as departure of the annual average; (B) fishing 

 effort index, represented as a monthly proportion of the year; (Cl 

 maturity index, reflecting diameter of oocytes. 



F(^^midsize,£') 

 (/( ^^midsize,£) £'(^, midsize) 



(14) 



For the population size, the participation of the three 

 fleets can be incorporated. 



(15) 



Despite the potential use of the catchability coeffi- 

 cient in some stock assessment models (i.e. age-based 

 virtual population analysis, VPA, Pope, 1972; and 

 length-based VPA, Jones 1981, 1984; Gulland^), 

 Equations 14 and 15 suggest an alternative stock 

 assessment tool, based on length-composition data. 

 A detailed description of catchability through the 

 additive model reflecting fish behavior and fishei-y 

 practices could be very useful for management pur- 

 poses when it is incorporated into assessment mod- 



Gulland, J. A. 196.5. Estimation of mortality rates. Annex 

 to rep. Arctic Fish. Working Group. ICES Council Meeting 

 (CM I, 196.5. paper .3, 9 p. 



els such as the above. Currently the red grouper fish- 

 ery is subjected to heavy fishing where the main prob- 

 lems are intensive fishing of juveniles and the high 

 vulnerability of adults. Because the additive catcha- 

 bility model describes these processes and incorpo- 

 rates all fleets, results can strongly aid management 

 decisions based on a differential control of fishing mor- 

 tality within the stock structure and between fleets. 



Even when the model can describe the study well, 

 we observed some critical aspects during application. 

 The first is that we must know red grouper behavior 

 sufficiently well to decide the form of the catchability- 

 at-length relation (Eq. 4). Statistical criteria (i.e. a 

 correlation coefficient) are not sufficient. A wrong in- 

 terpretation of this could mean a disaster for the fish- 

 ery. A second and similar aspect can occur for den- 

 sity-dependent catchability. The third aspect is the 

 significance of sources of variation. Because the 

 catchability model is based on the addition of the 

 slopes of each particular variable and relation (i.e. 

 with length, time, etc. ), we must test that these slopes 

 are significantly different from zero (see Equations 

 4, 7, 9, and 11), and if they are not different, the 

 source of variation tested does not help to explain 

 changes in q. 



The fourth aspect involves the number of para- 

 meters to be estimated, which usually is taken as 

 proportional to the complexity of the model compu- 

 tations, and inversely related to applicability. For the 

 present case, the number of parameters in the model 

 is /; + 2, where n is the number of sources of varia- 



