746 



Abstract.— We applied a length-based 

 additive catchability model that ac- 

 counts for several sources of variation, 

 namely time (i.e. years, months!, den- 

 sity-dependence effects, and different 

 fishing fleets. The model is based on 1) 

 a transition matrix and 2i population 

 length-structured data expressed as 

 catch per unit of effort. Other sources 

 of variation were estimated as anoma- 

 lies from the average pattern and in- 

 corporated as additions to the slope of 

 the catchability-at-length equation. 

 The catchability model was applied to 

 the red grouper \Epinephelus morio) 

 fishery of the north continental shelf 

 of Yucatan, a demersal fish resource ex- 

 ploited by three different fleets. A sig- 

 moidal shape catchability-at-length 

 function was fitted on the basis of grou- 

 per population biology and behavior, 

 particularly reproductive aggregation. 

 Catchability of immature fish was con- 

 stant but increased with size for adult 

 fish, especially during the reproductive 

 season. Time- and density-dependent 

 catchability responded to reproductive 

 behavior and the allocation of fishing 

 effort. When differences between fleets 

 were incorporated, catchability differ- 

 ences emerged. The catchability model 

 has the ability to identify the main 

 properties of the fish resource and fish- 

 ery that affect the relation between 

 fishing effort and population abun- 

 dance; it may therefore be helpful as 

 an alternative stock assessment tool. 



Catchability estimates and their application 

 to the red grouper (Epinephelus morio) 

 fishery of the Campeche Bank, Mexico 



Francisco Arreguin-Sanchez 



Centre Interdisciplinano de Ciencias Mannas del IPN, CICIMAR 

 Apartado Postal 592, 23000, La Paz, Baia California Sur, Mexico 

 E-mail address, farreguiffflvmredipn ipn mx 



Tony J. Pitcher 



Fisheries Centre 



University of British Columbia 



Vancouver, V6T 1Z4, Canada 



Manuscript accepted 19 November 1998. 

 Fish. Bull. 97:746-757 (1999). 



Catchability has been considered in 

 fisheries science as a parameter in 

 the catch equation that relates fish- 

 ing effort to population abundance: 



C = qsEN, (1) 



where C = catch in numbers; 

 q - catchability; 

 s = probability of gear 



selection; 

 E = fishing effort; and 

 N = the stock size in 



numbers. 



From this relation it is easy to un- 

 derstand the key role of g. Because 

 s and E are controlled by man, 

 changes in population abundance 

 will be reflected in catch through q. 

 Although classically considered a 

 constant, q represents different 

 sources of variation affecting stock 

 size. Most of the existing catcha- 

 bility models deal with only one 

 source of variation related to school- 

 ing of fish (e.g. MacCall, 1976; 

 Csirke, 1988, 1989), although a few 

 of them also consider environmen- 

 tal factors (Table 1), 



Investigations on catchability 

 have developed mainly in two direc- 

 tions (Arreguin-Sanchez, 1996): 1) 

 those related to measuring and in- 

 creasing gear efficiency, and 2 ) those 

 that use catchability as a parameter 



to relate fishing effort to fishing 

 mortality and population abun- 

 dance for stock assessment and 

 management purposes. The aim of 

 this contribution is to apply a 

 catchability model that accounts for 

 several sources of variation related 

 to fishing and to population pro- 

 cesses, as proposed by Arreguin- 

 Sanchez (1996). 



The red grouper (Epinephelus 

 morio) stock over the Campeche 

 Bank is one of the largest in the 

 world, distributed on a continental 

 shelf of more than 100,000 km^. As 

 with many serranids. the red grou- 

 per stock over the Campeche Bank, 

 Gulf of Mexico, aggregates for re- 

 production, a fact that is well docu- 

 mented in the literature (Arreguin- 

 Sanchez et al., 1996). While they 

 aggregate, these fish are highly vul- 

 nerable to fishing; therefore this 

 fish behavior is a key aspect for 

 management of the resource. Three 

 fleets target this fish species: two 

 from Mexico (an artisanal and a 

 midsize fleet); and a third from 

 Cuba. These fleets do not com- 

 pletely overlap in respect to their 

 fishing grounds, and their catch 

 structure, efficiency, and the fish- 

 ing mortality that they cause to the 

 stock are different. Our contribution 

 is aimed to estimate catchability for 

 the red grouper fishery. 



