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



749 



Ln[q{gJ,f)/q{hj,t}] = a(f) + [i(f)(, (11) 



where /" indexes fishing fleets. 



In this case, the intercept a(/") is the relative dif- 

 ference in catchabiUty between fleets for the small- 

 est fish. The slope Pif) reflects the difference in fish- 

 ing performance measured as the anomaly in 

 catchability of the fleets with respect to the fleet /;. 



The additive catchability model 



The deterministic model that incorporates the pro- 

 cesses discussed can now be set out. It relies on the 

 changes of the slope [ii i , • ), representing the 

 catchability-at-length pattern, by the addition of the 

 slopes of the partial effects described by Equations 

 7, 9, and 11. The slope of the catchability model, with 

 the form defined by Equation 4, is represented by 



p{i.t,EJ) = l3ii.») + p(t) + l3(E) + p{f). 



112) 



The value of /3( ' , /, E, f) represents the slope of the 

 catchability-at-length function without restriction to 

 equilibrium, which has been compensated by the 

 addition of the term fid), where t refers to any ap- 

 propriate unit of time. 



The red grouper (Epinephelus morio) fishery in the 

 Campeche Bank, Mexico 



The red grouper on the North continental shelf of 

 Yucatan is exploited by three fleets: an artisanal and 

 a mid-size fleet from Mexico, and a large-scale fleet 

 from Cuba. These fleets overlap in respect to their 

 fishing grounds ( Moreno et al.M: Mexican fleets over- 

 lap in a range of 60*^ to lQ9c\ the midsize fleet from 

 Mexico and large-scale fleet from Cuban, around 609f ; 

 and the artisanal and Cuban fleets, between 12% and 

 16%. This overlap in fishing gi-ounds means that each 

 fleet causes fishing mortality on different sizes of the 

 stock and thus necessitates that the fleets be consid- 

 ered separately for stock assessment purposes. 



The artisanal fleet of Mexico is composed of ves- 

 sels of approximately 9 m long, operating from the 

 coast to 20 m depth, and catching mainly juvenile 

 and preadult fish. The midsize fleet uses 15-m ves- 

 sels operating at depths of 10 to 80 m, and catch com- 

 prises both juvenile and adult fish, according to the 

 season. The Cuban fleet fishes mainly with 27-m 



vessels, operates between 20 and 90 m depth, and 

 catches adult fish. Both Mexican fleets have free ac- 

 cess and move seasonally in the area following 

 changes in fish density (i.e. with reproductive aggre- 

 gation). The Cuban fleet has a catch quota of 3900 t 

 of demersal fish, of which more than 80% is red grou- 

 per. This fleet remains in the central and eastern 

 region of the continental shelf ofYucatan most of the 

 time. 



Differences related to gear, fishing effort, and fish- 

 ing strategies among fleets are described in Moreno 

 (1980), Burgos (1987), and Fuentes (1987) for the 

 midsize fleet; Saenz et al. ( 1987 ), Salazar ( 1988), and 

 Solana-Sansores and Arreguin-Sanchez ( 1991 ) for the 

 artisanal fleet; Valdes and Padron (1980) for the 

 Cuban fleet; and Seijo (1986), Gonzalez-Cano et al. 

 (1993), and Arreguin-Sanchez et al. (1996) for the 

 three fleets. In this paper we used standardized fish- 

 ing days as the unit of fishing effort. 



For the catchability model, available data for the 

 red grouper fishery are summarized in Table 2. De- 

 tailed information is derived from the midsize fieet, 

 which harvests around 70% of the total annual yield. 

 Other fleets share the remaining 30% more or less 

 equally. Because the midsize fleet also catches a size 

 range that overlaps the other two, this fleet is the 

 start of our analysis. Later, we will incorporate the 

 other fleets into the catchability model. 



To solve Equation 3, we assumed that individual 

 growth follows the von Bertalanffy equation with 

 values ofL„ = 87 cm total length (TL) and iC = 0.12/ 

 year (Arreguin-Sanchez-), and the natural mortal- 

 ity coefficient M = 0.3/year (Doi et al., 1981; Contreras 

 etal., 1994). 



The selection factor for each length class s( ( ), rep- 

 resenting a probability term directly affecting the 

 abundance of length classes in the catch, was set to 

 be s( O = 1. For simplicity, red grouper fishery gears 

 were assumed nonselective (hook-and-line and hand 

 lines with different sizes and baits). 



Annual catch-per-unit-of-effort( t7)-at-length data 

 for the period 1973 to 1987 for the midsize fleet was 

 used. The iterative procedure described for Equation 

 3 was applied to each pair of yearly data to obtain 

 initial values of catchability per length class and year. 

 Catchability values for each length class g( /, y) were 

 used to fit the trend with length (Fig. 1) and to de- 

 scribe variability o{ q( i ,•). The solution for Equa- 

 tion 3 does not require a previous knowledge of re- 

 cruits at [/( ' , /) and [/( ' , ^ + 1), and it was solved for 



Moreno, V., F. Arreguin-Sanchez, M. Contreras, and R. Burgos. 

 1991. Analysis of usage patterns in shared stocks: the red grou- 

 per fishery from the continental shelf of Yucatan. Mexico. Proc. 

 44th Ann. Sess. Gulf and Canbb. Fish. Inst., 18 p. IMimeo.l 



- Arreguin-Sanchez, F. 1996. Length-based growth estimation 

 for the red grouper iEpinephelus morio) in the North continen- 

 tal shelf of Yucatan, Mexico. Centr. Interdiscip. Cienc. Mar., 

 Mexico, 19 p. IManuscript.l 



