750 



Fishery Bulletin 97(4), 1999 



n-l or n-2 catchability values, 

 with differences in n caused by 

 the absence of recruitment es- 

 timates. Because we fitted the 

 general tendency as a catcha- 

 bility-at-length pattern, one or 

 two missing points will not af- 

 fect the estimates. 



Results 



Length-dependent catchability 



The fitting process required 

 some consideration of popula- 

 tion behavior because trend 

 could be adjusted to an expo- 

 nential or sigmoidal function. 

 We decided on a sigmoidal form 

 because of reproductive behav- 

 ior. During reproductive aggre- 

 gation, adult fish (>50 cm TL) 



form groups with a sex ratio (females: males) close 

 to 6:1, comprising individuals of around the same 

 size, but without any apparent size segregation be- 

 tween groups. This is well known by fishermen, and 

 has been described by Moe (1969), Shapiro (1987), 

 and Mexicano-Ci'ntora (1990). In terms of fishing, 

 adults within a specific area have the same prob- 

 ability of catch. In the catchability-at-length trajec- 

 tory, we think this reproductive behavior can be well 

 represented by an asymptotic trend of catchability 

 for large fish. 



The variation in catchability of young fish, as ex- 

 pressed by one standard deviation (Fig. 1) was simi- 



50 60 



Total Length (cm) 



Figure 1 



Catchability-at-length pattern for the Mexican midsize fleet of the red grouper fish- 

 ery estimated with Equation :3. The bold line indicates average values over the pe- 

 riod from 197:3 to 1987; thin lines denote one standard deviation, dashed lines rep- 

 resent absolute minimum and maximum values. 



lar for lengths between 20 to 50 cm and increased 

 sharply after first maturity (at 50 cm TL, as defined 

 by Mexicano-Cintora, 1990). 



The generalized catchability-at-length equation 

 fitted for the red grouper was 



£/(/,•): 



0.00004256 



l-i-e 



|;j H9(i.(l IH)H-4 ' 



(1.3) 



with the standard error (SE) of the ordinate SEa = 

 0.773, and SE^, = 0.012 for the slope; R- = 0.728 

 (df=10). 



