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Fishery Bulletin 90(2). 1992 



Figure 2 



Trend in the ratio R (number of nonharvestable:harvestable 

 stone crabs Menippe mercenaris) when the assumption of a 

 closed population is not met. The value of b is positive, as in 

 the upper curve in Fig. 1, but recruitment of harvestable crabs 

 occurs in months 5, 6, and 7. 



illustrate how the model can be applied. The data set 

 I used (Sullivan 1979) was collected during 1975 and 

 1976 in an area where the fishery has been traditionally 

 most intense. This data set contains detailed informa- 

 tion on every individual captured, including carapace 

 size, claw sizes, and claw status (presence/absence, 

 regeneration stage, etc.). 



The first step in analyzing the data is to define ex- 

 actly how to categorize crabs in order to meet the 

 assumption that unharvestable crabs do not become 

 harvestable due to claw regeneration during the study 

 period. One way to do so is as follows (Restrepo 1990): 

 "Harvestable" crabs are those with two normal, legal- 

 sized claws (normal claws are defined as those that have 

 no signs of regeneration); "nonharvestable" are those 

 without claws. 



With this definition, all harvestable crabs that are 

 caught will likely lose both claws and hence become 

 part of the nonharvestable population if they survive. 

 Conversely, crabs without any claws will not quickly 

 become part of the harvestable population because it 

 would take several regenerative molts (years) before 

 their claws looked normal. Note that the definition 

 above excludes from the analysis all crabs that have 

 either one or two sublegal claws which could, through 

 molting, become part of the harvestable population. In 

 terms of meeting the model's assumptions, the above 

 definition still poses a problem in that crabs with only 

 one claw of legal size (which are relatively uncommon), 

 whether normal or not, may become part of the non- 

 harvestable stock upon declawing. 



Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct 



Figure 3 



Observed values of the ratio of male stone crabs Menippe 

 mercenaria without claws to those with two normal (not 

 regenerated) claws, by size-group. Data from Sullivan (1979). 



Figure 3 shows the observed trend in the ratio R [0 

 claws: 2 normal claws] of male stone crabs from Sul- 

 livan's (1979) data, for several size-groups. (Female 

 crabs are also harvested, but they are excluded from 

 this analysis because few of them reach sizes at which 

 both claws are of legal size.) Note that R is relatively 

 constant and near zero for crabs < 90 mm in carapace 

 width (CW) (Fig. 3). Based on claw size— carapace 

 width relationships (Restrepo 1990), the smaller of the 

 crabs' claws (the "pincer") becomes harvestable only 

 when the carapace reaches 90 mm in width. Thus males 

 with two normal claws are not expected to lose both 

 claws to fishing at sizes <90mmCW, a fact which is 

 corroborated by Figure 3. Otherwise, R values for the 

 smaller crabs would show larger deviations from the 

 zero line in Figure 3. For this reason, the analyses were 

 conducted with crabs >90mmCW (Fig. 4). 



The trend in the observed R values (Fig. 4, filled 

 squares) is reminiscent of that in Figure 2: it appears 

 to increase concavely upwards from November to Feb- 

 ruary, suggesting that "M<''M-t-F, and it then de- 

 creases starting in March. This decline is possibly a 

 consequence of recruitment of large crabs with normal 

 claws into the fishing grounds, suggesting a failure of 

 the closed-population assumption. Empirical evidence 

 for a similar recruitment peak of large males in the 

 spring was found by Ehrhardt et al. (1990) in Ever- 

 glades National Park. In addition to recruitment, the 

 decline in R after February could also be attributed to 

 declawed crabs being removed from the study site in 

 greater numbers after this month (some vessels may 

 remove the claws at the end of the day as they travel 

 from the fishing grounds to port). Because of these 



