NOTE Restrepo: Estimating fishing mortality rates for Menippe mercenarid 



415 



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

 Month (1975 1976) 



Figure 4 



Grouped values from Fig. 3 for crabs >90mmCW (symbols). 

 Solid line: fit of Eq. (5) t» the first four observations (estimates 

 of fitted parameters are given in Table 1). 



problems, only the first four data points in the series 

 were used to estimate the parameters in Equation (5). 

 The least-squares parameter estimates, standard 

 errors and correlation matrix are given in Table 1 (fit 

 shown in Fig. 4). Note that the errors and correlations 

 are extremely high, owing to the small amount of data 

 used (4 data points to estimate 3 parameters). From 

 these estimates, the following are obtained: 



"Nn 



= a - c = 0.016 



hNo 



FS = c b = 0.109 



F + hM - nM = b = 0.618. 



Thus by fitting Equation (5) to the data, the relevant 

 parameters that are estimated are the initial ratio 



(which could be measured directly, anyway) and the 

 product FS. Due to the indeterminacy in the esti- 

 mates of FS and F-i-*'M-"M, auxiliary information is 

 required before the harvest rate (F) can be deduced. 

 One possibility is to assume that the natural mortalities 

 of clawed and clawless crabs are identical. If so, then 

 F = b and S = c. This would result in F = 0.618/month 

 and S = 17.6%; instantaneous mortality due to fishing 

 would be F(l-S) = 0.51/month. If "M>hM as sug- 

 gested by Bert et al. (1978), then the value of F will 

 be less than that estimated by b. Note that F = b = 

 0.618/month translates into about 4.3/year (during a 

 7-month fishing season), which appears to be unrea- 

 sonably high, giving indirect support to Bert et al.'s 

 (1978) contention. 



Conclusions 



An application of the model to estimate current ex- 

 ploitation rates has not been carried out. As shown in 

 the previous section, the data required to do so are 

 relatively simple (crab size, number of claws, and type 

 of claws) but cannot be obtained from the fishery 

 landing statistics. Therefore, a research sampling pro- 

 gram would have to be set up to monitor the popula- 

 tion and obtain an estimate using the model. Such a 

 sampling program should give consideration to the 

 following requirements: 



1 The areal coverage should be large enough to en- 

 sure that declawed crabs are not removed from the 

 study site by the fishing vessels. 



2 Time-periods when recruitment, immigration, or 

 emigration take place should not be included in the 

 analyses. 



3 Counts of both harvestable and nonharvestable in- 

 dividuals should be made periodically (e.g., weekly) so 

 the counts represent the number of individuals at a par- 

 ticular time, rather than the average number of in- 

 dividuals during a long time-period as was done in the 

 preceding section. 



4 To avoid imprecision and parameter correlations 

 such as those in Table 1, a large number of R values 

 should be available for parameter estimation. 



Acknowledgments 



I am grateful to Nelson Ehrhardt, David Die, and Clay 

 Porch for their discussions and to an anonymous 

 reviewer for helpful comments. Special thanks are due 

 to the Marine Research Lab of the Florida Department 

 of Natural Resources for allowing me the use of their 

 data. Financial support for this study was provided by 



