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Fishery Bulletin 90(3), 1992 



n 



o 

 a 

 Pi 



05 



u 



1 2 3 4 5 6 7 B 9 10 11 12 

 Day of Experiment 



Figure 3 



Distributions of carapace length for male and female 

 Heterocarpus laevigatiLS during the depletion experi- 

 ment. Open squares are means bracketed by ± 1 SD; 

 dashed lines represent maximum and minimum ob- 

 served sizes. 



For each sex, the von Bertalanffy asymptotic length 

 (CL^) and the ratio (0) of the total mortality rate 

 (Z/yr) to the von Bertalanffy growth coefficient (K/yr) 

 were estimated from a weighted regression of mean 

 lengths (CL^i) on full vulnerability cutoff lengths 

 (CLei). In the analysis, the CLd were incremented in 

 1.0 mm steps above CL^o, the minimum size of full 

 vulnerability to the gear, and the CLj^j were recalcu- 

 lated at each step. Using the morphometric functional 

 regressions presented in Dailey and Ralston (1986), 

 CLco was set equal to 30 mm (the length of H. laeviga- 

 ^Ms ■■Anth carapace width = 12.7mm), corresponding to 

 the least dimension of the wire mesh covering the 

 traps. This approach to estimating CLpo deviates from 

 that used in previous applications of the regression 

 method to H. laevigatus stocks. Dailey and Ralston 

 (1986) and Moffitt and Polovina (1987) both assumed 

 that shrimp were not fully selected by baited traps until 

 reaching a CL greater than the modal size of length- 

 frequency distributions from trap catches. 



Because the size-structure we observed was similar 

 to the unexploited stock (see above), it follows that 

 = M/K, where M is natural mortality/yr. Likewise, 

 using the length-weight regressions of Dailey and 

 Ralston (1986), we estimated the asymptotic weights 



(W^) for each sex as the predicted weight at CL = 

 CL^. The average size at entry to the fishery (CLp 

 sensu Beverton and Holt 1957) was obtained by averag- 

 ing the minimum size caught and CLj-^,. Given esti- 

 mates of M/K, W^, and CLp, we used the tables 

 presented in Beverton and Holt (1966) to determine 

 sex-specific values of yield-per-recruit (Y/R) at various 

 levels of exploitation (F/M). From these data we com- 

 puted values of Fq j/M, the exploitation level at which 

 the marginal increase in Y/R declines to 10% of its 

 value at the origin (Gulland and Boerema 1973, Gulland 

 1983). 



Results 



Depletion experiment 



During the depletion experiment, 123 pyramid shrimp 

 traps were set at the Kaulakahi Channel study site. Of 

 these, 19 were lost, resulting in 104 effective trap- 

 nights of standard fishing effort and a gear loss rate 

 of 15%. A total of 45,482 H. laevigatus were caught, 

 which collectively weighed 1499 kg. The average size 

 of each shrimp was therefore 33. Og. During the 12-day 

 course of the experiment, no change occurred in the 

 daily mean size of shrimp caught (Fig. 3; r<j = 0.32, 

 df 10; ro.= -0.28, df 10). 



Individual trap catches were regressed on values of 

 corrected cumulative removals to date (Fig. 4). Traps 

 that did not fish properly (e.g., the funnel entrance was 

 ajar upon retrieval) were not included, although cumu- 

 lative removals (Kj) included all shrimp caught in the 

 study area (<695m or 380 fm). Therefore, each point 

 represents an observation of CPUE from one valid 



