FISHERY BULLETIN: VOL. 84, NO. 4 



15 



10- 



5- 



15 



10- 



 



5- 



15 



1-9-84 

 695 m 

 n = 132 

 X = 37.4 



fl/ 



1-16-84 

 530 m 

 n = 103 

 X = 40.2 



N 



ru 



_DL 



^ 



Carapace Length -mm 



Figure 4.— Length-frequency distributions of Heterocarpus 

 laevigatas taken in shrimp traps. 



von Bertalanffy asymptotic size (L^). This is true 

 if the following conditions hold: 1) the growth of in- 

 dividuals follows a deterministic von Bertalanffy 

 growth curve, 2) mortality is constant and uniform 

 for all ages, and 3) recruitment is constant and con- 

 tinuous over time (Beverton and Holt 1956). 



Results presented in Dailey and Ralston (1986) 

 provide the basis for estimating the minimum CL 

 when H. laevigatus becomes fully recruited to the 

 trap fishery. They provide a regression equation 

 relating carapace width (CW) to CL. In this study 

 the smallest mesh dimension of standard shrimp 

 traps was 1.27 cm. This provides a logical cutoff 

 point for measurement of least CW for shrimp that 

 are fully vulnerable to the gear. Based on their func- 

 tional regression this corresponds to 30 mm CL. 



It is evident from the three panels in Figure 4 that 

 the size distribution of H. laevigatus above 30 mm 

 CL is characterized by both rising and descending 

 portions. As shown by Powell (1979) this indicates 

 a ZIK ratio of less than unity (i.e., instantaneous 

 mortality rate is less than the growth coefficient). 



Alternatively, it is possible that the rising portions 

 of the length distributions are not representative of 

 the population sampled, but are instead a reflection 

 of behavioral interactions among shrimp of differ- 

 ent sizes. Chittleborough (1974), for example, has 

 shown that the presence of large individuals of the 

 decapod crustacean Panulirus cygnus inhibited 

 smaller conspecifics from entering baited traps, 

 even though smaller lobsters were vulnerable to the 

 traps in the absence of large ones. If this kind of 

 behavioral interaction was also in evidence here, the 

 effective least size of H. laevigatus when fully 

 vulnerable to the traps may be as large as 41 mm 

 CL, the mode of the pooled length-frequency distri- 

 bution. This would indicate a ZIK ratio of 2.0 

 because of the linearity of the descending portions 

 of the size-frequency distributions. Only further 

 experimentation will resolve this issue. 



With respect to the intensive fishing experiment 

 it is useful to consider whether or not the basic 

 assumptions of the Leslie model were violated dur- 

 ing the course of the study. The first of these was 

 closure of the population. Two factors support the 

 contention that the study population was effective- 

 ly isolated and that the effects of immigration and 

 emigration were negligible. First, the hydrographic 

 survey showed that the study site comprised a semi- 

 isolated extension of the main island. Continuity of 

 prime habitat (600-800 m depth) with the island 

 proper extended along two narrow corridors to the 

 southeast and southwest. The shrimp has been taken 

 as shallow as 400 m and as deep as 950 m in the 

 Mariana Archipelago, but the 600-800 m depth 

 range encompasses the preponderance of the 

 region's shrimp stock (Moffitt and Polovina fn. 2), 

 although elsewhere (e.g., Fiji, Vanuatu, and Samoa) 

 the depth distribution apparently extends into some- 

 what shallower water (King 1984). The second fac- 

 tor arguing for closure is that the catch rate of H. 

 laevigatus remained low after a 4-mo hiatus in fish- 

 ing. If movements or migrations of shrimp were 

 biologically significant over this time interval, a 

 larger change in CPUE would be expected. It is 

 tempting to attribute the small increase in catch rate 

 (4.9%) to some type of biological recovery, but the 

 estimate of mean squared error in CPUE from 

 Figure 3 (0.3754 kg 2 /trap-night 2 ) indicates that 

 background variation is too large for the observed 

 difference to be significant. Regardless, the data 

 support the assumption that the population is closed. 



The second assumption was that growth, natural 

 mortality, and recruitment are negligible factors in 

 accounting for changes in CPUE. That the experi- 

 ment was completed in only 16 d and the popula- 



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