RALSTON: FISHING EXPERIMENT FOR CARIDEAN SHRIMP 



removals included catches from the large commer- 

 cial trap. As in Ricker (1975), CPUE is regressed 

 against corrected cumulative catch, defined as the 

 cumulative catch prior to the start of an interval plus 

 half the catch taken during the interval (see also von 

 Geldern 1961). 



Standard daily CPUE is plotted against cumula- 

 tive catch removed in Figure 3. The slope of the 

 regression is significantly less than zero (one-tailed 

 test, t = -2.80, df = 13, P = 0.01). Estimates of 

 slope, intercept, and mean squared error were 

 -0.001945 trap-night' 1 , 3.334 kg/trap-night, and 

 0.3754 (kg/trap-night) 2 , respectively. Consequently, 

 the catchability coefficient is estimated to be q = 

 0.001945 trap-night -1 and the initial population 

 size prior to the start of fishing to be n = 1,714 kg. 

 Confidence intervals for these estimates are 

 P(0.0004 < q < 0.0034) = 0.95 and P(1150 < n < 

 6005) = 0.95 (Ricker 1975). Notice that the con- 

 fidence interval for the estimate of initial popula- 

 tion biomass (n) is asymmetrical about the point 

 estimate. 



Crittenden (1983) and others have warned against 

 unequal variance in plots of CPUE against cumula- 

 tive catch. To test for this possibility, the absolute 

 values of the residuals from Figure 3 were ranked 

 and the corrected cumulative catches were ranked. 

 A Spearman rank correlation coefficient was then 

 calculated, resulting in r s = -0.189, P = 0.50. 

 From this analysis there is no evidence of hetero- 

 scedasticity. Further, there is little to suggest curvi- 

 linearity in Figure 3. A runs test (Tate and Clelland 

 1957) on the signs of the residuals indicates they are 



5.0-1 



~ 4.(H 



.C 

 O) 



c 



a 



«J 3. OH 



a> 

 I 



LU 



3 

 a 

 U 



2.0- 



1.0- 



200 400 600 



Cumulative Catch - kg 



800 



Figure 3.— Leslie model applied to Heterocarpus laevigatus at 

 Alamagan. Each point represents 1 day of fishing. Data from Table 

 1. 



randomly sequenced (P > 0.40). This result supports 

 the assumption of constant catchability. 



At the time the experiment was terminated, 776 

 kg of shrimp had been removed by trapping. An 

 estimate of the concomitant catch rate can be cal- 

 culated from the regression equation of Figure 3. 

 This estimate of CPUE is 1.82 kg/trap-night. When 

 the Townsend Cromwell returned to the study site, 

 4 mo later, the mean catch rate was 1.91 kg/trap- 

 night (42 effective standard trap-nights of effort, 

 s = 1.33), this based on a total catch of 80.08 kg 

 H. laevigatus. The preceding calculations include 

 only those traps which were baited comparably to 

 the experimental traps (three chopped Pacific 

 mackerel). Traps with two whole baits (n = 42) 

 yielded an average catch rate of 1.39 kg/trap-night 

 (s = 1.09). 



Length-Frequency Distributions 



Examination of size-composition data can help 

 interpret changes in weight CPUE. Declining trap 

 catch rates could, for example, represent fewer in- 

 dividuals of the same size. Conversely, a decline in 

 the average size of individuals caught with no 

 change in numbers would also result in declining 

 CPUE. 



The three length-frequency distributions of H. 

 laevigatus sampled during the period of experimen- 

 tal fishing are presented in Figure 4. For each dis- 

 tribution the date of capture, depth of capture, sam- 

 ple size, and mean carapace length are provided. 

 Although appearing superficially similar, the results 

 of ANOVA show that significant differences exist 

 in size composition among the three samples (F = 

 10.03, df = 2, 343, P < 0.001). These differences, 

 however, do not explain the decline in CPUE. The 

 data in the figure show that the mean size of H. 

 laevigatus actually increased over time, and that the 

 overall decline in CPUE observed in Figure 2 must 

 therefore have been due to a decrease in the number 

 of shrimps caught. 



DISCUSSION 



Powell (1979) has shown that the shape of the 

 descending limb of length-frequency distributions 

 can provide useful information concerning the rela- 

 tionship between mortality and growth. Specifical- 

 ly, the ratio of Z (instantaneous total mortality rate) 

 to K (von Bertalanffy growth coefficient) is defined 

 in a simple way by the interrelationship of the least 

 size when fully vulnerable to the gear, the mean size 

 in the catch of fully recruited individuals, and the 



931 



