FISHERY BULLETIN: VOL. 84, NO. 2 



5.0 1 r 



4.0 



UJ 



a. 



u 



3.0 



2.0 



1.0- 



-i r 



Pristipomoides zonotus 



Table 4.— Percent of catch by depth (in fathoms, 1 fathom 

 = 1 .83 m). 



UJ 



a. 



u 



I00 



200 300 100 



CUMULATIVE CATCH 



200 



300 



400 



Figure 2.— Daily catch per unit effort (CPUE) and adjusted 

 cumulative catch for Pristipomoides zonatus, P. auricilla, and 

 Etelis carbunculus. 



but rather the population size of those fish that can 

 be caught by the fishing gear which will be termed 

 the exploitable population. Although the constant 

 catchability Leslie model does not explain as much 

 of the variation for E. carbunculus (R 2 = 0.35) as 

 it does for P. zonatus, the regression is significant 

 and the pattern of residuals supports the linear fit. 

 The estimates for catchability and initial exploitable 

 population size for E. carbunculus from the fit of 

 this model are 0.0025 per line-hour and 583 fish. The 

 positive slope for the regression of CPUE on 

 cumulative catch for P. auricilla does not make 

 sense biologically under the constant catchability 

 Leslie model. 



The depth of capture data show that P. zonatus 

 and P. auricilla were caught in the same depth 

 range, whereas E. carbunculus was typically caught 

 at somewhat greater depths (Table 4). Thus, species 

 interactions would most likely occur between P. 

 zonatus and P. auricilla. If P. zonatus is more ag- 

 gressive than P. auricilla in pursuing fishing baits 

 or in some other way affects the behavior of the lat- 

 ter, then the initial catchability for P. auricilla will 



be low but will rise as the population of P. zonatus 

 is reduced. Applying the variable catchability Leslie 

 model to the P. auricilla data, with the assumption 

 that P. zonatus is the dominant species and that P. 

 auricilla is the subordinate species so that the catch- 

 ability of P. auricilla depends on the population size 

 of P. zonatus, results in the following relationship: 



CPUE(a,0 = q(a)(K(z,t)/N(z,0)) 



x (N(a,Q) - K(a,t)), 



(6) 



where q(a) is the catchability of P. auricilla in the 

 absence of P. zonatus and N(z,0) and N(a,0) are the 

 initial exploitable population sizes of P. zonatus and 

 P. auricilla, respectively, and K(z,t) andK(a,t) are 

 the cumulative catch of P. zonatus and P. auricilla 

 to time t, respectively. 



Using the estimate of N(z,0), 1,066 fish, from the 

 fit of the constant catchability model to P. zonatus 

 data, Equation (6) has two unknowns to be esti- 

 mated— q(a) and N(a,0). A multiple linear regression 

 model estimates the initial exploitable population 

 size of P. auricilla, N(a,0), at 2,007 fish and q(a) at 

 0.00087. The variable catchability Leslie model fits 

 the P. auricilla CPUE data well and produces an 

 R 2 of 0.89 (Fig. 3). The estimates of initial popula- 

 tion sizes for the three species are summarized in 

 Table 5 together with their 95% confidence inter- 

 vals. For the constant catchability model, the 

 population size confidence interval is computed from 

 a relationship derived by Delury (1958), whereas the 

 confidence interval for the variable catchability 

 model is computed from the variance expression 

 given in Equation (5). 



DISCUSSION 



The constant catchability Leslie model fit the P. 

 zonatus and E. carbunculus data well but was not 

 appropriate for the P. auricilla data. The variable 

 catchability Leslie model fit the P. auricilla data 

 well and provided a plausible explanation for the 

 observed increase in CPUE. Given that there was 

 a time delay between the first 10 d of the intensive 



426 



