A VARIABLE CATCHABILITY VERSION OF THE LESLIE MODEL WITH 

 APPLICATION TO AN INTENSIVE FISHING EXPERIMENT ON 



A MULTISPECIES STOCK 



Jeffrey J. Polovina 1 



ABSTRACT 



A variable catchability version of the Leslie model is developed which permits the catchability of one 

 species to vary inversely with the abundance of competing species. This model is used to fit data from 

 an intensive fishing experiment conducted on a multispecies bottom fish stock in the Marianas where 

 catchability of a subordinate species is inversely related to the abundance of a more dominant species. 

 Analysis of this multispecies intensive fishing experiment produced estimates of exploitable bottom fish 

 density in the 150-275 m depth range of 10,156 fish per nmi 2 or 1,354 fish per nmi of 183 m (100-fathom) 

 contour. 



Intensive fishing of a closed population can produce 

 data to estimate the initial population size and the 

 catchability coefficient of fish stocks. Two frequently 

 used models applied to intensive fishing data are the 

 Leslie model and the Delury model (Ricker 1975). 

 The Leslie model expresses catch per unit effort 

 (CPUE) at any point during the period of intensive 

 fishing as a linear function of the cumulative catch 

 to that point, whereas the Delury model expresses 

 the logarithm of CPUE at any point during the in- 

 tensive fishing experiment as a linear function of 

 the cumulative effort. From a statistical viewpoint 

 the Leslie model is often preferable to the Delury 

 model, since a predictive linear regression is used 

 to estimate the parameters of both models and since 

 typically catch is measured more accurately than 

 effort. 



Both the Leslie and Delury models assume that 

 catchability is constant during the period of inten- 

 sive fishing. However, experience indicates that this 

 assumption may not always be satisfied (Pope and 

 Garrod 1975; Schaaf 1975; MacCall 1976; Ulltang 

 1976; Garrod 1977; Peterman and Steer 1981; Fox 2 ). 

 Several authors have found that competition for 

 baits between fish of different size or species can 

 alter catchability (Allen 1963; Rothschild 1967). In 

 this paper a variable catchability Leslie model will 

 be developed for multispecies application where, due 



1 Southwest Fisheries Center Honolulu Laboratory, National 

 Marine Fisheries Service, NOAA, P.O. Box 3830, Honolulu, HI 

 96812. 



2 Fox, W. W. 1974. An overview of production modelling. 

 U.S. National Marine Fisheries Service, Southwest Fisheries 

 Center, Administrative Report LJ-74-10, La Jolla, CA. 



to species interactions, the catchability of one 

 species is altered by the presence of other species. 

 This variable catchability Leslie model will be ap- 

 plied to multispecies intensive fishing data from 

 snapper (family Lutjanidae) populations where the 

 application of the constant catchability Leslie model 

 leads to biologically untenable results. 



VARIABLE CATCHABILITY 

 LESLIE MODEL 



The CPUE during a time interval t (CPUE(O) is 

 defined as the product of catchability (q) and the 

 mean population size (number of individuals) pres- 

 ent during the period t (N(t)), thus 



CPUE(0 - qN(t). 



(1) 



Suppose that up to the beginning of period t, K(t) 

 fish have been caught and removed. If the period 

 t is relatively short, the population of fish closed or 

 isolated, and the fishing pressure heavy enough so 

 that it can be assumed that mortality from other fac- 

 tors is negligible, then N(t) can be expressed as 



N(t) = N(0) - K(t), 



where N(0) is the initial population size at the begin- 

 ning of the experiment (t = 0). Inserting this ex- 

 pression for N(t) in Equation (1) produces the Leslie 

 model: 



CPUE(0 = q(N(0) - K(t)). 



Manuscript accepted August 1985. 



FISHERY BULLETIN: VOL. 84, NO. 2, 1986. 



(2) 

 423 



