VETTER: NATURAL MORTALITY IN FISH STOCKS 



Predation Methods 



A third class of estimators extends single spe- 

 cies cohort analysis to a multispecies assemblage 

 incorporating the major predators and alterna- 

 tive prey of the stock in question. Single species 

 cohort analysis is used to estimate population 

 abundances and annual values for the instanta- 

 neous rate of fishing mortality (F) for single 

 groups, usually year classes, of fish (e.g., Pope 

 1972; Ricker 1975; Gulland 1983). The multispe- 

 cies extension simply combines cohort analyses 

 for several species (e.g., Anderson and Ursin 

 1977). The methods all generate estimates of M as 

 the sum of some constant rate of nonpredatory, 

 nonfishing mortality plus the total estimated flux 

 of prey (stock) to each of the major predators. This 

 feeding flux to predators is estimated by first 

 using cohort analyses to reconstruct population 

 sizes of the various groups of predator and prey, 

 then combining these population sizes with ob- 

 served growth rates for the predators and with 

 estimated preferences for various prey. Thus it 

 becomes possible to estimate the predatory com- 

 ponent of M. 



Versions of the method have been described by 

 Anderson and Ursin (1977), Majkowski (1981), 

 and Pope and Knights (1982). Applications in a 

 marine system (North Sea) have been described 

 by Anderson and Ursin (1977), in an ecosystem 

 context, by Laevastu et al. (1982) and in lake 

 systems by Forney (1977) and Stein et al. (1981). 



The predation method has been developed pri- 

 marily from analyses of marine systems, espe- 

 cially the North Sea, and much of the literature 

 exists only as "mimeos" or notes associated with 

 ICES (International Council for the Exploration 

 of the Seas) activities. The most readily available 

 discussion of this approach appeared in Mercer 

 (1982), which includes a critical review and dis- 

 cussion by Ursin (1982) of the various methods. 

 Several other discussions appear in Pauly and 

 Murphy's (1982) volume of collected papers from 

 a symposium on theory and management of trop- 

 ical fisheries. Most of these papers specifically 

 address tropical multispecies systems, but the 

 concepts are broadly applicable. References to 

 other, often less accessible, works can be found in 

 these two general references. 



The predation method is elegant in concept but 

 often difficult to apply. Studies by Forney (1977) 

 and Stein (1981) had the distinct advantages of 

 limited species numbers in a small system, and 

 direct quantification of stomach contents. Yet 



even in lake systems, the sampling problems of 

 estimating Z, population abundances, and so 

 forth, remain often as intractable as in large 

 marine systems. The two greatest problems are 1) 

 the difficulty in defining vulnerability and prefer- 

 ence functions for the various prey stocks (e.g., 

 Ursin 1982) and 2) the need to include cohort 

 analyses of all the major interacting species, some 

 or many of which may not be available commer- 

 cially (and for which therefore data will be 

 scarce). 



Despite these problems the approach can cer- 

 tainly generate, for stocks that suffer heavy 

 predatory mortality from other fished stocks, 

 more realistic estimates of M than approaches 

 that simply generate a globally fixed and invari- 

 ant M. More importantly (and in contrast to the 

 age-frequency or life history methods) the preda- 

 tion method has the advantage of being mecha- 

 nistic. Predation-related causes and conse- 

 quences of age, size, site, stock, geographic, or 

 time trends in M can be investigated via pertur- 

 bation and sensitivity analysis in computer simu- 

 lation studies or, alternatively, investigated 

 through analysis of existing catch data. It be- 

 comes possible (not necessarily feasible) to inves- 

 tigate the implications of varying age or abun- 

 dance structures of interacting fishery resources. 



Thus the predation approach has considerable 

 conceptual appeal for fairly simple systems in 

 which 1 ) predation is the major force controlling 

 prey abundance, 2) predators have few alterna- 

 tive prey, 3) the possibility can be ignored that 

 predators prefer moribund prey which were about 

 to die anyway, and 4) all major species of predator 

 and prey are sought commercially so that data on 

 abundances and feeding preferences are or can be 

 made available. 



Unfortunately, the number of systems satisfy- 

 ing these requirements appears to be fairly small, 

 and of course where predation is a relatively 

 small fraction of M, the multispecies predation 

 method will be particularly ineffective. 



III. SENSITIVITY OF FISHERY MODELS 

 TO CHOICES FOR M 



Although catch-analysis, life history, and pre- 

 dation methods all exist currently for estimating 

 M in fish stocks, in practice the only method used 

 extensively is the first — direct estimation of M 

 from analysis of catch structure. Thus the discus- 

 sion below of model sensitivity to M is based on 

 this type of estimate. The conclusions reached are 



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