Dynamics of Fisheries that Affect the Population Growth Rate Coefficient

Conventional surplus production models indicate that destruction of fish populations by overfishing is difficult, if not impossible, but catastrophic declines in abundance of exploited populations are common. Surplus production models also do not predict large continuing fluctuations in yield, but large fluctuations in yield are common. Conventional surplus production models assume that fisheries do not impact the population's capacity to increase, but changes in age structure or a decrease in age-specific fecundity resulting from fishing can decrease the coefficient of increase. A surplus production model is developed in which fishing reduces the capacity of a population to increase; the model is applied to describe the fluctuations observed in yield of lake herring (Coregonus artedii) from the upper Great Lakes. The fisheries of the Great Lakes were decimated by the combined effects of heavy fishing and a changing environment. For some species, yield increased to high levels and then the fisheries collapsed; for other species, yield and effort fluctuated greatly. Conventional surplus production models for management of fisheries indicate that fish populations are difficult to destroy through overexploitation (Pella and Tomlinson 1969), but many fish populations have collapsed and abundance often varies greatly as a result of heavy exploitation. For example, changes in the commercial fisheries of the Great Lakes have been dramatic, with wide fluctuations in yield and extinction of several species that were commercially important (Smith 1968, Christie 1974). There is a tendency to attribute such catastrophic variation in catch to environmental factors. This occurs in part, perhaps, because such events are not predicted by conventional fishery models. A minor modification in the logistic surplus production model, a modification in which fishing has an impact on the capacity of a population to increase, results in a model that predicts large fluctuations in yield. The new model is developed and its properties are compared with those of the logistic surplus production model. Both models are applied to describe the dynamics of the lake herring (Coregonus artedii) fishery in the upper Great Lakes. T h e G r e a t L a k e s F i s h e r i e s Many changes have occurred during the past 100 years in the fish populations and the fisheries of the Great Lakes (Berst and Spangler 1973, Wells and McLain 1973, Lawrie and Rahrer 1973). In the upper Great Lakes, that is, Lake Superior, Lake Huron, and Lake Michigan, the commercial fisheries have caught mostly lake trout (Salvelinus namaycush ), lake whitefish (Coregonus clupeaforrnis), chubs (Coregonus spps.), and lake herring (Coregonus artedii). Lake trout supported a large and stable fishery in the upper Great Lakes for many decades before the combined impacts of sea lamprey (Petromyzon rnarinus) predation and heavy exploitation