A simple two-species population model in which the predator is partially coupled to the prey is developed. The model is an extension of traditional two-species models but less complex than a three-species system. The growth rate of the predator depends upon predation on the modeled and alternate prey; this formulation provides greater realism in describing marine piscivores, such as spiny dogfish (Squalus acanthias), than two-species predator–prey models. Two stable equilibria separated by a saddle point potentially exist for the predator–prey system, and stochastic variability can lead to movement between equilibrium abundance levels. In addition, endogenous limit cycles may exist in the presence of predator fishing mortality. The model is applied to the predation of spiny dogfish on a representative groundfish species, the Georges Bank haddock (Melanogrammus aeglefinus). Stochastic variability is input to the model in the form of ‘‘red noise’’ (variance is a decreasing function of frequency), a feature observed in marine environments. Predator abundance can increase when the modeled prey abundance is low, due to consumption of alternate prey, consistent with the pattern observed in the spiny dogfish–haddock abundances. Increased harvesting on the predator species allows the prey species to spend a greater proportion of time at the high equilibrium. The model presented here poses the interesting management problem of finding the optimal combination of fishing mortality rates for the two species.
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