Modeling Predator–Prey Dynamics in a Fluctuating Environment

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Abstract
Large fluctuations in the abundance of marine fish are revealed in scale deposits from before the twentieth century and are thought to be environmentally induced. We investigated how a fluctuating environment and predation may combine to cause abrupt shifts in fish abundance on decadal time scales. For example, the biomass of Pacific herring (Clupea pallasi) off Vancouver Island appears to be negatively related to sea surface temperature (SST) and the abundance of its predator, Pacific hake (Merluccius productus). We used first-order differential equations to develop a two-species, predator–prey model forced with stochastic variability. A nonlinear, predator functional response potentially gives rise to multiple equilibrium abundance levels. Environmental variability was simulated as "red noise" (variance is a decreasing function of frequency) with a spectrum derived from SST data. Stochastic variations caused the predator–prey abundances to shift between high and low equilibrium levels. Fishing the prey population can precipitate collapses to the low equilibrium level and prolong the time to recovery. When run with actual catches and SST anomalies from 1951 to 1988, the model simulated prey abundances with a pattern similar to the observed herring biomass.