The Effects of Enrichment of Three‐Species Food Chains with Nonlinear Functional Responses

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This article investigates the dynamic behavior of a model of an unstable food chain consisting of three species or trophic levels. The model assumes that each of the consumer species has a Holling type 2 functional response. The study examines how dynamic behaviors and top—level population densities change with the carrying capacity of the bottom level. In all cases examined, the mean population density of the top species initially increases, but eventually decreases as carrying is increased. In some cases, a sufficient increase in the carrying capacity of the bottom species leads to extinction of the top species. If the maximum rate of change of the top species is sufficiently slow relative to the middle species, the period of the population cycles in the top species can change rapidly with a small change in the carrying capacity of the bottom species. Low carrying capacities produce simple cycles with a long period, while high carrying capacities produce simple cycles with a short period. For intermediate carrying capacities, more complex dynamical behaviors, including chaos, may occur. Systems that have only one equilibrium point with all species present may have two alternative attractors with very different densities of the top—level species. The responses of the bottom two species to an increased carrying capacity are also discussed. The results imply that nutrient enrichment may adversely affect high—level consumers and that reductions in the density of top—level consumers may make it difficult or impossible to restore their populations.