Population dynamics of systems with consumers that maintain a constant ratio of intake rates of two resources
This article explores the population dynamics that result when either one- or two-consumer populations optimally exploit two nutritionally complementary or nonsubstitutable resources. It is assumed that the capture rates of the two resources are negatively related, the resources are self-reproducing, and the consumers adjust their capture rates to maximize individual fitness. The result is that consumers maintain a constant ratio of intake rates of the two resources. A model with a single-consumer and two logistically growing resources is analyzed. It is shown that different parameter values can result in a single stable equilibrium, a single unstable equilibrium, or three equilibria. When there are three equilibria, the one with intermediate resource densities is always an unstable node. At least one of the other two equilibria is locally stable. The third equilibrium may be locally stable, locally unstable, and surrounded by a limit cycle or more complex attractor, or may be globally unstable. Increasing consumer death rates in these systems may result in counterintuitive behavior that includes increasing equilibrium or average consumer population size. Modifications of the single-consumer models to include time lags in consumer response of different resource growth functions extends the possible behavior to include 2 alternative limit cycles. Two-consumer models have a single equilibrium point, which is unstable when the resource density at the equilibrium point is sufficiently low. The cycles that occur in such systems may be complex in form, and often involve highly correlated changes in the populations of the two competing consumers. Two competitively equal consumers with very different resource utilization may be unable to coexist in such models, and invasion analysis is inadequate to determine whether consumers will coexist. Several other unusual features of these consumer-resource models are discussed.
scientific article; zbMATH DE number 4083443