Population dynamics of systems with consumers that maintain a constant ratio of intake rates of two resources
type: Item
instance of: scholarly article
title: Population dynamics of systems with consumers that maintain a constant ratio of intake rates of two resources
zbMATH Open document ID: 0662.92023
DOI: 10.1016/0040-5809(89)90010-5
author: Peter A. Abrams
author: Lester Shen
published in: Theoretical Population Biology
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34D99
zbMATH DE Number: 4083443
zbMATH Keywords: optimal exploitation
zbMATH Keywords: nutritionally complementary resources
zbMATH Keywords: self- reproducing resources
zbMATH Keywords: two-consumer populations
zbMATH Keywords: nonsubstitutable resources
zbMATH Keywords: capture rates
zbMATH Keywords: individual fitness
zbMATH Keywords: constant ratio of intake rates
zbMATH Keywords: logistically growing resources
zbMATH Keywords: single stable equilibrium
zbMATH Keywords: single unstable equilibrium
zbMATH Keywords: three equilibria
zbMATH Keywords: limit cycle
zbMATH Keywords: attractor
zbMATH Keywords: consumer death rates
zbMATH Keywords: consumer population size
zbMATH Keywords: single-consumer models
zbMATH Keywords: time lags
zbMATH Keywords: resource growth functions
zbMATH Keywords: consumer-resource models
MaRDI profile type: Publication
full work available at URL: 0040-5809(89)90010-5
OpenAlex ID: W1965417053
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description: scientific article; zbMATH DE number 4083443