Persistence in models of three interacting predator-prey populations

• Published in: Mathematical biosciences 1984-04, Vol.68 (2), p.213-231
• Main Authors: Freedman, H.I., Waltman, Paul
• Format: Article
• Language: English
• Subjects: Animal and plant ecology; Animal, plant and microbial ecology; Animals; Biological and medical sciences; Demecology; Fundamental and applied biological sciences. Psychology
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/0025-5564(84)90032-4

This paper considers a class of deterministic models of three interacting populations with a view towards determining when all of the populations persist. In analytical terms persistence means that liminf t→∞ x( t)> 0 for each population x( t); in geometric terms, that each trajectory of the modeling system of differential equations is eventually bounded away from the coordinate planes. The class of systems considered allows three level food webs, two competing predators feeding on a single prey, or a single predator feeding on two competing prey populations. As a corollary to the last case it is shown that the addition of a predator can lead to persistence of a three population system where, without a predator, the two competing populations on the lower trophic level would have only one survivor. The basic models are of Kolmogorov type, and the results improve several previous theorems on persistence.