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Predator–prey dynamics with intraspecific competition and an Allee effect in the predator population

Predator–prey dynamics with intraspecific competition and an Allee effect in the predator population The study of the Allee e ect on the stability of equilibria of predator-prey systems is of recent interest to mathematicians, ecologists, and conservationists. Many theoret- ical models that include the Allee e ect result in an unstable coexistence equilibrium. However, empirical evidence suggests that predator-prey systems that exhibit density- dependent growth at small population densities still can achieve coexistence in the long term. In this talk, I will review an often cited model that incorporates an Allee e ect in the predator population and results in an unstable coexistence equilibrium, and then I will present a novel extension to this model that includes a term that models in- traspeci c competition within the predator population. The additional term penalizes predator population growth for large predator densities relative to the prey density. Standard methods of equilibrium analysis show that there exist biologically reasonable parameter sets which produce a stable coexistence equilibrium for the modi ed model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Letters in Biomathematics Unpaywall

Predator–prey dynamics with intraspecific competition and an Allee effect in the predator population

Letters in BiomathematicsJan 1, 2017

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Publisher
Unpaywall
ISSN
2373-7867
DOI
10.1080/23737867.2017.1282843
Publisher site
See Article on Publisher Site

Abstract

The study of the Allee e ect on the stability of equilibria of predator-prey systems is of recent interest to mathematicians, ecologists, and conservationists. Many theoret- ical models that include the Allee e ect result in an unstable coexistence equilibrium. However, empirical evidence suggests that predator-prey systems that exhibit density- dependent growth at small population densities still can achieve coexistence in the long term. In this talk, I will review an often cited model that incorporates an Allee e ect in the predator population and results in an unstable coexistence equilibrium, and then I will present a novel extension to this model that includes a term that models in- traspeci c competition within the predator population. The additional term penalizes predator population growth for large predator densities relative to the prey density. Standard methods of equilibrium analysis show that there exist biologically reasonable parameter sets which produce a stable coexistence equilibrium for the modi ed model.

Journal

Letters in BiomathematicsUnpaywall

Published: Jan 1, 2017

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