Stochastic eco-evolutionary model of a prey-predator community

Authored by Nicolas Loeuille, Sylvie Meleard, Manon Costa, Celine Hauzy

Date Published: 2016

DOI: 10.1007/s00285-015-0895-y

Sponsors: French National Research Agency (ANR)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic coevolution of prey and predators. The community evolves as a multi-type birth and death process with mutations. We first consider the infinite particle approximation of the process without mutation. In this limit, the process can be approximated by a system of differential equations. We prove the existence of a unique globally asymptotically stable equilibrium under specific conditions on the interaction among prey individuals. When mutations are rare, the community evolves on the mutational scale according to a Markovian jump process. This process describes the successive equilibria of the prey-predator community and extends the polymorphic evolutionary sequence to a coevolutionary framework. We then assume that mutations have a small impact on phenotypes and consider the evolution of monomorphic prey and predator populations. The limit of small mutation steps leads to a system of two differential equations which is a version of the canonical equation of adaptive dynamics for the prey-predator coevolution. We illustrate these different limits with an example of prey-predator community that takes into account different prey defense mechanisms. We observe through simulations how these various prey strategies impact the community.

Tags

Coevolution Population-dynamics Size Natural-selection Food webs Genetic-variation Red-queen dynamics Ecological communities Stable equilibrium Plant defense