2014/07/11 by Manon Costa, Costa, Manon, Céline Hauzy +5
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · doi:10.48550/arxiv.1407.3069
openalex publication_date 2014/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.