Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations. Issue 1 (1st January 2018)

• Record Type: Journal Article
• Authors: Pouchol, Camille; Trélat, Emmanuel
• Is Part Of: Journal of biological dynamics. Volume 12:Issue 1(2018)
• Page Start: 872
• Page End: 893
• Publication Date: 2018-01-01
• Subjects: Integro-differential equations -- population dynamics -- asymptotic analysis -- non-local model -- steady-states; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2018.1515994
• Languages: English
• ISSNs: 1751-3758

Abstract

ABSTRACT: We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer, and they generalize the usual Lotka-Volterra ordinary differential equations. Our aim is to give conditions under which there is persistence of all species. Through the analysis of a Lyapunov function, our first main result gives a simple and general condition on the matrix of interactions, together with a convergence rate. The second main result establishes another type of condition in the specific case of mutualistic interactions. When either of these conditions is met, we describe which traits are asymptotically selected.