Integrating eco-evolutionary dynamics into matrix population models for structured populations: Discrete and continuous frameworks

Abstract

State-structured populations are ubiquitous in biology, from the age-structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco-evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco-evolutionary dynamics in structured population, such methods are wholly lacking in the (Formula presented.) function evolutionary game theoretic framework. In this paper, we integrate standard matrix population modelling into the (Formula presented.) function framework to create a theoretical framework to probe eco-evolutionary dynamics in structured populations. This framework encompasses age- and stage-structured matrix models with basic density- and frequency-dependent transition rates and probabilities. For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco-evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models. The methods developed in this paper for state-structured populations and their extensions to multistate-structured populations provide a simple way to create, analyse and simulate eco-evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution.