Eco-evolutionary dynamics of a trait-structured predator-prey model

TL;DR

This paper develops a tractable mathematical model to analyze how eco-evolutionary dynamics influence predator-prey interactions, focusing on population heterogeneity and trait distribution effects over time.

Contribution

It generalizes a moment-based method to include time-dependent mortality and birth, enabling analysis of transient and long-term eco-evolutionary dynamics in trait-structured models.

Findings

Prey trait distribution is approximately Gaussian with constant variance.

The mean trait dynamics are governed by an autonomous ODE.

Eco-evolutionary dynamics significantly affect prey survival and transient behavior.

Abstract

The coupling between evolutionary and ecological changes (eco-evolutionary dynamics) has been shown to be relevant among diverse species, and is also of interest outside of ecology, i.e. in cancer evolution. These dynamics play an important role in determining survival in response to climate change, motivating the need for mathematical models to capture this often complex interplay. Models incorporating eco-evolutionary dynamics often sacrifice analytical tractability to capture the complexity of real systems, do not explicitly consider the effect of population heterogeneity, or focus on long-term behaviour. In order to capture population heterogeneity, both transient, and long-term dynamics, while retaining tractability, we generalise a moment-based method applicable in the regime of small segregational variance to the case of time-dependent mortality and birth. These results are applied to a predator-prey model, where ecological parameters such as the contact rate between species are trait-structured. The trait-distribution of the prey species is shown to be approximately Gaussian with constant variance centered on the mean trait, which is asymptotically governed by an autonomous ODE. In this way, we make explicit the impact of eco-evolutionary dynamics on the transient behaviour and long-term fate of the prey species.