Adaptation in shifting and size-changing environments under selection

TL;DR

This paper develops a model to understand how populations adapt in environments that shift and change size periodically, revealing new insights into persistence and extinction under dynamic conditions.

Contribution

It introduces a novel model incorporating periodic environmental shifts and size changes, analyzing population adaptation and extinction in such dynamic habitats.

Findings

Population persistence depends on the interplay between habitat movement and selection.

Numerical simulations illustrate the impact of environmental dynamics on adaptation.

The finite element approach effectively captures complex population-environment interactions.

Abstract

We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After studying the underlying periodic parabolic principal eigenelements, we address the extinction vs. persistence issue, taking into account the interplay between the moving habitat and periodic selection. Subsequently, we employ a space-time finite element approach, establish the well-posedness of the approximation scheme, and conduct numerical simulations to explore these dynamics.