The effect of climate shift on a species submitted to dispersion, evolution, growth and nonlocal competition

TL;DR

This paper analyzes how climate change impacts a structured population considering dispersion, evolution, and nonlocal competition, identifying critical speeds for survival and extinction under various environmental assumptions.

Contribution

It introduces a comprehensive model incorporating climate shift effects on populations with nonlocal competition, and determines critical speeds for survival and propagation in different scenarios.

Findings

Critical climate change speed for population extinction or survival.

Population can follow climate shift by migration and evolution.

Propagation speed can differ from climate shift speed in unconfined cases.

Abstract

We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. We introduce theclimate shift due to {\it Global Warming} and discuss the dynamicsof the population by studying the long time behavior of thesolution of the Cauchy problem. We consider three sets ofassumptions on the growth function. In the so-called {\it confinedcase} we determine a critical climate change speed for theextinction or survival of the population, the latter case taking place by "strictly following the climate shift". In the so-called {\itenvironmental gradient case}, or {\it unconfined case}, we additionally determine the propagation speedof the population when it survives: thanks to a combination of migration and evolution, it can here be different from the speed of the climate shift. Finally, we consider {\it mixed scenarios}, that are complex situations, where thegrowth function satisfies the conditions of the confined case on the right, and the conditions of the unconfined case on the left.The main difficulty comes from the nonlocal competition term that prevents the use of classical methods based on comparison arguments. This difficulty is overcome thanks to estimates on the tails of the solution, and a careful application of the parabolic Harnack inequality.