Climate change and integrodifference equations in a stochastic environment

TL;DR

This paper models how stochastic variability in climate-induced habitat shifts and growth rates affects species persistence, revealing that increased environmental uncertainty reduces the likelihood of population survival.

Contribution

It introduces a stochastic integrodifference equation framework to analyze population persistence under variable habitat shifts and growth rates, extending previous deterministic models.

Findings

Variability in habitat shift and growth rates decreases population persistence.

A threshold criterion for persistence is derived based on a stochastic growth rate metric.

Numerical simulations show increased environmental variance reduces species survival likelihood.

Abstract

Climate change impacts population distributions, forcing some species to migrate poleward if they are to survive and keep up with the suitable habitat that is shifting with the temperature isoclines. Previous studies have analyzed whether populations have the capacity to keep up with shifting temperature isoclines, and have mathematically determined the combination of growth and dispersal that is needed to achieve this. However, the rate of isocline movement can be highly variable, with much uncertainty associated with yearly shifts. The same is true for population growth rates. Growth rates can be variable and uncertain, even within suitable habitats for growth. In this paper we reanalyze the question of population persistence in the context of the uncertainty and variability in isocline shifts and rates of growth. Specifically, we employ a stochastic integrodifference equation model on a patch of suitable habitat that shifts poleward at a random rate. We derive a metric describing the asymptotic growth rate of the linearized operator of the stochastic model and yielding a threshold criterion for population persistence. We demonstrate that the variability in the yearly shift and in the growth rate has a significant negative effect on the persistence in the sense that it decreases the threshold criterion for population persistence. Mathematically, we show how the persistence metric can be connected to the principal eigenvalue problem for a related integral operator, at least for the case where isocline shifting speed is deterministic. Analysis of dynamics for the case where the dispersal kernel is Gaussian leads to the existence of a critical shifting speed. Finally we illustrate our different results for butterfly population using numerical simulations and demonstrate how increased variances in isocline shifts and growth rates translate into decreased likelihoods of persistence.