Persistence and Spread of a Species with a Shifting Habitat Edge

Abstract

We study a reaction-diffusion model that describes the growth and spread of a species along a shifting habitat gradient on which the species' growth increases. It is assumed that the linearized species growth rate is positive near positive infinity and is negative near negative infinity. We show that the persistence and spreading dynamics depend on the speed of the shifting habitat edge c and a number c * (∞) that is determined by the maximum linearized growth rate and the diffusion coefficient. We demonstrate that if c > c * (∞), then the species will become extinct in the habitat, and that if c < c * (∞), then the species will persist and spread along the shifting habitat gradient at an asymptotic spreading speed c * (∞).

Moving forward: insights and applications of moving‐habitat models for climate change ecology

“…; Berestycki, Desvillettes & Diekmann ; Li et al . ). These models can accommodate single species (Berestycki et al .…”

“…An interesting way to incorporate climate change would be to develop the IDE analogue of the RDE found in Li et al . (). Their model including only one shifting habitat edge, with the other end open to represent a population invading novel, suitable area.…”

“…; Li et al . ) as well as competing species (Potapov & Lewis ; Berestycki, Desvillettes & Diekmann ). RDEs can easily incorporate field data to provide risk estimates (Leroux et al .…”

“…Recent RDEs have modelled climate change using shifting boundary conditions or shifting growth functions that force populations to track suitable habitat (Potapov & Lewis 2004;Berestycki et al 2009;Leroux et al 2013;Berestycki, Desvillettes & Diekmann 2014;Li et al 2014). These models can accommodate single species (Berestycki et al 2009;Leroux et al 2013;Li et al 2014) as well as competing species (Potapov & Lewis 2004;Berestycki, Desvillettes & Diekmann 2014). RDEs can easily incorporate field data to provide risk estimates (Leroux et al 2013), but care must be taken since RDEs cannot capture frequent long-distance dispersal events.…”

A spectral condition for Liouville-type result of monostable KPP equation in periodic shear flows

“…(1.2) In [2,3,7,8], assumption (1.2) means that the environment of species is completely unfavorable outside a compact set and it may be favorable inside. This kind of model is newly investigated in one dimensional space by Li et al [12] under assumption that ∂ u f (z, 0) is positive near positive infinity and is negative near negative infinity. The Liouville type result for entirely semilinear elliptic equation a i j (z)∂ i j u(z) + q(z) · ∇u(z) + f (z, u) = 0, z ∈ R N was also studied by Berestycki et al [4] with the condition lim inf…”