Influence of a road on a population in an ecological niche facing climate change

Henri Berestycki (1) , Romain Ducasse (2) , Luca Rossi (3, 1)

1 CAMS - Centre d'Analyse et de Mathématique sociales
2 MMCS - Modélisation mathématique, calcul scientifique
3 Dipartimento di Matematica [padova]

We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche. This model consists of a system of coupled reaction-diffusion equations set on domains with different dimensions (line / plane). We first show that the presence of the line is always deleterious and can even lead the population to extinction. Next, we consider the case where the niche is subject to a displacement, representing the effect of a climate change or of seasonal variation of resources. We find that in such case the presence of the line with fast diffusion can help the population to persist. We also study several qualitative properties of this system. The analysis is based on a notion of generalized principal eigenvalue developed by the authors in [5].

Mots clés: gen- eralized principal eigenvalue; line with fast diffusion; 92D25; eco- logical niche MSC: 35K57; ecological niche; forced speed; moving environment; climate change; generalized principal eigenvalue; KPP equations; reaction-diffusion system; 35B40; 35K40; 35B53

Domaines: Equations aux dérivées partielles [math.AP]

Henri Berestycki, Romain Ducasse, Luca Rossi. Influence of a road on a population in an ecological niche facing climate change. Journal of Mathematical Biology, 2020, 81, pp.1059-1097. ⟨10.1007/s00285-020-01537-3⟩. ⟨hal-02057753v2⟩