Influence of a road on a population in an ecological niche facing climate change
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Journal of Mathematical Biology https://doi.org/10.1007/s00285-020-01537-3
Influence of a road on a population in an ecological niche facing climate change Henri Berestycki1 · Romain Ducasse2
· Luca Rossi1
Received: 10 December 2019 / Revised: 17 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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, in a stationary climate, 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. We find that in such case 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 and studied by the authors (2019). Keywords KPP equations · Reaction-diffusion system · Line with fast diffusion · Generalized principal eigenvalue · Moving environment · Climate change · Forced speed · Ecological niche Mathematics Subject Classification 35K57 · 92D25 · 35B40 · 35K40 · 35B53
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Romain Ducasse [email protected] Henri Berestycki [email protected] Luca Rossi [email protected]
1
Centre d’Analyse et Mathématiques Sociales, Ecole des Hautes Etudes en Sciences Sociales, CNRS, 54 boulevard Raspail, Paris 75006, France
2
Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, France
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H. Berestycki et al.
1 Setting of the problem and main results 1.1 Introduction It has long been known that the spreading of invasive species can be enhanced by human transportations. This was the case for instance for the “tiger mosquito”, Aedes Albopictus. Originating from south-east Asia, eggs of this mosquito were introduced in several places around the world, mostly via shipments of used tires (Hawley et al. 1987). Recently, there has been evidence of passive dispersal of adult tiger mosquitoes by cars, leading to the colonizations of new territories along road networks (Millner and Loaiza 2015; Eritja et al. 2017). Other kind of networks with fast transportation appear to help the dispersal of biological entities. For instance, rivers can accelerate the spreading of plant pathogens (Jung and Blaschke 2004). It has also been observed by Mckenzie et al. (2012) and Hillen and Painter (2013) that populations of wolves in the Western Canadian Forest move and concentrate along seismic lines (paths traced in forests by oil companies for testing of oil reservoirs). In a different register, we mention that the road network is known to have a driving effect on the spreading of epidemics. The “black death” plague, for instance, spread first along the silk road and then spread alon
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