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

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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).

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Acknowledgements

This work has been supported by the ERC Advanced Grant 2013 n. 321186 “ReaDi - Reaction-Diffusion Equations, Propagation and Modelling” held by H. Berestycki. This work was also partially supported by the French National Research Agency (ANR), within project NONLOCAL ANR-14-CE25-0013. During this research, L. Rossi was on academic leave from the University of Padova. This paper was completed while Henri Berestycki was visiting the institute of Advanced Study of Hong Kong University of Science and Technology and its support is gratefully acknowledged.

The authors would like to thank the anonymous reviewers for their careful reading and insightful remarks.

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Authors and Affiliations

  1. Centre d’Analyse et Mathématiques Sociales, Ecole des Hautes Etudes en Sciences Sociales, CNRS, 54 boulevard Raspail, Paris, 75006, France

    Henri Berestycki & Luca Rossi

  2. Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, France

    Romain Ducasse

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  1. Henri Berestycki
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  2. Romain Ducasse
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  3. Luca Rossi
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Correspondence to Romain Ducasse.

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Berestycki, H., Ducasse, R. & Rossi, L. Influence of a road on a population in an ecological niche facing climate change. J. Math. Biol. 81, 1059–1097 (2020). https://doi.org/10.1007/s00285-020-01537-3

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  • DOI: https://doi.org/10.1007/s00285-020-01537-3

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