Influence of the mode of reproduction on dispersal evolution during species invasion

Vincent Calvez; Joachim Crevat; Léonard Dekens; Benoit Fabrèges; Frédéric Kuczma; Florian Lavigne; Gaël Raoul

doi:10.1051/proc/202067008

Geodesic

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Influence of the mode of reproduction on dispersal evolution during species invasion

Vincent Calvez ¹ ; Joachim Crevat ² ; Léonard Dekens ³ ; Benoit Fabrèges ¹ ; Frédéric Kuczma ⁴ ; Florian Lavigne ^5,⁶ ; Gaël Raoul ⁷

¹ Institut Camille Jordan, Université Claude Bernard Lyon 1 in Lyon
² Institut de Mathématiques de Toulouse; UMR5219, Université de Toulouse; UPS IMT, F-31062 Toulouse Cedex 9 France
³ École Normale Supérieure de Lyon
⁴ Laboratoire de Mathématiques et de Physique Théorique de Tours
⁵ BioSP, INRA, 84914, Avignon, France
⁶ Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
⁷ Centre de Mathématiques Appliquées, École Polytechnique, Palaiseau

ESAIM. Proceedings, Tome 67 (2020), pp. 120-134.

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Résumé

We consider a reaction-diffusion-reproduction equation, modeling a population which is spatially heterogeneous. The dispersion of each individuals is influenced by its phenotype. In the literature, the asymptotic propagation speed of an asexual population has already been rigorously determined. In this paper we focus on the difference between the asexual reproduction case, and the sexual reproduction case, involving a non-local term modeling the reproduction. This comparison leads to a different invasion speed according to the reproduction.After a formal analysis of both cases, leading to a heuristic of the asymptotic behaviour of the invasion fronts, we give some numerical evidence that the acceleration rate of the spatial spreading of a sexual population is slower than the acceleration rate of an asexual one. The main difficulty to get sharper results on a transient comes from the non-local sexual reproduction term.

DOI : 10.1051/proc/202067008

Affiliations des auteurs :

Vincent Calvez ¹ ; Joachim Crevat ² ; Léonard Dekens ³ ; Benoit Fabrèges ¹ ; Frédéric Kuczma ⁴ ; Florian Lavigne ^{5, 6} ; Gaël Raoul ⁷

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     author = {Vincent Calvez and Joachim Crevat and L\'eonard Dekens and Benoit Fabr\`eges and Fr\'ed\'eric Kuczma and Florian Lavigne and Ga\"el Raoul},
     title = {Influence of the mode of reproduction on dispersal evolution during species invasion},
     journal = {ESAIM. Proceedings},
     pages = {120--134},
     publisher = {mathdoc},
     volume = {67},
     year = {2020},
     doi = {10.1051/proc/202067008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202067008/}
}

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Vincent Calvez; Joachim Crevat; Léonard Dekens; Benoit Fabrèges; Frédéric Kuczma; Florian Lavigne; Gaël Raoul. Influence of the mode of reproduction on dispersal evolution during species invasion. ESAIM. Proceedings, Tome 67 (2020), pp. 120-134. doi : 10.1051/proc/202067008. http://geodesic.mathdoc.fr/articles/10.1051/proc/202067008/

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