Geodesic
Influence of the mode of reproduction on dispersal evolution during species invasion
Vincent Calvez1 ; Joachim Crevat2 ; Léonard Dekens3 ; Benoit Fabrèges1 ; Frédéric Kuczma4 ; Florian Lavigne5, 6 ; Gaël Raoul7
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 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

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

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 
@article{EP_2020_67_a8,
     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},
     year = {2020},
     volume = {67},
     doi = {10.1051/proc/202067008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202067008/}
}
TY  - JOUR
AU  - Vincent Calvez
AU  - Joachim Crevat
AU  - Léonard Dekens
AU  - Benoit Fabrèges
AU  - Frédéric Kuczma
AU  - Florian Lavigne
AU  - Gaël Raoul
TI  - Influence of the mode of reproduction on dispersal evolution during species invasion
JO  - ESAIM. Proceedings
PY  - 2020
SP  - 120
EP  - 134
VL  - 67
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/202067008/
DO  - 10.1051/proc/202067008
LA  - en
ID  - EP_2020_67_a8
ER  - 
%0 Journal Article
%A Vincent Calvez
%A Joachim Crevat
%A Léonard Dekens
%A Benoit Fabrèges
%A Frédéric Kuczma
%A Florian Lavigne
%A Gaël Raoul
%T Influence of the mode of reproduction on dispersal evolution during species invasion
%J ESAIM. Proceedings
%D 2020
%P 120-134
%V 67
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/202067008/
%R 10.1051/proc/202067008
%G en
%F EP_2020_67_a8
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

Cité par Sources :