Influence of a mortality trade-off on the spreading rate of cane toads fronts

Emeric Bouin (1) , Matthew H. Chan (2) , Christopher Henderson (3) , Peter S. Kim (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Mathematics, University of Sydney
3 Department of Mathematics [Chicago]

In this paper, we study the influence of the mortality trade-off in a cane-toad equation, a nonlocal reaction-diffusion-mutation equation modelling the invasion of cane toads in Australia that has attracted attention recently. The population of toads is structured by a phenotypical trait that governs the spatial diffusion. We are concerned with the case when the diffusivity can take unbounded values and the mortality trade-off depends only on the trait variable. Depending on the rate of increase of the penalization from the trade-off as diffusivity approaches infinity, we obtain the rate of spreading of the population. We identify two regimes, an acceleration regime when the penalization is weak and a linear spreading regime when the penalization is strong.

Mots clés: Structured populations; reaction-diffusion equations; front acceleration

Domaines: Equations aux dérivées partielles [math.AP]

Emeric Bouin, Matthew H. Chan, Christopher Henderson, Peter S. Kim. Influence of a mortality trade-off on the spreading rate of cane toads fronts. 2017. ⟨hal-01451448v1⟩