Apparaît dans la collection : 2022 - T1 - WS3 - Mathematical models in ecology and evolution

Joint work with Florence Débarre, Lena Klay and Vincent Calvez.

The topic of this two-part talk will be reaction-diffusion models for the fixation and invasion of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring) in a spatially structured population. The originality of the models that will be presented is that the gene drive is susceptible of decreasing the total carrying capacity of the population locally in space. This tends to generate an opposing demographic advection that the gene drive has to overcome in order to invade. Due to these opposing forces, the prediction of the sign of the traveling wave speed is difficult.

The first part will report on a joint work with F. Debarre on the simplest case where heterozygous individuals are nonexistent or negligible. Despite the simplifying assumptions, we only achieved partial analytical results. These will be presented, commented and completed by numerical simulations.

In the second part I will present recent new findings due to Lena Klay, in collaboration with V. Calvez, F. Debarre and myself, on asymptotic regimes and on more complex cases where the heterozygous population is non-negligible.