Pulled, pushed or failed: the demographic impact of a gene drive can change the nature of its spatial spread.

Understanding the temporal spread of gene drive alleles-alleles that bias their own transmission-through modeling is essential before any field experiments. In this paper, we present a deterministic reaction-diffusion model describing the interplay between demographic and allelic dynamics, in a one-dimensional spatial context. We focused on the traveling wave solutions, and more specifically, on the speed of gene drive invasion (if successful).

Demographic feedbacks can hamper the spatial spread of a gene drive.

This paper is concerned with a reaction-diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has a negative effect on the fitness of individuals carrying it, and is therefore 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.

The effect of random dispersal on competitive exclusion - A review.

Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical model with two populations differing only in dispersal ability and whose one-dimensional territories are spatially segregated. Although the motion of the border between the two territories remains elusive in general, all cases investigated in the literature concur: either the border does not move at all because of some environmental heterogeneity or the fast diffuser chases the slow diffuser.

Catch Me If You Can: A Spatial Model for a Brake-Driven Gene Drive Reversal.

Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may, however, have to be stopped. "Antidotes" (brakes) have been suggested, but have been so far only studied in well-mixed populations.