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This paper is concerned with a reaction--diffusion system modeling thefixation and the invasion in a population of a gene drive (an allele biasinginheritance, increasing its own transmission to offspring). In our model, thegene drive has a negative effect on the fitness of individuals carrying it, andis therefore susceptible of decreasing the total carrying capacity of thepopulation locally in space. This tends to generate an opposing demographicadvection that the gene drive has to overcome in order to invade. Whileprevious reaction--diffusion models neglected this aspect, here we focus on itand try to predict the sign of the traveling wave speed. It turns out to be ananalytical challenge, only partial results being within reach, and we completeour theoretical analysis by numerical simulations. Our results indicate thattaking into account the interplay between population dynamics and populationgenetics might actually be crucial, as it can effectively reverse the directionof the invasion and lead to failure. Our findings can be extended to otherbistable systems, such as the spread of cytoplasmic incompatibilities caused byWolbachia.

Demographic feedbacks can hamper the spatial spread of a gene drive