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). We considered various timings of gene conversion (in the zygote or in the germline) and different probabilities of gene conversion (instead of assuming 100[Formula: see text] conversion as done in a previous work). We compared the types of propagation when the intrinsic growth rate of the population takes extreme values, either very large or very low. When it is infinitely large, the wave can be either successful or not, and, if successful, it can be either pulled or pushed, in agreement with previous studies (extended here to the case of partial conversion). In contrast, it cannot be pushed when the intrinsic growth rate is vanishing. In this case, analytical results are obtained through an insightful connection with an epidemiological SI model. We conducted extensive numerical simulations to bridge the gap between the two regimes of large and low growth rate. We conjecture that, if it is pulled in the two extreme regimes, then the wave is always pulled, and the wave speed is independent of the growth rate. This occurs for instance when the fitness cost is small enough, or when there is stable coexistence of the drive and the wild-type in the population after successful drive invasion. Our model helps delineate the conditions under which demographic dynamics can affect the spread of a gene drive.

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. While previous reaction-diffusion models neglected this aspect, here we focus on it and try to predict the sign of the traveling wave speed. It turns out to be an analytical challenge, only partial results being within reach, and we complete our theoretical analysis by numerical simulations. Our results indicate that taking into account the interplay between population dynamics and population genetics might actually be crucial, as it can effectively reverse the direction of the invasion and lead to failure. Our findings can be extended to other bistable systems, such as the spread of cytoplasmic incompatibilities caused by Wolbachia.

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. Counterintuitively, it is better to randomly explore the hostile enemy territory, even if it means highly probable death of some individuals, than to "stay united". This directly contradicts a celebrated result on the intermediate competition case, emphasizing the importance of the competition intensity. Overall, the larger picture remains unclear and the optimal strategy regarding dispersal remains ambiguous. Several open problems worthy of a special attention are raised.

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. Here, we consider a reaction-diffusion system modeling the release of a gene drive (of fitness [Formula: see text]) and a brake (fitness [Formula: see text], [Formula: see text]) in a wild-type population (fitness 1). We prove that whenever the drive fitness is at most 1/2 while the brake fitness is close to 1, coextinction of the brake and the drive occurs in the long run. On the contrary, if the drive fitness is greater than 1/2, then coextinction is impossible: the drive and the brake keep spreading spatially, leaving in the invasion wake a complicated spatiotemporally heterogeneous genetic pattern. Based on numerical experiments, we argue in favor of a global coextinction conjecture provided the drive fitness is at most 1/2, irrespective of the brake fitness. The proof relies upon the study of a related predator-prey system with strong Allee effect on the prey. Our results indicate that some drives may be unstoppable and that if gene drives are ever deployed in nature, threshold drives, that only spread if introduced in high enough frequencies, should be preferred.