Spatial gene drives and pushed genetic waves.

Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics before potential applications. Here, we use a reaction-diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, although it possesses a selective disadvantage s > 0. Using methods developed by Barton and collaborators, we show that socially responsible gene drives require 0.5 < s < 0.697, a rather narrow range. In this "pushed wave" regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called "critical propagule," which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable ("sensitizing drive") in a way that is harmless for a wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped, even by imperfect barriers perforated by a series of gaps.

Population dynamics of engineered underdominance and killer-rescue gene drives in the control of disease vectors.

A number of different genetics-based vector control methods have been proposed. Two approaches currently under development in Aedes aegypti mosquitoes are the two-locus engineered underdominance and killer-rescue gene drive systems. Each of these is theoretically capable of increasing in frequency within a population, thus spreading associated desirable genetic traits. Thus they have gained attention for their potential to aid in the fight against various mosquito-vectored diseases. In the case of engineered underdominance, introduced transgenes are theoretically capable of persisting indefinitely (i.e. it is self-sustaining) whilst in the killer-rescue system the rescue component should initially increase in frequency (while the lethal component (killer) is common) before eventually declining (when the killer is rare) and being eliminated (i.e. it is temporally self-limiting). The population genetics of both systems have been explored using discrete generation mathematical models. The effects of various ecological factors on these two systems have also been considered using alternative modelling methodologies. Here we formulate and analyse new mathematical models combining the population dynamics and population genetics of these two classes of gene drive that incorporate ecological factors not previously studied and are simple enough to allow the effects of each to be disentangled. In particular, we focus on the potential effects that may be obtained as a result of differing ecological factors such as strengths of larval competition; numbers of breeding sites; and the relative fitness of transgenic mosquitoes compared with their wild-type counterparts. We also extend our models to consider population dynamics in two demes in order to explore the effects of dispersal between neighbouring populations on the outcome of UD and KR gene drive systems.

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.