# Spatial gene drives and pushed genetic waves

## TL;DR

This paper models the spatial spread of gene drives in populations, identifying conditions for safe deployment and methods to contain or stop their spread using reaction-diffusion equations and threshold-based safeguards.

## Contribution

It introduces a reaction-diffusion model for gene drives, defining a narrow parameter range for safe spread, and proposes strategies for containment using sensitized drives and barriers.

## Key findings

- Gene drives require specific selective disadvantage range (0.5<s<0.697) for safe spread.
- A threshold 'critical propagule' prevents accidental spread of gene drives.
- Sensitizing drives and barriers can effectively halt spatial spread.

## Abstract

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 prior to potential applications. Here, we employ 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, even though it possesses a selective disadvantage $s>0$. Using methods developed by N. 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.