Modeling the impacts of a simple meiotic gene drive on small, homeostatic populations

Gene drives offer unprecedented control over the fate of natural ecosystems by leveraging non-Mendelian inheritance mechanisms to proliferate synthetic genes across wild populations. However, these benefits are offset by a need to avoid the potentially disastrous consequences of unintended ecological interactions. The efficacy of many gene-editing drives has been brought into question due to predictions that they will inevitably be thwarted by the emergence of drive-resistant mutations, but these predictions derive largely from models of large or infinite populations that cannot be driven to extinction faster than mutations can fixate. To address this issue, we characterize the impact of a simple, meiotic gene drive on a small, homeostatic population whose genotypic composition may vary due to the stochasticity inherent in natural mating events (e.g., partner choice, number of offspring) or the genetic inheritance process (e.g., mutation rate, gene drive fitness). To determine whether the ultimate genotypic fate of such a population is sensitive to such stochastic fluctuations, we compare the results of two dynamical models: a deterministic model that attempts to predict how the genetics of an average population evolve over successive generations, and an agent-based model that examines how stable these predictions are to fluctuations. We find that, even on average, our stochastic model makes qualitatively distinct predictions from those of the deterministic model, and we identify the source of these discrepancies as a dynamic instability that arises at short times, when genetic diversity is maximized as a consequence of the gene drive's rapid proliferation. While we ultimately conclude that extinction can only beat out the fixation of drive-resistant mutations over a limited region of parameter space, the reason for this is more complex than previously understood, which could open new avenues for engineered gene drives to circumvent this weakness.