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Understanding the temporal spread of gene drive alleles -- alleles that biastheir own transmission -- through modeling is essential before any fieldexperiments. In this paper, we present a deterministic reaction-diffusion modeldescribing the interplay between demographic and allelic dynamics, in aone-dimensional spatial context. We focused on the traveling wave solutions,and more specifically, on the speed of gene drive invasion (if successful). Weconsidered various timings of gene conversion (in the zygote or in thegermline) and different probabilities of gene conversion (instead of assuming100$\%$ conversion as done in a previous work). We compared the types ofpropagation when the intrinsic growth rate of the population takes extremevalues, either very large or very low. When it is infinitely large, the wavecan be either successful or not, and, if successful, it can be either pulled orpushed, in agreement with previous studies (extended here to the case ofpartial conversion). In contrast, it cannot be pushed when the intrinsic growthrate is vanishing. In this case, analytical results are obtained through aninsightful connection with an epidemiological SI model. We conducted extensivenumerical simulations to bridge the gap between the two regimes of large andlow growth rate. We conjecture that, if it is pulled in the two extremeregimes, then the wave is always pulled, and the wave speed is independent ofthe growth rate. This occurs for instance when the fitness cost is smallenough, or when there is stable coexistence of the drive and the wild-type inthe population after successful drive invasion. Our model helps delineate theconditions under which demographic dynamics can affect the spread of a genedrive.

Pulled, pushed or failed: the demographic impact of a gene drive can change the nature of its spatial spread