How mutation shapes the rate of population spread in the presence of a mate-finding Allee effect

Although past work has considered how evolution and Allee effects each shape population spread, these factors have rarely been considered together. We develop an integrodifference equation model that tracks individuals of multiple dispersal types (i.e., short- and long-distance dispersers) of male and female individuals subject to a strong Allee effect due to mate-finding process. We use our model to explore how mutation between different dispersal types affects the rate of population spread, since this evolutionary mechanism has been shown to lead to both faster and slower spread in a previous individual-based model. We ask, under what conditions does mutation cause the population to spread faster (or slower) than it spreads without mutation (from the same initial conditions)? We find that mutation can both speed up and slow down invasions. Speeding up occurs in a relatively small range of parameter space near the Allee threshold of the population. Slowing down occurs across a broad range of parameters.