How does the magnitude of genetic variation affect eco-evolutionary dynamics in character displacement?

While previous studies on character displacement tended to focus on trait divergence and convergence as a result of long-term evolution, recent studies suggest that character displacement can be a special case of evolutionary rescue, where rapid evolution prevents population extinction by weakening negative interspecific interactions. When the magnitude of genetic variation is small, however, the speed of trait divergence can be slow and populations may go extinct before the completion of character displacement. Here we analyzed a simple model to examine how the magnitude of genetic variation affects evolutionary rescue via ecological and reproductive character displacement that weakens resource competition and reproductive interference, respectively. We found that the large additive genetic variance is more important for preventing extinction in reproductive character displacement than in ecological character displacement. This is because reproductive interference produces a locally stable coexistence equilibrium with positive frequency-dependence (i.e., minority disadvantage) whereas ecological character displacement results in a globally stable coexistence equilibrium. Furthermore, population extinction becomes less likely when ecological and reproductive character displacement occur simultaneously due to positive covariance between ecological and reproductive traits. Our results suggest that while reproductive character displacement may be rarer than ecological character displacement, it is more likely to occur when there exists positive trait covariance, such as the case of a magic trait in reinforcement of speciation processes.