Are anomalous invasion speeds robust to demographic stochasticity?

Two important issues for conservation are the range expansion of species as a result of climate change and the invasion of exotic species. Being able to predict the rate at which species spread is key for successful management. In deterministic models, the invasion speed of a polymorphic population can be faster than that of any of the component phenotypes, and these "anomalous" invasion speeds persist even when the mutation rate between phenotypes is vanishingly small. Here we investigate whether the same phenomenon is observed in a model with demographic stochasticity. The model that we use is discrete in time and space and we carry out numerical simulations to determine the invasion speed of a population that has two morphs which differ in their dispersal abilities. We find that anomalous speeds are observed in the stochastic model, but only when the carrying capacity of the population is large or the mutation rate between morphs is high enough. These results suggest that only species with large population sizes, such as many insect species, may be able to invade faster if they are polymorphic than if there is only a single morph present in the population.