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Temporally variable dispersal and demography can accelerate the spread of invading species

We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines state-structured local demography (specified by an integral or matrix projection model) with general dispersal distributions that may depend on the state of the individual or its parent, and it allows very general patterns of stationary temporal variation in both local demography and in the frequency and distribution of dispersal distances. We show that expressions for the asymptotic spread rate and its sensitivity to parameters, that have been derived previously for less general models, continue to hold. Using these results, we show that random temporal variability in dispersal can accelerate population spread. Demographic variability can further accelerate spread if it is positively correlated with dispersal variability, for example if high-fecundity years are also years in which juveniles tend to settle further away from their parents. A simple model for the growth and spread of patches of an invasive plant (perennial pepperweed, Lepidium latifolium) illustrates these effects and shows that they can have substantial impacts on the predicted speed of an invasion wave. Temporal variability in dispersal has gotten very little attention in both the theoretical and empirical literatures on invasive species spread. Our results suggest that this needs to change.