2011/06/08 by Stephen P. Ellner, Sebastian J. Schreiber, Ellner, Stephen P. +1
Environmental Science · Medicine · Agricultural and Biological Sciences · #Ecology and Vegetation Dynamics Studies #Mathematical and Theoretical Epidemiology and Ecology Models #Plant and animal studies
paper · pdf · doi:10.48550/arxiv.1106.1612
We analyze how temporal variability in local demography and dispersal combine\nto affect the rate of spread of an invading species. Our model combines\nstate-structured local demography (specified by an integral or matrix\nprojection model) with general dispersal distributions that may depend on the\nstate of the individual or its parent, and it allows very general patterns of\nstationary temporal variation in both local demography and in the frequency and\ndistribution of dispersal distances. We show that expressions for the\nasymptotic spread rate and its sensitivity to parameters, that have been\nderived previously for less general models, continue to hold. Using these\nresults, we show that random temporal variability in dispersal can accelerate\npopulation spread. Demographic variability can further accelerate spread if it\nis positively correlated with dispersal variability, for example if\nhigh-fecundity years are also years in which juveniles tend to settle further\naway from their parents. A simple model for the growth and spread of patches of\nan invasive plant (perennial pepperweed, Lepidium latifolium) illustrates these\neffects and shows that they can have substantial impacts on the predicted speed\nof an invasion wave. Temporal variability in dispersal has gotten very little\nattention in both the theoretical and empirical literatures on invasive species\nspread. Our results suggest that this needs to change.\n