  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.
