  We live in a time where climate models predict future increases in
environmental variability and biological invasions are becoming increasingly
frequent. A key to developing effective responses to biological invasions in
increasingly variable environments will be estimates of their rates of spatial
spread and the associated uncertainty of these estimates. Using stochastic,
stage-structured, integro-difference equation models, we show analytically that
invasion speeds are asymptotically normally distributed with a variance that
decreases in time. We apply our methods to a simple juvenile-adult model with
stochastic variation in reproduction and an illustrative example with published
data for the perennial herb, \emph{Calathea ovandensis}. These examples
buttressed by additional analysis reveal that increased variability in vital
rates simultaneously slow down invasions yet generate greater uncertainty about
rates of spatial spread. Moreover, while temporal autocorrelations in vital
rates inflate variability in invasion speeds, the effect of these
autocorrelations on the average invasion speed can be positive or negative
depending on life history traits and how well vital rates ``remember'' the
past.

Populations and Evolution;Quantitative Methods