  Models of invasive species spread often assume that landscapes are spatially
homogeneous; thus simplifying analysis but potentially reducing accuracy. We
extend a recently developed partial differential equation model for invasive
conifer spread to account for spatial heterogeneity in parameter values and
introduce a method to obtain key outputs (e.g. spread rates) from computational
simulations. Simulations produce patterns of spatial spread remarkably similar
to observed patterns in grassland ecosystems invaded by exotic conifers,
validating our spatially explicit strategy. We find that incorporating spatial
variation in different parameters does not significantly affect the evolution
of invasions (which are characterised by a long quiescent period followed by
rapid evolution towards to a constant rate of invasion) but that distributional
assumptions can have a significant impact on the spread rate of invasions. Our
work demonstrates that spatial variation in site-suitability or other
parameters can have a significant impact on invasions
