Projecting rates of spread for invasive species.

All else being equal, the faster an invading species spreads, the more dangerous its invasion. The projection of spread rate therefore ought to be a central part of the determination of invasion risk. Originally formulated in the 1970s to describe the spatial spread of advantageous alleles, integrodifference equation (IDE) models have since been co-opted by population biologists to describe the spread of populations. More recently, they have been modified to include population structure and environmental variability. We review how IDE models are formulated, how they are parameterized, and how they can be analyzed to project spread rates and the sensitivity of those rates to changes in model parameters. For illustrative purposes, we apply these models to Cytisus scoparius, a large shrub in the legume family that is considered a noxious invasive species in eastern and western North America, Chile, Australia, and New Zealand.