Models of spatial spread: A synthesis Original Research Article

I review models describing the dynamics of range expansion (spatial spread) of invading organisms, emphasizing two apparently robust results. First, there appears to be a linear rate of spread with time, and second, this rate is proportional to the per capita growth rate of the population when the invading species is rare. Both results hold for a variety of single-species and two-species models. I then present two models, one stochastic, and one with an Allee effect, that demonstrate that the constant linear rate of spread may only hold after an initial period of slower spread. Finally, I emphasize that the dependence of the rate of spread on the per capita growth rate need only hold when this is maximized when the species is rare. This last observation may have important implications for understanding the rate of spread for precisely those species which are likely to cause the most disruption to the communities they invade.