Realistic models for biological invasion

Almost half a century ago Charles Elton (1958) warned of the increasing frequency of foreign species introduction, and of the inevitable biological dislocations that follow. Today, the number and type of invading organisms is growing --- understanding and monitoring the process of alien species spread is an important applied ecological problem. A key element of this process is prediction of spread rate for the invader. It was thought for many years that this issue of spread rate was essentially resolved by analysis of an equation derived by Fisher (1937) for invading genotypes. It is now clear that the Fisher spread model does not hold for many relevant biological situations. In particular, the model tacitly ignores rare, long distance dispersal events that initiate secondary invasion foci, far ahead of the bulk of invasion. These events can be shown to drive the invasion process at much higher speeds than previously thought, speeds which may continue to increase as the invasion progresses. The resulting spatial pattern of spread is patchy, with the patches linked historically via long-distance dispersal.

In my talk I will discuss these and other issues related to the effects of environmental variability on spread rates. I will propose a nonparametric method for estimating spread rate which makes no assumptions about the underlying distribution of dispersal distances, and will discuss the role of mathematical models in explaining dynamics of several well-studied biological invasions, including the house finch in eastern North America, and the historical spread of trees in response to climate change.