Whether plants can migrate fast enough to track climate change depends on dispersal. Seed rain data collected in forest understories indicate that seed shadows for most species possess `fat tails' describing rare, long-distance dispersal events. Simple diffusion models do a poor job of describing migration rates when these long-distance dispersal events dominate. Models based on spatial dispersal kernels do a better job, but predicted rates are not robust to small changes in the parametric form of the kernel.
I will discuss a non-parametric estimator for migration rates which is based on discrete seed rain data. It is possible to construct confidence intervals for the estimated migration speed---a new development in the context of invasion theory. If time permits I will discuss a version of the model which incorporates stochastic spatial interactions.