Reid's paradox describes the fact that classical models cannot account for the rapid (10(2)-10(3) m yr-1) spread of trees at the end of the Pleistocene. I use field estimates of seed dispersal with an integrodifference equation and simulation models of population growth to show that dispersal data are compatible with rapid spread. Dispersal estimates lay to rest the possibility that rapid spread occurred by diffusion. The integrodifference model predicts that, if the seed shadow has a long 'fat' tail, then rapid spread is possible, despite short average dispersal distances. It further predicts that velocity is more sensitive to life history than is classical diffusion. Application of such models is frustrated because the tail of the seed shadow cannot be fitted to data. However, the data can be used to test a 'long-distance' hypothesis against alternative ('local') models of dispersal using Akaike's Information Criterion and likelihood ratio tests. Tests show that data are consistent with >10% of seed dispersed as a long (10(2) m) fat-tailed kernel. Models based on such kernels predict spread as rapid as that inferred from the pollen record. If fat-tailed dispersal explains these rapid rates, then it is surprising not to see large differences in velocities among taxa with contrasting life histories. The inference of rapid spread, together with lack of obvious life-history effects, suggests velocities may have not reached their potentials, being stalled by rates of climate change, geography, or both.