Estimating population spread: What can we forecast and how well?

Recent literature on plant population spread advocates quantification of long-distance dispersal (LDD). These estimates could provide insights into rates of migration in response to climate change and rates of alien invasions. LDD information is not available for parameterization of current models because it is hard to obtain. We combine a new stochastic model with a flexible framework that permits assimilation of evidence that might be derived from a range of sources. Results are consistent with the prediction of traditional diffusion that population spread has a finite asymptotic velocity. Unlike traditional diffusion, spread is not well described by the mean; it is erratic. In contrast with deterministic models, our results show that inherent uncertainty, rather than parameter sensitivity, thwarts informative forecasts of spread velocity. Analysis shows that, because LDD is inherently unpredictable, even full knowledge of LDD parameters might not provide informative estimates of velocity for populations characterized by LDD. Although predictive distributions are too broad to provide precise estimates of spread rate, they are valuable for comparing spread potential among species and for identifying potential for invasion. Using combinations of dispersal data and the estimates provided by dispersal biologists that derive from multiple sources, the model predicts spread rates that are much slower than those from traditional (deterministic) fat-tailed models and from simulation models of spread, but for different reasons. Deterministic fat-tailed models overestimate spread rate, because they assume that fractions of individuals can rapidly occupy distant sites. Stochastic models recognize that distant colonization is limited to discrete individuals. Stochastic simulations of plant migration overestimate migration of trees, because they typically assume values of R-0 that are too large.