Plant propagation fronts and wind dispersal: an analytical model to upscale from seconds to decades using superstatistics.

Scale separation crossing many orders of magnitude is a consistent challenge in the ecological sciences. Wind dispersal of seed that generates plant propagation fronts is a typical case where timescales range from less than a second for fast turbulent processes to interannual timescales governing plant growth and climatic forcing. We show that the scale separation can be overcome by developing mechanistic and statistical links between processes at the different timescales. A mechanistic model is used to scale up from the turbulent regime to hourly timescales, while a superstatistical approach is used to relate the half-hourly timescales to annual vegetation migration speeds. We derive a semianalytical model to predict vegetation front movement as a function of wind-forcing statistics and characteristics of the species being dispersed. This model achieves better than order-of-magnitude agreement in a case study of tree dispersal from the early Holocene, a marked improvement over diffusion models. Plant migration is shown to depend nonlinearly on the wind environment forcing the movement but linearly on most physiological parameters. Applications of these analytical results to parameterizing models of plant dispersion and the implications of the superstatistical approach for addressing other ecological problems plagued by similar "dimensionality curses" are outlined.