Neutral evolution in the presence of long-range dispersal

Stochastic effects have an outsize influence on the genetics of range
expansions. Individuals that, by chance, end up at the edge of an expanding
population can take over a significant fraction of the population even if they
do not harbour advantageous mutations. Whereas the evolutionary consequences of
these rare events have been studied extensively for populations that advance
diffusively, they are still poorly understood in situations where genetic
information spreads through long-range dispersal events as is ubiquitous in
plants, animals, and pathogens riding on humans. Using simulations,
we investigate the evolution of neutral standing variation as a population
expands spatially via long-distance jumps, whose probability falls off as a
power law with distance. Strikingly, we find that the diversity at long times is
non-monotonic in the exponent characterizing the steepness of the jump
distribution: diversity is partially preserved for very steep (effectively
short-ranged) distributions, lost completely for distributions of intermediate breadth,
and maintained almost perfectly for extremely broad jump distributions. These
results are explained by a recently-developed iterative scaling theory for the
spread of the core population through rare jumps.