Isolation by distance in populations with power-law dispersal

Limited dispersal of individuals between generations results in isolation by distance, in which individuals further apart in space tend to be less related. Classic models of isolation by distance assume that dispersal distances are drawn from a thin-tailed distribution and predict that the proportion of the genome that is identical by descent between a pair of individuals should decrease exponentially with the spatial separation between them. However, in many natural populations, individuals occasionally disperse over very long distances. In this work, we use mathematical analysis and coalescent simulations to study the effect of long-range (power-law) dispersal on patterns of isolation by distance. We find that it leads to power-law decay of identity-by-descent at large distances with the same exponent as dispersal. We also find that broad power-law dispersal produces another, shallow power-law decay of identity-by-descent at short distances. These results suggest that the distribution of long-range dispersal events could be estimated from sequencing large population samples taken from a wide range of spatial scales.

Automated summary

Limited dispersal results in isolation by distance, with individuals further apart being less related. Classic models assume thin-tailed dispersal distances and predict exponential decay of identity-by-descent with spatial separation. However, long-range dispersal leads to power-law decay at large distances, with the same exponent as dispersal. Broad power-law dispersal also produces shallow power-law decay at short distances, and the distribution of long-range dispersal events could be estimated from sequencing large population samples.