Limited dispersal results in isolation by distance in spatially structured populations, in which individuals found further apart tend to be less related to each other. Models of populations undergoing short-range dispersal predict a close relation between the distance individuals disperse and the length scale over which two sampled individuals are likely to be closely related. In this work, we study the effect of long jumps on patterns of isolation by distance by replacing the typical short-range dispersal kernel with a long-range, power-law kernel. We find that incorporating long jumps leads to a slower decay of relatedness with distance, and that the quantitative form of this slow decay contains visible signatures of the underlying dispersal process. K 1 (y|t) = 1 2π ∞ −∞ dk exp (−iky − D α t|k| α ) .(1)