Long-distance dispersal (LDD) plays an important role in many population processes like colonization, range expansion, and epidemics. LDD of small particles like fungal spores is often a result of turbulent wind dispersal and is best described by functions with power-law behavior in the tails (“fat tailed”). The influence of fat-tailed LDD on population genetic structure is reported in this article. In computer simulations, the population structure generated by power-law dispersal with exponents in the range of −2 to −1, in distinct contrast to that generated by exponential dispersal, has a fractal structure. As the power-law exponent becomes smaller, the distribution of individual genotypes becomes more self-similar at different scales. Common statistics like GST are not well suited to summarizing differences between the population genetic structures. Instead, fractal and self-similarity statistics demonstrated differences in structure arising from fat-tailed and exponential dispersal. When dispersal is fat tailed, a log–log plot of the Simpson index against distance between subpopulations has an approximately constant gradient over a large range of spatial scales. The fractal dimension D2 is linearly inversely related to the power-law exponent, with a slope of ∼ −2. In a large simulation arena, fat-tailed LDD allows colonization of the entire space by all genotypes whereas exponentially bounded dispersal eventually confines all descendants of a single clonal lineage to a relatively small area.
