Originally published as Genetics Published Articles Ahead of Print on July 29, 2007.

Genetics, Vol. 177, 435-448, September 2007, Copyright © 2007
doi:10.1534/genetics.107.077206

The Population Genetic Structure of Clonal Organisms Generated by Exponentially Bounded and Fat-Tailed Dispersal

Luzie U. Wingen*,1, James K. M. Brown* and Michael W. Shaw{dagger}

* Department of Disease and Stress Biology, John Innes Centre, Norwich NR4 7UH, United Kingdom and {dagger} School of Biological Sciences, University of Reading, Reading RG7 6AS, United Kingdom

1 Corresponding author: Department of Disease and Stress Biology, John Innes Centre, Colney, Norwich NR4 7UH, United Kingdom.
E-mail: luzie.wingen{at}bbsrc.ac.uk

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.