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

Abstract

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 À2 to À1, in distinct contrast to that generated by exponential dispersal, has a fractal structure. As the powerlaw exponent becomes smaller, the distribution of individual genotypes becomes more self-similar at different scales. Common statistics like G ST 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 D 2 is linearly inversely related to the power-law exponent, with a slope of $ À2. 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.

Long distance dispersal and the fate of a gene from the colonization front

“…Thus, the way LDD is taken into account in colonization models is not a trivial choice, as previously demonstrated for demographic aspects of colonization (Shaw, 1995; Kot et al. , 1996; Wingen et al. , 2007).…”

Liberating Lévy walk research from the shackles of optimal foraging

“…As a consequence, local sources of spores dominate disease dynamics when the contact distribution has an exponential tail, and long-distance dispersal dominates when the contact distribution has a heavy tail [83]. The latter can give rise to clustering of new foci of infection and disease beyond the original source [91][92][93][94]. Identifying the functional form of the contact distribution is therefore of considerable practical importance when examining the potential effectiveness of disease management strategies, as these are dependent on an accurate evaluation of 'immigrant' inoculum coming into a managed area [95].…”

Comparable ecological dynamics underlie early cancer invasion and species dispersal, involving self-organizing processes

“…Power-law functions and fractal geometry characterize species dispersal by LDD (Cannas et al, 2006; Wingen et al, 2007), and they reflect the invariance of some property over a range of temporal and spatial scales. There is increasing consensus in that they can be a byproduct of self-organizing processes of populations and communities (Sutherland and Jacobs, 1994; Pascual et al, 2002; Scanlon et al, 2007).…”