The effect of the dispersal kernel on isolation-by-distance in a continuous population
Tara N. Furstenau, Reed A. Cartwright
Comments: 18 pages (main); 4 pages (supp)
Subjects: Populations and Evolution (q-bio.PE)

Under models of isolation-by-distance, population structure is determined by the probability of identity-by-descent between pairs of genes according to the geographic distance between them. Well established analytical results indicate that the relationship between geographical and genetic distance depends mostly on the neighborhood size of the population, $N_b = 4{\pi}{\sigma}^2 D_e$, which represents a standardized measure of dispersal. To test this prediction, we model local dispersal of haploid individuals on a two-dimensional torus using four dispersal kernels: Rayleigh, exponential, half-normal and triangular. When neighborhood size is held constant, the distributions produce similar patterns of isolation-by-distance, confirming predictions. Considering this, we propose that the triangular distribution is the appropriate null distribution for isolation-by-distance studies. Under the triangular distribution, dispersal is uniform within an area of $4{\pi}{\sigma}^2$ (i.e. the neighborhood area), which suggests that the common description of neighborhood size as a measure of a local panmictic population is valid for popular families of dispersal distributions. We further show how to draw from the triangular distribution efficiently and argue that it should be utilized in other studies in which computational efficiency is important

Limits to adaptation along environmental gradients
Jitka Polechová, Nick Barton
doi: http://dx.doi.org/10.1101/012690

Why do species not adapt to ever-wider ranges of conditions, gradually expanding their ecological niche? Theories of niche evolution typically omit spatial context, yet all species experience spatially variable conditions. Gene flow across environments has two conflicting effects on adaptation: while it increases genetic variation, which is a prerequisite for adaptation, gene flow may swamp adaptation to local conditions. We show that genetic drift can generate a sharp margin to a species’ range, by reducing genetic variance below the level needed for adaptation to spatially variable conditions. Dimensional arguments and separation of ecological and evolutionary time scales reveal a simple threshold that predicts when adaptation at the range margin fails. Two observable parameters describe the threshold: i) the effective environmental gradient, which can be measured by the loss of fitness due to dispersal to a different environment, and ii) the efficacy of selection relative to genetic drift. The theory predicts sharp range margins even in the absence of abrupt changes in the environment. Furthermore, it implies that gradual worsening of conditions across a species’ habitat may suddenly lead to range fragmentation – as adaptation to a wide span of conditions within a single species becomes impossible.

The competition between simple and complex evolutionary trajectories in asexual populations
Ian E. Ochs, Michael M. Desai
Comments: 8 pages, 3 figures
Subjects: Populations and Evolution (q-bio.PE)

On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial “uphill” mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the evolutionary process determine the probability that evolution will take any specific path among a variety of competing possible trajectories. Understanding this evolutionary choice is essential if we are to understand the outcomes and predictability of adaptation on rugged landscapes. We present a simple model to analyze the probability that evolution will eschew immediately uphill paths in favor of crossing fitness valleys or plateaus that lead to higher fitness but less accessible genotypes. We calculate how this probability depends on the population size, mutation rates, and relevant selection pressures, and compare our analytical results to Wright-Fisher simulations. We find that the probability of valley crossing depends nonmonotonically on population size: intermediate size populations are most likely to follow a “greedy” strategy of acquiring immediately beneficial mutations even if they lead to evolutionary dead ends, while larger and smaller populations are more likely to cross fitness valleys to reach distant advantageous genotypes. We explicitly identify the boundaries between these different regimes in terms of the relevant evolutionary parameters. Above a certain threshold population size, we show that the degree of evolutionary “foresight” depends only on a single simple combination of the relevant parameters.