Density behavior of spatial birth-and-death stochastic evolution of mutating genotypes under selection rates
Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy, Stanislav Molchanov, Elena Zhizhina
(Submitted on 5 Jun 2013)

We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which corresponds to a selection effect. We study an asymptotic behavior of a density for an infinite collection of genotypes. The cases of space homogeneous and space heterogeneous densities are considered.

Coalescence, genetic diversity and adaptation in sexual populations
Richard A. Neher, Taylor A. Kessinger, Boris I. Shraiman
(Submitted on 5 Jun 2013)

In diverse sexual populations, selection operates neither on the whole genome — which is repeatedly taken apart and reassembled by recombination — nor on individual alleles which are tightly linked to the chromosomal neighborhood. Those tightly linked alleles affect each others dynamics which reduces the efficiency of selection and distorts patterns of genetic diversity. Inference of evolutionary history from diversity shaped by linked selection requires an understanding of these patterns. Here, we reexamine this problem in the light of recent progress in coalescent theory of rapidly adapting asexual populations. We present a simple but powerful scaling analysis identifying the unit of selection as the genomic “linkage block” with characteristic length \xi_b, which is determined in a self-consistent manner by the condition that the rate of recombination within the block is comparable to the fitness differences between different alleles of the block. We find that an asexual model with strength of selection tuned to that of the linkage block provides an excellent description of genetic diversity and the site frequency spectra when compared to computer simulations of population dynamics. This correspondence holds for the entire spectrum of strength of selection. When fitness differentials arise from the collective contribution of numerous weakly selected polymorphisms, the rate of adaptation increases as the square root of the recombination rate. Linkage block approximation thus provides a simple but powerful tool for understanding interference and collective behavior of dense weakly selected loci.

Interference limits resolution of selection pressures from linked neutral diversity
Benjamin H. Good, Aleksandra M. Walczak, Richard A. Neher, Michael M. Desai
(Submitted on 5 Jun 2013)

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a “linkage block”). We exploit this insensitivity in a new “coarse-grained” coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations with the same variance in fitness. This approximation generates accurate and efficient predictions for the genetic diversity that cannot be summarized by a simple reduction in effective population size. However, these results suggest a fundamental limit on our ability to resolve individual selection pressures from contemporary sequence data alone, since a wide range of parameters yield nearly identical patterns of sequence variability.

The Dynamics of Genetic Draft in Rapidly Adapting Populations
Katya Kosheleva, Michael Desai
(Submitted on 30 May 2013)

The accumulation of beneficial mutations on many competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the frequencies of observed mutations, randomizes the fixation times of successful mutations, and leaves distinct signatures on patterns of genetic variation. Here, we show how this form of `genetic draft’ affects the forward-time dynamics of site frequencies in rapidly adapting asexual populations. We calculate the probability that mutations at individual sites shift in frequency over a characteristic timescale, extending Gillespie’s original model of draft to the case where many strongly selected beneficial mutations segregate simultaneously. We then derive the sojourn time of mutant alleles, the expected fixation time of successful mutants, and the site frequency spectrum of beneficial and neutral mutations. We show how this form of draft affects inferences in the McDonald-Kreitman test, and how it relates to recent observations that some aspects of genetic diversity are described by the Bolthausen-Sznitman coalescent in the limit of very rapid adaptation. Finally, we describe how our method can be extended to model evolution on fitness landscapes that include some forms of epistasis, such as landscapes that are partitioned into two or more incompatible evolutionary trajectories.