Genetic draft, selective interference, and population genetics of rapid adaptation

To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if positive selection operates on many loci simultaneously, as has recently been suggested for many species including animals such as flies, a different approach is necessary. In this review, I discuss recent progress in characterizing and understanding evolution in rapidly adapting populations where random associations of mutations with genetic backgrounds of different fitness, i.e., genetic draft, dominate over genetic drift. As a result, neutral genetic diversity depends weakly on population size, but strongly on the rate of adaptation or more generally the variance in fitness. Coalescent processes with multiple mergers, rather than Kingman's coalescent, are appropriate genealogical models for rapidly adapting populations with important implications for population genetic inference.Comment: supplementary illustrations and scripts are available at http://webdav.tuebingen.mpg.de/interference

FFPopSim: An efficient forward simulation package for the evolution of large populations

The analysis of the evolutionary dynamics of a population with many polymorphic loci is challenging since a large number of possible genotypes needs to be tracked. In the absence of analytical solutions, forward computer simulations are an important tool in multi-locus population genetics. The run time of standard algorithms to simulate sexual populations increases as 8^L with the number L of loci, or with the square of the population size N. We have developed algorithms that allow to simulate large populations with a run-time that scales as 3^L. The algorithm is based on an analog of the Fast-Fourier Transform (FFT) and allows for arbitrary fitness functions (i.e. any epistasis) and genetic maps. The algorithm is implemented as a collection of C++ classes and a Python interface.Comment: available from: http://code.google.com/p/ffpopsi

Competition between recombination and epistasis can cause a transition from allele to genotype selection

Biochemical and regulatory interactions central to biological networks are expected to cause extensive genetic interactions or epistasis affecting the heritability of complex traits and the distribution of genotypes in populations. However, the inference of epistasis from the observed phenotype-genotype correlation is impeded by statistical difficulties, while the theoretical understanding of the effects of epistasis remains limited, in turn limiting our ability to interpret data. Of particular interest is the biologically relevant situation of numerous interacting genetic loci with small individual contributions to fitness. Here, we present a computational model of selection dynamics involving many epistatic loci in a recombining population. We demonstrate that a large number of polymorphic interacting loci can, despite frequent recombination, exhibit cooperative behavior that locks alleles into favorable genotypes leading to a population consisting of a set of competing clones. When the recombination rate exceeds a certain critical value that depends on the strength of epistasis, this "genotype selection" regime disappears in an abrupt transition, giving way to "allele selection"-the regime where different loci are only weakly correlated as expected in sexually reproducing populations. We show that large populations attain highest fitness at a recombination rate just below critical. Clustering of interacting sets of genes on a chromosome leads to the emergence of an intermediate regime, where blocks of cooperating alleles lock into genetic modules. These haplotype blocks disappear in a second transition to pure allele selection. Our results demonstrate that the collective effect of many weak epistatic interactions can have dramatic effects on the population structure.Comment: Supplementary Material available on PNAS websit

Inferring HIV escape rates from multi-locus genotype data

Cytotoxic T-lymphocytes (CTLs) recognize viral protein fragments displayed by major histocompatibility complex (MHC) molecules on the surface of virally infected cells and generate an anti-viral response that can kill the infected cells. Virus variants whose protein fragments are not efficiently presented on infected cells or whose fragments are presented but not recognized by CTLs therefore have a competitive advantage and spread rapidly through the population. We present a method that allows a more robust estimation of these escape rates from serially sampled sequence data. The proposed method accounts for competition between multiple escapes by explicitly modeling the accumulation of escape mutations and the stochastic effects of rare multiple mutants. Applying our method to serially sampled HIV sequence data, we estimate rates of HIV escape that are substantially larger than those previously reported. The method can be extended to complex escapes that require compensatory mutations. We expect our method to be applicable in other contexts such as cancer evolution where time series data is also available

Coalescence, genetic diversity in sexual populations under selection

In sexual populations, selection operates neither on the whole genome, which is repeatedly taken apart and reassembled by recombination, nor on individual alleles that are tightly linked to the chromosomal neighborhood. The resulting interference between linked alleles 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 present a simple but powerful scaling analysis identifying the unit of selection as the genomic "linkage block" with a characteristic length 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 the 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. This linkage block approximation is accurate for the entire spectrum of strength of selection and is particularly powerful in scenarios with many weakly selected loci. The latter limit allows us to characterize coalescence, genetic diversity, and the speed of adaptation in the infinitesimal model of quantitative genetics

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex