Coalescence and genetic diversity in sexual populations under selection

Abstract

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, ξ b , 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 compared with 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.Hill-Robertson interference | genealogy | Bolthausen-Sznitman coalescent I n asexual populations, different genomes compete for survival, and the fate of most new mutations depends more on the total fitness of the genome they reside in than on their own contribution to fitness. As a result, beneficial mutations on one genetic background can be lost to competition with other backgrounds, an effect known as "clonal interference" (1-3); likewise, deleterious mutations in very fit genomes can fix. This interference is reduced by recombination and disappears when recombination is rapid enough such that selection can act independently on different loci. Many eukaryotes recombine their genetic material by crossing-over of homologous chromosomes. As a result, distant loci evolve independently but nearby tightly linked loci remain coupled. Such interference, known as Hill-Robertson interference, reduces the efficacy of selection (4, 5) and reduces levels of neutral variation. Neutral diversity is indeed correlated with local recombination rates in several species, suggesting that linked selection is an important evolutionary force (6, 7). One typically distinguishes background selection against deleterious mutations (8, 9) from sweeping beneficial mutations, which lead to hitchhiking (10, 11). Both of these processes reduce diversity at linked loci and probably contribute to the observed correlation (12). Another piece of evidence for the importance of linked selection comes from the weak correlation between levels of genetic diversity and the population size (13). Whereas classic neutral models predict that diversity should increase linearly with the population size (14), in models dominated ...

The Rate of Adaptation in Large Sexual Populations with Linear Chromosomes

“…In the opposite case, m b . 1, in which individual mutations are only weakly selected, Neher et al (2013a) follow a very similar approach to find a result analogous to Equation 1, with r 3 s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m b =log½g ffiffiffiffiffi ffi m b p q in our notation. (In this regime, the chunk asexual traveling waves are described by Cohen et al 2005a andHallatschek 2011 rather than by Rouzine et al 2008.…”

“…The dependence of the rate of adaptation on the rate of recombination is much weaker than the nearly linear relation found in our model. We have already discussed the connections between our analysis and the closely related work by Weissman and Barton (2012) and Neher et al (2013a), who examine the same question in the parameter regimes m b & 1/(Ns) and m b . 1, respectively.…”

“…In this article, we analyze adaptation under strong interference in such populations with large ranges of recombination fractions among loci, focusing on populations in which crossovers occur more frequently than beneficial mutations. Recently, Neher et al (2013a) …”

“…It is useful to consider the rate of beneficial mutation per unit map length, Table 1 for definitions of symbols.) We focus on the case in which beneficial mutations are infrequent relative to recombination (m b , 1); Neher et al (2013a) consider the opposite case. …”

Fighting the good cause: meaning, purpose, difference, and choice

“…As recombination between sites lessens, and as the strength of epistatic selection increases, a point is reached at which different sites can no longer be considered as belonging to different evolutionary genes (cf. Neher et al 2013). For sites sufficiently close together, non---additive interactions on the axis of expression contribute to an additive effect on the axis of transmission (Neher and Shraiman 2009;Haig 2011a).…”