Effect of selection on ancestry: An exactly soluble case and its phenomenological generalization

Brunet, Éric; Derrida, Bernard; Mueller, Dieter; Munier, S.

doi:10.1103/physreve.76.041104

Cited by 137 publications

(281 citation statements)

References 50 publications

(133 reference statements)

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“…This result is consistent with the time constant for coalescence in the wave tip obtained by a phenomenological approach (Brunet et al 2007). …”

Section: Invasion Wavessupporting

confidence: 81%

“…Interestingly, we find that while the longest relaxation time t 0 increases linearly with wave speed, the next higher relaxation time approaches a constant value, t 1 D 1=3 : The timescale separation t 0 t n for vD 22=3 1 can be used to derive a very general approximation for the timescale for the decay of genetic diversity (Appendix B), t 0 hw 2 ci 21 ; which is also shown in Figure 5. Moreover, we hypothesize that this timescale separation could be relevant for the question of why the Bolthausen-Sznitman coalescent is found in many models of adaptation and invasion waves of the Fisher-Kolmogorov type (Brunet et al 2007;Desai et al 2013;Neher and Hallatschek 2013). Details of the relaxation spectrum of our model, including the form of the eigenfunctions and the timescale separation, can be understood from an analogy to the physical problem of a (quantum) particle trapped in a potential well, as we describe in Appendix B.…”

Section: Fluctuations In Dynamics Of Adaptation 1209mentioning

confidence: 99%

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Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

Hallatschek

Geyrhofer

2016

Genetics

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The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuationinduced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated ("pulled") waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.KEYWORDS traveling-wave models; asexual adaptation; Fisher waves; tuned models; stochastic modeling; higher-order correlation functions; exact approaches M ANY important evolutionary and ecological processes rely on the behavior of a small number of individuals that have a large dynamical influence on the population as a whole. This is, perhaps, most obvious in the case of biological adaptation in asexual species, such as microbes (over timescales where horizontal gene transfer is irrelevant). Future generations descend from a small number of currently welladapted individuals. The genetic footprint of the large majority of the population is wiped out over time by the fixation of more fit genotypes. For a large influx of beneficial mutations, these dynamics can be visualized as a traveling wave in fitness space; see Figure 1A. At any time, the currently most fit "pioneer" individuals reside in the small tip of the wave. As time elapses, the wave moves toward higher fitness and the formerly rare most fit individuals dominate the population. By that time, however, a new wave tip of even more fit mutants has formed by mutations and the cycle of transient dominance continues. Evolu...

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“…This result is consistent with the time constant for coalescence in the wave tip obtained by a phenomenological approach (Brunet et al 2007). …”

Section: Invasion Wavessupporting

confidence: 81%

Section: Fluctuations In Dynamics Of Adaptation 1209mentioning

confidence: 99%

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

Hallatschek

Geyrhofer

2016

Genetics

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“…As Nσ increases, coalescence is more and more driven by the amplification of fit genomes, which generates a very skewed offspring number distribution over time scales of order σ −1 . As a result, the genealogies resemble the Bolthausen-Sznitman coalescent (BSC) (25,29) with very different statistical properties. Two representative coalescent trees sampled from asexual populations, one neutral and one rapidly adapting, are shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…We build on recent progress in our understanding of genealogies in adapting asexual populations (23)(24)(25), and we will first review these results briefly.…”

mentioning

confidence: 99%

Coalescence and genetic diversity in sexual populations under selection

Neher

Kessinger

Shraiman

2013

Proc. Natl. Acad. Sci. U.S.A.

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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 ...

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“…Kingman's coalescent (KC) allows only pairwise mergers-at most two ancestral lines can merge at each coalescence event-and the branches of the coalescent tree are distributed evenly (Kingman 1982). In spatially expanding or panmictic adapting populations, multiple mergers of ancestral lines occurring at a single step are not rare in the genealogical trees, and (Brunet et al 2007) showed that a special case of the multiple-merger coalescent, the Bolthausen-Sznitman coalescent (BSC) (Bolthausen and Sznitman 1998), describes their genealogies. More recently, (Desai et al 2013) and (Neher and Hallatschek 2013) showed that, in rapidly adapting populations, exponential amplification of fit lineages leads to multiple mergers, and the resulting genealogies are well described by the BSC.…”

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confidence: 99%

Correlated Mutations and Homologous Recombination Within Bacterial Populations

Lin

Kussell

2017

Genetics

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Inferring the rate of homologous recombination within a bacterial population remains a key challenge in quantifying the basic parameters of bacterial evolution. Due to the high sequence similarity within a clonal population, and unique aspects of bacterial DNA transfer processes, detecting recombination events based on phylogenetic reconstruction is often difficult, and estimating recombination rates using coalescent model-based methods is computationally expensive, and often infeasible for large sequencing data sets. Here, we present an efficient solution by introducing a set of mutational correlation functions computed using pairwise sequence comparison, which characterize various facets of bacterial recombination. We provide analytical expressions for these functions, which precisely recapitulate simulation results of neutral and adapting populations under different coalescent models. We used these to fit correlation functions measured at synonymous substitutions using whole-genome data on Escherichia coli and Streptococcus pneumoniae populations. We calculated and corrected for the effect of sample selection bias, i.e., the uneven sampling of individuals from natural microbial populations that exists in most datasets. Our method is fast and efficient, and does not employ phylogenetic inference or other computationally intensive numerics. By simply fitting analytical forms to measurements from sequence data, we show that recombination rates can be inferred, and the relative ages of different samples can be estimated. Our approach, which is based on population genetic modeling, is broadly applicable to a wide variety of data, and its computational efficiency makes it particularly attractive for use in the analysis of large sequencing datasets.KEYWORDS bacteria; homologous recombination; population diversity; sample selection bias; sample ages; adapting populations; Bolthausen-Sznitman coalescent B ACTERIA can receive DNA fragments from their environment by different mechanisms, and integrate them into their genome in a set of processes collectively known as horizontal gene transfer (HGT) (Thomas and Nielsen 2005). While the importance of HGT in bacterial evolution is increasingly appreciated (Koonin and Wolf 2008;Shapiro et al. 2012;Oren et al. 2014;Ravenhall et al. 2015;Rosen et al. 2015), quantifying its impact across bacterial genomes, and in diverse environmental samples, remains a key challenge (Maynard Smith 1991;Soucy et al. 2015). In particular, a prevalent form of HGT involves homologous recombination of fragments that bear a high degree of sequence similarity to the recipient genome (Andam and Gogarten 2011;Williams et al. 2012). Such transfer events are particularly difficult to detect, since they leave no obvious marks, and are indistinguishable based on nucleotide composition, yet they are likely to represent the majority of HGT events in bacteria (Fraser et al. 2007).Three major mechanisms of HGT-transformation, conjugation, and transduction-mediate the passage of external DNA into bacte...

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Effect of selection on ancestry: An exactly soluble case and its phenomenological generalization

Cited by 137 publications

References 50 publications

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

Coalescence and genetic diversity in sexual populations under selection

Correlated Mutations and Homologous Recombination Within Bacterial Populations

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