The genetic composition of a naturally developing population is considered as due to mutation, selection, genetic drift and recombination. Selection is modeled as single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). The problem is posed to infer epistatic fitness from population-wide whole-genome data from a time series of a developing population. We generate such data in silico, and show that in the Quasi-Linkage Equilibrium (QLE) phase of Kimura, Neher and Shraiman, that pertains at high enough recombination rates and low enough mutation rates, epistatic fitness can be quantitatively correctly inferred using inverse Ising/Potts methods.
Mounting evidence suggests that natural populations can harbor extensive fitness diversity with numerous genomic loci under selection. It is also known that genealogical trees for populations under selection are quantifiably different from those expected under neutral evolution and described statistically by Kingman's coalescent. While differences in the statistical structure of genealogies have long been used as a test for the presence of selection, the full extent of the information that they contain has not been exploited. Here we shall demonstrate that the shape of the reconstructed geneal…
The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is to sample as many genotypes as possible, measure their fitnesses, and fit a statistical model of the landscape that includes additive and pairwise interactive effects between loci. Here we elucidate the pitfalls of using such regressions, by studying artificial but mathematically convenient fitness landscapes. We identify two sources of bias inherent in thes…
Biological fitness is not an observable quantity and must be inferred from population dynamics. Bayesian inference applied to the Moran process and variants yields a robust inference method that can infer fitness in populations evolving via a Moran dynamic and generalizations. Information about fitness is derived solely from birth-events in birth-death and death-birth processes in which selection acts proportionally to fitness, which allows the method to be applied to populations on a network where the network itself may be changing in time. Populations may also be allowed to change size while…
We consider a population evolving due to mutation, selection and recombination, where selection includes single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). We further consider the problem of inferring fitness in the evolutionary dynamics from one or several snap-shots of the distribution of genotypes in the population. In the recent literature this has been done by applying the Quasi-Linkage Equilibrium (QLE) regime first obtained by Kimura in the limit of high recombination. Here we show that the approach also works in the interesting regime where the effec…
Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait under time-dependent selection, which arises from environmental changes or through fitness interactions with other co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude, which determines the time-dep…
Horizontal gene transfer is an important factor in bacterial evolution that can act across species boundaries. Yet, we know little about rate and genomic targets of cross-lineage gene transfer, and about its effects on the recipient organism's physiology and fitness. Here, we address these questions in a parallel evolution experiment with two Bacillus subtilis lineages of 7% sequence divergence. We observe rapid evolution of hybrid organisms: gene transfer swaps ~12% of the core genome in just 200 generations, and 60% of core genes are replaced in at least one population. By genomics, transcri…
The comparative genomics revolution of the past decade has enabled the discovery of functional elements in the human genome via sequence comparison. While that is so, an important class of elements, those specific to humans, is entirely missed by searching for sequence conservation across species. Here we present an analysis based on variation data among human genomes that utilizes a supervised machine learning approach for the identification of human specific purifying selection in the genome. Using only allele frequency information from the complete low coverage 1000 Genomes Project dataset …
A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and phenotypic variation is driven by the cumulative effects of genetic and environmental variation. The field of quantitative genetics aims to quantify the additive genetic component of this trait variance (i.e. the "heritability"), often with the underlying assumption that trait variance is driven by many loci of infinitesimal effects throughout the genome. This appro…
Locating recombination hotspots in genomic data is an important but difficult task. Current methods frequently rely on estimating complicated models at high computational cost. In this paper we develop an extremely fast, scalable method for inferring recombination hot spots in a population of genomic sequences that is based on the singular value decomposition. Our method performs well in several synthetic data scenarios. We also apply our technique to a real data investigation of the evolution of drug therapy resistance in a population of HIV genomic sequences. Finally, we compare our method b…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution builds on genome evolution in a complicated way, which involves selection, genetic drift, mutations and recombination. Here we develop a coarse-grained evolutionary statistics for phenotypes, which decouples from details of the underlying genotypes. We derive approximate evolution equations for the distribution of phenotype values within and across populations.…
Many microbial populations rapidly adapt to changing environments with multiple variants competing for survival. To quantify such complex evolutionary dynamics in vivo, time resolved and genome wide data including rare variants are essential. We performed whole-genome deep sequencing of HIV-1 populations in 9 untreated patients, with 6-12 longitudinal samples per patient spanning 5-8 years of infection. We show that patterns of minor diversity are reproducible between patients and mirror global HIV-1 diversity, suggesting a universal landscape of fitness costs that control diversity. Reversion…
The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of nonneutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advanc…
In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the population eventually adopts a steady state characterized by mutation-selection-drift balance. Although new alleles continue to be explored through mutation, the statistics of the population, and in particular the probabilities of seeing specific allelic configurations in samples taken from a population, do not change with time. In the absence of selection, proba…
We introduce a system for experimental evolution consisting of populations of short oligonucleotides (Oli populations) evolving in a modified quantitative Polymerase Chain Reaction (qPCR). It is tractable at the genetic, genomic, phenotypic and fitness levels. The Oli system uses DNA hairpins designed to form structures that self-prime under defined conditions. Selection acts on the phenotype of self-priming, after which differences in fitness are amplified and quantified using qPCR. We outline the methodological and bioinformatics tools for the Oli system here, and demonstrate that it can be …
Since its introduction, landscape genomics has developed quickly with the increasing availability of both molecular and topo-climatic data. The current challenges of the field mainly involve processing large numbers of models and disentangling selection from demography. Several methods address the latter, either by estimating a neutral model from population structure or by inferring simultaneously environmental and demographic effects. Here we present Sam$β$ada, an integrated approach to study signatures of local adaptation, providing rapid processing of whole genome data and enabling assessme…
Ultrafast topological data analysis reveals pandemic-scale dynamics of convergent evolution
Heidelberg University（海德堡大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Columbia University（哥伦比亚大学）；Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院）；Centre Inria d’Université Côte d’Azur（蔚蓝海岸大学Inria中心）；TUM Department of Mathematics and Munich Data Science Institute（慕尼黑工业大学数学系与慕尼黑数据科学研究所）；Wellcome Trust Sanger Institute（惠康信托桑格研究所）
Cancer progression is an example of a rapid adaptive process where evolving new traits is essential for survival and requires a high mutation rate. Precancerous cells acquire a few key mutations that drive rapid population growth and carcinogenesis. Cancer genomics demonstrates that these few 'driver' mutations occur alongside thousands of random 'passenger' mutations-a natural consequence of cancer's elevated mutation rate. Some passengers can be deleterious to cancer cells, yet have been largely ignored in cancer research. In population genetics, however, the accumulation of mildly deleterio…
Identifying the complete set of functional elements within the human genome would be a windfall for multiple areas of biological research including medicine, molecular biology, and evolution. Complete knowledge of function would aid in the prioritization of loci when searching for the genetic bases of disease or adaptive phenotypes. Because mutations that disrupt function are disfavored by natural selection, purifying selection leaves a detectable signature within functional elements; accordingly this signal has been exploited through the use of genomic comparisons of distantly related species…
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 dif…
One of the outstanding challenges in comparative genomics is to interpret the evolutionary importance of regulatory variation between species. Rigorous molecular evolution-based methods to infer evidence for natural selection from expression data are at a premium in the field, and to date, phylogenetic approaches have not been well-suited to address the question in the small sets of taxa profiled in standard surveys of gene expression. We have developed a strategy to infer evolutionary histories from expression profiles by analyzing suites of genes of common function. In a manner conceptually …
Defining the extent of epistasis - the non-independence of the effects of mutations - is essential for understanding the relationship of genotype, phenotype, and fitness in biological systems. The applications cover many areas of biological research, including biochemistry, genomics, protein and systems engineering, medicine, and evolutionary biology. However, the quantitative definitions of epistasis vary among fields, and its analysis beyond just pairwise effects remains obscure in general. Here, we show that different definitions of epistasis are versions of a single mathematical formalism …
Maintenance of sexual reproduction and genetic recombination imposes physiological costs when compared to parthenogenic reproduction, most prominently: for maintaining the corresponding (molecular) machinery, for finding a mating partner, and through the decreased fraction of females in a population, which decreases the reproductive capacity. Based on principles from information theory, we have previously developed a new population genetic model, and applying it in simulations, we have recently hypothesized that all species maintain the maximum genomic complexity that is required by their nich…
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 c…
Genome sizes have evolved to vary widely, from 250 bases in viroids to 670 billion bases in amoeba. This remarkable variation in genome size is the outcome of complex interactions between various evolutionary factors such as point mutation rate, population size, insertions and deletions, and genome editing mechanisms that may be specific to certain taxonomic lineages. While comparative genomics analyses have uncovered some of the relationships between these diverse evolutionary factors, we still do not understand what drives genome size evolution. Specifically, it is not clear how primordial m…
The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher-Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each …
