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Genome-wide association studies have revealed that the genetic architectures of complex traits vary widely, including in terms of the numbers, effect sizes, and allele frequencies of significant hits. However, at present we lack a principled way of understanding the similarities and differences among traits. Here, we describe a probabilistic model that combines mutation, drift, and stabilizing selection at individual sites with a genome-scale model of phenotypic variation. In this model, the architecture of a trait arises from the distribution of selection coefficients of mutations and from two scaling parameters. We fit this model for 95 diverse, highly polygenic quantitative traits from the UK Biobank. Notably, we infer similar distributions of selection coefficients across all these traits. This shared distribution implies that differences in architectures of highly polygenic traits arise mainly from the two scaling parameters: the mutational target size and heritability per site, which vary by orders of magnitude across traits. When these two scale factors are accounted for, the architectures of all 95 traits are nearly identical.

In many species, meiotic recombination events tend to occur in narrow intervals of the genome, known as hotspots. In humans and mice, double strand break (DSB) hotspot locations are determined by the DNA-binding specificity of the zinc finger array of the PRDM9 protein, which is rapidly evolving at residues in contact with DNA. Previous models explained this rapid evolution in terms of the need to restore PRDM9 binding sites lost to gene conversion over time, under the assumption that more PRDM9 binding always leads to more DSBs. In recent experimental work, however, it has become apparent that PRDM9 binding on both homologs facilitates DSB repair, and moreover that, in the absence of enough symmetric binding, meiosis no longer progresses reliably. We therefore consider the possibility that the benefit of PRDM9 stems from its role in coupling DSB formation and efficient repair. To this end, we model the evolution of PRDM9 from first principles: from its binding dynamics to the population processes that govern the evolution of the zinc finger array and its binding sites in the genome. As we show, the loss of a small number of strong binding sites leads to the use of a greater number of weaker ones, resulting in a sharp reduction in symmetric binding and favoring new PRDM9 alleles that restore the use of a smaller set of strong binding sites. This decrease in PRDM9 binding symmetry and in its ability to promote DSB repair drive the rapid zinc finger turnover. These results imply that the advantage of new PRDM9 alleles is in limiting the number of binding sites used effectively, rather than in increasing net PRDM9 binding, as previously believed. By extension, our model suggests that the evolutionary advantage of hotspots may have been to increase the efficiency of DSB repair and/or homolog pairing.

Polygenic adaptation is thought to be ubiquitous, yet remains poorly understood. Here, we model this process analytically, in the plausible setting of a highly polygenic, quantitative trait that experiences a sudden shift in the fitness optimum. We show how the mean phenotype changes over time, depending on the effect sizes of loci that contribute to variance in the trait, and characterize the allele dynamics at these loci. Notably, we describe the two phases of the allele dynamics: The first is a rapid phase, in which directional selection introduces small frequency differences between alleles whose effects are aligned with or opposed to the shift, ultimately leading to small differences in their probability of fixation during a second, longer phase, governed by stabilizing selection. As we discuss, key results should hold in more general settings and have important implications for efforts to identify the genetic basis of adaptation in humans and other species.

Mutation rates and spectra differ among human populations. Here, we examine whether this variation could be explained by evolution at mutation modifiers. To this end, we consider genetic modifier sites at which mutations, “mutator alleles”, increase genome-wide mutation rates and model their evolution under purifying selection due to the additional deleterious mutations that they cause, genetic drift, and demographic processes. We solve the model analytically for a constant population size and characterize how evolution at modifier sites impacts variation in mutation rates within and among populations. We then use simulations to study the effects of modifier sites under a plausible demographic model for Africans and Europeans. When comparing populations that evolve independently, weakly selected modifier sites (2Nes ≈ 1), which evolve slowly, contribute the most to variation in mutation rates. In contrast, when populations recently split from a common ancestral population, strongly selected modifier sites (2Nes ≫ 1), which evolve rapidly, contribute the most to variation between them. Moreover, a modest number of modifier sites (e.g., 10 per mutation type in the standard classification into 96 types) subject to moderate to strong selection (2Nes > 1) could account for the variation in mutation rates observed among human populations. If such modifier sites indeed underlie differences among populations, they should also cause variation in mutation rates within populations and their effects should be detectable in pedigree studies.

Analyses of genetic variation in many taxa have established that neutral genetic diversity is shaped by natural selection at linked sites. Whether the mode of selection is primarily the fixation of strongly beneficial alleles (selective sweeps) or purifying selection on deleterious mutations (background selection) remains unknown, however. We address this question in humans by fitting a model of the joint effects of selective sweeps and background selection to autosomal polymorphism data from the 1000 Genomes Project. After controlling for variation in mutation rates along the genome, a model of background selection alone explains ∼60% of the variance in diversity levels at the megabase scale. Adding the effects of selective sweeps driven by adaptive substitutions to the model does not improve the fit, and when both modes of selection are considered jointly, selective sweeps are estimated to have had little or no effect on linked neutral diversity. The regions under purifying selection are best predicted by phylogenetic conservation, with ∼80% of the deleterious mutations affecting neutral diversity occurring in non-exonic regions. Thus, background selection is the dominant mode of linked selection in humans, with marked effects on diversity levels throughout autosomes.

In human populations, the relative levels of neutral diversity on the X and autosomes differ markedly from each other and from the naive theoretical expectation of 3/4. Here we propose an explanation for these differences based on new theory about the effects of sex-specific life history and given pedigree-based estimates of the dependence of human mutation rates on sex and age. We demonstrate that life history effects, particularly longer generation times in males than in females, are expected to have had multiple effects on human X-to-autosome (X:A) diversity ratios, as a result of male-biased mutation rates, the equilibrium X:A ratio of effective population sizes, and the differential responses to changes in population size. We also show that the standard approach of using divergence between species to correct for male mutation bias results in biased estimates of X:A effective population size ratios. We obtain alternative estimates using pedigree-based estimates of the male mutation bias, which reveal that X:A ratios of effective population sizes are considerably greater than previously appreciated. Finally, we find that the joint effects of historical changes in life history and population size can explain the observed X:A diversity ratios in extant human populations. Our results suggest that ancestral human populations were highly polygynous, that non-African populations experienced a substantial reduction in polygyny and/or increase in the male-to-female ratio of generation times around the Out-of-Africa bottleneck, and that current diversity levels were affected by fairly recent changes in sex-specific life history.

Over the past decade, there has been both great interest and confusion about whether recent demographic events—notably the Out-of-Africa-bottleneck and recent population growth—have led to differences in mutation load among human populations. The confusion can be traced to the use of different summary statistics to measure load, which lead to apparently conflicting results. We argue, however, that when statistics more directly related to load are used, the results of different studies and data sets consistently reveal little or no difference in the load of non-synonymous mutations among human populations. Theory helps to understand why no such differences are seen, as well as to predict in what settings they are to be expected. In particular, as predicted by modeling, there is evidence for changes in the load of recessive loss of function mutations in founder and inbred human populations. Also as predicted, eastern subspecies of gorilla, Neanderthals and Denisovans, who are thought to have undergone reductions in population sizes that exceed the human Out-of-Africa bottleneck in duration and severity, show evidence for increased load of non-synonymous mutations (relative to western subspecies of gorillas and modern humans, respectively). A coherent picture is thus starting to emerge about the effects of demographic history on the mutation load in populations of humans and close evolutionary relatives.

Polygenic adaptation in response to selection on quantitative traits is thought to be ubiquitous in humans and other species, yet this mode of adaptation remains poorly understood. We investigate the dynamics of this process, assuming that a sudden change in environment shifts the optimal value of a highly polygenic quantitative trait. We find that when the shift is not too large relative to the genetic variance in the trait and this variance arises from segregating loci with small to moderate effect sizes (defined in terms of the selection acting on them before the shift), the mean phenotype’s approach to the new optimum is well approximated by a rapid exponential process first described by Lande (1976). In contrast, when the shift is larger or large effect loci contribute substantially to genetic variance, the initially rapid approach is succeeded by a much slower one. In either case, the underlying changes to allele frequencies exhibit different behaviors short and long-term. Over the short term, strong directional selection on the trait introduces small differences between the frequencies of minor alleles whose effects are aligned with the shift in optimum versus those with effects in the opposite direction. The phenotypic effects of these differences are dominated by contributions from alleles with moderate and large effects, and cumulatively, these effects push the mean phenotype close to the new optimum. Over the longer term, weak directional selection on the trait can amplify the expected frequency differences between opposite alleles; however, since the mean phenotype is close to the new optimum, alleles are mainly affected by stabilizing selection on the trait. Consequently, the frequency differences between opposite alleles translate into small differences in their probabilities of fixation, and the short-term phenotypic contributions of large effect alleles are largely supplanted by contributions of fixed, moderate ones. This process takes on the order of ~4 N e generations (where N e is the effective population size), after which the steady state architecture of genetic variation around the new optimum is restored.

In human populations, relative levels of neutral polymorphism on the X and autosomes differ markedly from each other and from the naive theoretical expectation of ¾. These differences have attracted considerable attention, with studies highlighting several potential causes, including male biased mutation and reproductive variance, historical changes in population size, and selection at linked loci. We revisit this question in light of our new theory about the effects of life history and given pedigree-based estimates of the dependence of human mutation rates on sex and age. We demonstrate that life history effects, particularly higher generation times in males than females, likely had multiple effects on human X-to-autosomes (X:A) polymorphism ratios, through the extent of male mutation bias, the equilibrium X:A ratios of effective population sizes, and differential responses to changes in population size. We also show that the standard approach of using divergence between species to correct for the male bias in mutation results in biased estimates of X:A effective population size ratios. We obtain alternative estimates using pedigree-based estimates of the male mutation bias, which reveal X:A ratios of effective population sizes to be considerably greater than previously appreciated. We then show that the joint effects of historical changes in life history and population size can explain X:A polymorphism ratios in extant human populations. Our results suggest that ancestral human populations were highly polygynous; that non-African populations experienced a substantial reduction in polygyny and/or increase in male-biased generation times around the out of Africa bottleneck; and that extant diversity levels were affected by fairly recent changes in sex-specific life history.Significance StatementAll else being equal, the ratio of diversity levels on X and autosomes at selectively neutral sites should mirror the ratio of their numbers in the population and thus equal ¾. In reality, the ratios observed across human populations differ markedly from ¾ and from each other. Because from a population perspective, autosomes spend an equal number of generations in both sexes while the X spends twice as many generations in females, these departures from the naïve expectations likely reflect differences between male and female life histories and their effects on mutation processes. Indeed, we show that the ratios observed across human populations can be explained by demographic history, assuming plausible, sex-specific mutation rates, generation times and reproductive variances.

Many traits of interest are highly heritable and genetically complex, meaning that much of the variation they exhibit arises from differences at numerous loci in the genome. Complex traits and their evolution have been studied for more than a century, but only in the last decade have genome-wide association studies (GWASs) in humans begun to reveal their genetic basis. Here, we bring these threads of research together to ask how findings from GWASs can further our understanding of the processes that give rise to heritable variation in complex traits and of the genetic basis of complex trait evolution in response to changing selection pressures (i.e., of polygenic adaptation). Conversely, we ask how evolutionary thinking helps us to interpret findings from GWASs and informs related efforts of practical importance.

In numerous applications, from working with animal models to mapping the genetic basis of human disease susceptibility, it is useful to know whether a single disrupting mutation in a gene is likely to be deleterious1–4. With this goal in mind, a number of measures have been developed to identify genes in which protein-truncating variants (PTVs), or other types of mutations, are absent or kept at very low frequency in large population samples—genes that appear “intolerant to mutation”3,5–9. One measure in particular, pLI, has been widely adopted7. By contrasting the observed versus expected number of PTVs, it aims to classify genes into three categories, labelled “null”, “recessive” and “haploinsufficient”7. Such population genetic approaches can be useful in many applications. As we clarify, however, these measures reflect the strength of selection acting on heterozygotes, and not dominance for fitness or haploinsufficiency for other phenotypes.

Populations of organisms show genetic differences called polymorphisms. Understanding the effects of polymorphisms is important for biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under trade-offs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that trade-offs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under trade-offs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species. This article is part of the theme issue ‘Self-organization in cell biology’.

Populations of organisms show prevalent genetic differences called polymorphisms. Understanding the effects of polymorphisms is of central importance in biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under tradeoffs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that tradeoffs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under tradeoffs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species.

Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes—notably, by mutation, natural selection, and genetic drift. Because many quantitative traits are subject to stabilizing selection and because genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed-form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They predict that the distribution of variances contributed by loci identified in GWASs is well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. We test this prediction against the results of GWASs for height and body mass index (BMI) and find that it fits the data well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose shortly before or during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10−3., Author summary One of the central goals of evolutionary genetics is to understand the processes that give rise to phenotypic variation in humans and other taxa. Genome-wide association studies (GWASs) in humans provide an unprecedented opportunity in that regard, revealing the genetic basis of variation in numerous traits. However, exploiting this opportunity requires models that relate genetic and population genetic processes with the discoveries emerging from GWASs. We present such a model and show that it can help explain the results of GWASs for height and body mass index. More generally, our results offer a simple interpretation of the findings emerging from GWASs and suggest how they relate to the evolutionary and genetic forces that give rise to phenotypic variation.

All else being equal, the ratio of genetic diversity levels on X and autosomes at selectively neutral sites should mirror the ratio of their numbers in the population and thus equal ¾. Because X chromosomes spend twice as many generations in females as in males, however, the ratio of diversity levels is also affected by sex differences in life history. The effects of life history on diversity levels, notably those of sex-specific age structures and reproductive variances, have been studied for decades, yet existing theory relies on many parameters that are difficult to measure and lacks generality in ways that limit their applicability. We derive general yet simple expressions for these effects and show that life history effects on X-to-autosome (X:A) ratios of diversity levels depend only on sex-ratios of mutation rates, generation times, and reproductive variances. These results reveal that changing the sex-ratio of generation times has opposite effects on X:A ratios of polymorphism and divergence. They also explain how sex-specific life histories modulate the response of X:A polymorphism ratios to changes in population size. More generally, they clarify that sex-specific life history—generation times in particular—should have a marked effect on X:A polymorphism ratios in many taxa and enable the investigation of these effects.Significance StatementUnderstanding the determinants of neutral diversity patterns on autosomes and sex chromosomes provides a bedrock for our interpretation of population genetic data. Sex-specific age-structure and variation in reproductive success have long been thought to affect neutral diversity, but theoretical descriptions of these effects were complicated and/or lacked in generality, stymying attempts to relate diversity patterns of species with their life history. We derive general yet simple expressions for these effects, which clarify how they impact neutral diversity and should enable studies of relative diversity levels on the autosomes and sex chromosomes in many taxa.

Evolution experiments with microorganisms coupled with genome-wide sequencing now allow for the systematic study of population genetic processes under a wide range of conditions. In learning about these processes in natural, sexual populations, neutral models that describe the behavior of diversity and divergence summaries have played a pivotal role. It is therefore natural to ask whether neutral models, suitably modified, could be useful in the context of evolution experiments. Here, we introduce coalescent models for polymorphism and divergence under the most common experimental evolution assay, a serial transfer experiment. This relatively simple setting allows us to address several issues that could affect diversity patterns in evolution experiments, whether selection is operating or not: the transient behavior of neutral polymorphism in an experiment beginning from a single clone, the effects of randomness in the timing of cell division and noisiness in population size in the dilution stage. In our analyses and discussion, we emphasize the implications for experiments aimed at measuring diversity patterns and making inferences about population genetic processes based on these measurements.

The most common models of sequence evolution used to make inferences about adaptation rely on the assumption that selective pressures at a site remain constant through time. Instead, one might plausibly imagine that a change in the environment renders an allele beneficial and that when it fixes, the site is now constrained – until another change in the environment occurs that affects the selective pressures at that site. With this view in mind, we introduce a simple dynamic model for the evolution of coding regions, in which non-synonymous sites alternate between being fixed for the favored allele and being neutral with respect to other alleles. We use the pruning algorithm to derive closed forms for observable patterns of polymorphism and divergence in terms of the model parameters. Using our model, estimates of the fraction of beneficial substitutions α would remain similar to those obtained from existing approaches. In this framework, however, it becomes natural to ask how often adaptive substitutions originate from previously constrained or previously neutral sites, i.e., about the source of adaptive substitutions. We show that counts of coding sites that are both polymorphic in a sample from one species and divergent between two others carry information about this parameter. We also extend the basic model to include the effects of weakly deleterious mutations and discuss the importance of assumptions about the distribution of deleterious mutations among constrained non-synonymous sites. Finally, we derive a likelihood function for the parameters and apply it to a toy example, variation data for coding regions from chromosome 2 of the Drosophila melanogaster subgroup. This modeling work underscores how restrictive assumptions about adaptation have been to date, and how further work in this area will help to reveal unexplored and yet basic characteristics of adaptation.

© 2016 Elyashiv et al. Natural selection at one site shapes patterns of genetic variation at linked sites. Quantifying the effects of “linked selection” on levels of genetic diversity is key to making reliable inference about demography, building a null model in scans for targets of adaptation, and learning about the dynamics of natural selection. Here, we introduce the first method that jointly infers parameters of distinct modes of linked selection, notably background selection and selective sweeps, from genome-wide diversity data, functional annotations and genetic maps. The central idea is to calculate the probability that a neutral site is polymorphic given local annotations, substitution patterns, and recombination rates. Information is then combined across sites and samples using composite likelihood in order to estimate genome-wide parameters of distinct modes of selection. In addition to parameter estimation, this approach yields a map of the expected neutral diversity levels along the genome. To illustrate the utility of our approach, we apply it to genome-wide resequencing data from 125 lines in Drosophila melanogaster and reliably predict diversity levels at the 1Mb scale. Our results corroborate estimates of a high fraction of beneficial substitutions in proteins and untranslated regions (UTR). They allow us to distinguish between the contribution of sweeps and other modes of selection around amino acid substitutions and to uncover evidence for pervasive sweeps in untranslated regions (UTRs). Our inference further suggests a substantial effect of other modes of linked selection and of adaptation in particular. More generally, we demonstrate that linked selection has had a larger effect in reducing diversity levels and increasing their variance in D. melanogaster than previously appreciated.

The ABO histo-blood group, the critical determinant of transfusion incompatibility, was the first genetic polymorphism discovered in humans. Remarkably, ABO antigens are also polymorphic in many other primates, with the same two amino acid changes responsible for A and B specificity in all species sequenced to date. Whether this recurrence of A and B antigens is the result of an ancient polymorphism maintained across species or due to numerous, more recent instances of convergent evolution has been debated for decades, with a current consensus in support of convergent evolution. We show instead that genetic variation data in humans and gibbons as well as in Old World monkeys are inconsistent with a model of convergent evolution and support the hypothesis of an ancient, multiallelic polymorphism of which some alleles are shared by descent among species. These results demonstrate that the A and B blood groups result from a trans-species polymorphism among distantly related species and has remained under balancing selection for tens of millions of years—to date, the only such example in hominoids and Old World monkeys outside of the major histocompatibility complex.

Efforts to identify the genetic basis of human adaptations from polymorphism data have sought footprints of "classic selective sweeps" (in which a beneficial mutation arises and rapidly fixes in the population).Yet it remains unknown whether this form of natural selection was common in our evolution. We examined the evidence for classic sweeps in resequencing data from 179 human genomes. As expected under a recurrent-sweep model, we found that diversity levels decrease near exons and conserved noncoding regions. In contrast to expectation, however, the trough in diversity around human-specific amino acid substitutions is no more pronounced than around synonymous substitutions. Moreover, relative to the genome background, amino acid and putative regulatory sites are not significantly enriched in alleles that are highly differentiated between populations. These findings indicate that classic sweeps were not a dominant mode of human adaptation over the past ~250,000 years.

Because nearly neutral substitutions are thought to contribute substantially to molecular evolution, and much of our insight about the workings of nearly neutral evolution relies on theory, solvable models of this process are of particular interest. Here, I present an analytical method for solving models of nearly neutral evolution at steady state. The steady state solution applies to any constant fitness landscape under a dynamic of successive fixations, each of which occurs on the background of the population’s most recent common ancestor. Because this dynamic neglects the effects of polymorphism in the population beyond the mutant allele under consideration, the steady state solution provides a decent approximation of evolutionary dynamics when the population mutation rate is low ( N u ≪ 1 ) . To demonstrate the method, I apply it to two examples: Fisher’s geometric model (FGM), and a simple model of molecular evolution. Since recent papers have studied the steady state behavior of FGM under this dynamic, I analyze its behavior in detail and compare the results with previous work.

One of the foundational results in molecular evolution is that the rate at which neutral substitutions accumulate on a lineage equals the rate at which mutations arise. Traits that affect rates of mutation therefore also affect the phylogenetic "molecular clock." We consider the effects of sex-specific generation times and mutation rates in species with two sexes. In particular, we focus on the effects that the age of onset of male puberty and rates of spermatogenesis have likely had in hominids (great apes), considering a model that approximates features of the mutational process in mammals, birds, and some other vertebrates. As we show, this model can account for a number of seemingly disparate observations: notably, the puzzlingly low X-to-autosome ratios of substitution rates in humans and chimpanzees and differences in rates of autosomal substitutions among hominine lineages (i.e., humans, chimpanzees, and gorillas). The model further suggests how to translate pedigree-based estimates of human mutation rates into split times among extant hominoids (apes), given sex-specific life histories. In so doing, it largely bridges the gap reported between estimates of split times based on fossil and molecular evidence, in particular suggesting that the human-chimpanzee split may have occurred as recently as 6.6 Mya. The model also implies that the "generation time effect" should be stronger in short-lived species, explaining why the generation time has a major influence on yearly substitution rates in mammals but only a subtle one in human pedigrees.

Mutations can originate from the chance misincorporation of nucleotides during DNA replication or from DNA lesions that arise between replication cycles and are not repaired correctly. We introduce a model that relates the source of mutations to their accumulation with cell divisions, providing a framework for understanding how mutation rates depend on sex, age, and cell division rate. We show that the accrual of mutations should track cell divisions not only when mutations are replicative in origin but also when they are non-replicative and repaired efficiently. One implication is that observations from diverse fields that to date have been interpreted as pointing to a replicative origin of most mutations could instead reflect the accumulation of mutations arising from endogenous reactions or exogenous mutagens. We further find that only mutations that arise from inefficiently repaired lesions will accrue according to absolute time; thus, unless life history traits co-vary, the phylogenetic “molecular clock” should not be expected to run steadily across species., Modeling how the source of mutations relates to their rate of accumulation with age, sex, and number of cell divisions helps to explain perplexing observations about germline and somatic mutations., Author Summary We relate how mutations arise to how they accumulate in different sexes, with age and with cell division. This model provides a single framework within which to interpret emerging results from evolutionary biology, human genetics, and cancer genetics. We show that the accrual of mutations should track cell divisions not only when mutations originate during DNA replication but also when they arise through non-replicative mechanisms and are repaired efficiently. This realization means that previous observations of correlations between mutation and cell division rates actually provide little support to the commonly held belief that most germline and somatic mutations arise from replication errors. We further find that only mutations that arise from inefficiently repaired lesions will accrue according to absolute time; thus, without covariation in life history traits, the phylogenetic “molecular clock” should not be expected to run at constant rates across species.

The standard genetic code is the nearly universal system for the translation of genes into proteins. The code exhibits two salient structural characteristics: it possesses a distinct organization that makes it extremely robust to errors in replication and translation, and it is highly redundant. The origin of these properties has intrigued researchers since the code was first discovered. One suggestion, which is the subject of this review, is that the code's organization is the outcome of the coevolution of genes and genetic codes. In 1968, Francis Crick explored the possible implications of coevolution at different stages of code evolution. Although he argues that coevolution was likely to influence the evolution of the code, he concludes that it falls short of explaining the organization of the code we see today. The recent application of mathematical modeling to study the effects of errors on the course of coevolution, suggests a different conclusion. It shows that coevolution readily generates genetic codes that are highly redundant and similar in their error-correcting organization to the standard code. We review this recent work and suggest that further affirmation of the role of coevolution can be attained by investigating the extent to which the outcome of coevolution is robust to other influences that were present during the evolution of the code.

A number of fundamental mathematical models of the evolutionary process exhibit dynamics that can be difficult to understand analytically. Here we show that a precise mathematical analogy can be drawn between certain evolutionary and thermodynamic systems, allowing application of the powerful machinery of statistical physics to analysis of a family of evolutionary models. Analytical results that follow directly from this approach include the steady-state distribution of fixed genotypes and the load in finite populations. The analogy with statistical physics also reveals that, contrary to a basic tenet of the nearly neutral theory of molecular evolution, the frequencies of adaptive and deleterious substitutions at steady state are equal. Finally, just as the free energy function quantitatively characterizes the balance between energy and entropy, a free fitness function provides an analytical expression for the balance between natural selection and stochastic drift.

The standard genetic code poses a challenge in understanding the evolution of information processing at a fundamental level of biological organization. Genetic codes are generally coadapted with, or ‘frozen‘ by, the protein–coding genes that they translate, and so cannot easily change by natural selection. Yet the standard code has a significantly non–random pattern that corrects common errors in the transmission of information in protein–coding genes. Because of the freezing effect and for other reasons, this pattern has been proposed not to be due to selection but rather to be incidental to other evolutionary forces or even entirely accidental.We present results from a deterministic population genetic model of code–message coevolution. We explicitly represent the freezing effect of genes on genetic codes and the perturbative effect of changes in genetic codes on genes. We incorporate characteristic patterns of mutation and translational error, namely, transition bias and positional asymmetry, respectively. Repeated selection over small successive changes produces genetic codes that are substantially, but not optimally, error correcting. In particular, our model reproduces the error–correcting patterns of the standard genetic code. Aspects of our model and results may be applicable to the general problem of adaptation to error in other natural information–processing systems.

Evolution experiments with microorganisms coupled with genome-wide sequencing now allow for the systematic study of population genetic processes under a wide range of conditions. In learning about these processes in natural, sexual populations, neutral models that describe the behavior of diversity and divergence summaries have played a pivotal role. It is therefore natural to ask whether neutral models, suitably modified, could be useful in the context of evolution experiments. Here, we introduce coalescent models for polymorphism and divergence under the most common experimental evolution assay, a serial transfer experiment. This relatively simple setting allows us to address several issues that could affect diversity patterns in evolution experiments, whether selection is operating or not: the transient behavior of neutral polymorphism in an experiment beginning from a single clone, the effects of randomness in the timing of cell division and noisiness in population size in the dilution stage. In our analyses and discussion, we emphasize the implications for experiments aimed at measuring diversity patterns and making inferences about population genetic processes based on these measurements.

Instances in which natural selection maintains genetic variation in a population over millions of years are thought to be extremely rare. We conducted a genome-wide scan for long-lived balancing selection by looking for combinations of SNPs shared between humans and chimpanzees. In addition to the major histocompatibility complex (MHC), we identified 125 regions in which the same haplotypes are segregating in the two species, all but two of which are non-coding. In six cases, there is evidence for an ancestral polymorphism that persisted to the present in humans and chimpanzees. Regions with shared haplotypes are significantly enriched for membrane glycoproteins, and a similar trend is seen among shared coding polymorphisms. These findings indicate that ancient balancing selection has shaped human variation and point to genes involved in host-pathogen interactions as common targets.

How much does the intensity of purifying selection vary among populations and species? How uniform are the shifts in selective pressures across the genome? To address these questions, we took advantage of a recent, whole-genome polymorphism data set from two closely related species of yeast, Saccharomyces cerevisiae and S. paradoxus, paying close attention to the population structure within these species. We found that the average intensity of purifying selection on amino acid sites varies markedly among populations and between species. As expected in the presence of extensive weakly deleterious mutations, the effect of purifying selection is substantially weaker on single nucleotide polymorphisms (SNPs) segregating within populations than on SNPs fixed between population samples. Also in accordance with a Nearly Neutral model, the variation in the intensity of purifying selection across populations corresponds almost perfectly to simple measures of their effective size. As a first step toward understanding the processes generating these patterns, we sought to tease apart the relative importance of systematic, genome-wide changes in the efficacy of selection, such as those expected from demographic processes and of gene-specific changes, which may be expected after a shift in selective pressures. For that purpose, we developed a new model for the evolution of purifying selection between populations and inferred its parameters from the genome-wide data using a likelihood approach. We found that most, but not all changes seem to be explained by systematic shifts in the efficacy of selection. One population, the sake-derived strains of S. cerevisiae, however, also shows extensive gene-specific changes, plausibly associated with domestication. These findings have important implications for our understanding of purifying selection as well as for estimates of the rate of molecular adaptation in yeast and in other species.

Over the past four decades, the predominant view of molecular evolution saw little connection between natural selection and genome evolution, assuming that the functionally constrained fraction of the genome is relatively small and that adaptation is sufficiently infrequent to play little role in shaping patterns of variation within and even between species. Recent evidence from Drosophila, reviewed here, suggests that this view may be invalid. Analyses of genetic variation within and between species reveal that much of the Drosophila genome is under purifying selection, and thus of functional importance, and that a large fraction of coding and noncoding differences between species are adaptive. The findings further indicate that, in Drosophila, adaptations may be both common and strong enough that the fate of neutral mutations depends on their chance linkage to adaptive mutations as much as on the vagaries of genetic drift. The emerging evidence has implications for a wide variety of fields, from conservation genetics to bioinformatics, and presents challenges to modelers and experimentalists alike.

Much effort and interest have focused on assessing the importance of natural selection, particularly positive natural selection, in shaping the human genome. Although scans for positive selection have identified candidate loci that may be associated with positive selection in humans, such scans do not indicate whether adaptation is frequent in general in humans. Studies based on the reasoning of the MacDonald–Kreitman test, which, in principle, can be used to evaluate the extent of positive selection, suggested that adaptation is detectable in the human genome but that it is less common than in Drosophila or Escherichia coli. Both positive and purifying natural selection at functional sites should affect levels and patterns of polymorphism at linked nonfunctional sites. Here, we search for these effects by analyzing patterns of neutral polymorphism in humans in relation to the rates of recombination, functional density, and functional divergence with chimpanzees. We find that the levels of neutral polymorphism are lower in the regions of lower recombination and in the regions of higher functional density or divergence. These correlations persist after controlling for the variation in GC content, density of simple repeats, selective constraint, mutation rate, and depth of sequencing coverage. We argue that these results are most plausibly explained by the effects of natural selection at functional sites—either recurrent selective sweeps or background selection—on the levels of linked neutral polymorphism. Natural selection at both coding and regulatory sites appears to affect linked neutral polymorphism, reducing neutral polymorphism by 6% genome-wide and by 11% in the gene-rich half of the human genome. These findings suggest that the effects of natural selection at linked sites cannot be ignored in the study of neutral human polymorphism., Author Summary There is much reported evidence for positive selection at specific loci in the human genome. Additional papers based on comparisons between the genomes of humans and chimpanzees have also suggested that adaptive evolution may be quite common. At the same time, it has been surprisingly hard to find unambiguous evidence that either positive or negative (background) selection is affecting genome-wide patterns of variation at neutral sites. Here, we evaluate the prevalence of positive or background selection by using two genome-wide datasets of human polymorphism. We document that levels of neutral polymorphism are substantially lower in the regions of (i) higher density of genes and/or regulatory regions, (ii) higher protein or regulatory divergence, and (iii) lower recombination. These patterns are robust to a number of possible confounding factors and suggest that effects of selection at linked sites cannot be ignored in the study of the human genome.

The effect of recurrent selective sweeps is a spatially heterogeneous reduction in neutral polymorphism throughout the genome. The pattern of reduction depends on the selective advantage and recurrence rate of the sweeps. Because many adaptive substitutions responsible for these sweeps also contribute to nonsynonymous divergence, the spatial distribution of nonsynonymous divergence also reflects the distribution of adaptive substitutions. Thus, the spatial correspondence between neutral polymorphism and nonsynonymous divergence may be especially informative about the process of adaptation. Here we study this correspondence using genomewide polymorphism data from Drosophila simulans and the divergence between D. simulans and D. melanogaster. Focusing on highly recombining portions of the autosomes, at a spatial scale appropriate to the study of selective sweeps, we find that neutral polymorphism is both lower and, as measured by a new statistic QS, less homogeneous where nonsynonymous divergence is higher and that the spatial structure of this correlation is best explained by the action of strong recurrent selective sweeps. We introduce a method to infer, from the spatial correspondence between polymorphism and divergence, the rate and selective strength of adaptation. Our results independently confirm a high rate of adaptive substitution (∼1/3000 generations) and newly suggest that many adaptations are of surprisingly great selective effect (∼1%), reducing the effective population size by ∼15% even in highly recombining regions of the genome.

The Standard Genetic Code is organized such that similar codons encode similar amino acids. One explanation suggested that the Standard Code is the result of natural selection to reduce the fitness "load" that derives from the mutation and mistranslation of protein-coding genes. We review the arguments against the mutational load-minimizing hypothesis and argue that they need to be reassessed. We review recent analyses of the organization of the Standard Code and conclude that under cautious interpretation they support the mutational load-minimizing hypothesis. We then present a deterministic asexual model with which we study the mode of selection for load minimization. In this model, individual fitness is determined by a protein phenotype resulting from the translation of a mutable set of protein-coding genes. We show that an equilibrium fitness may be associated with a population with the same genetic code and that genetic codes that assign similar codons to similar amino acids have a higher fitness. We also show that the number of mutant codons in each individual at equilibrium, which determines the strength of selection for load minimization, reflects a long-term evolutionary balance between mutations in messages and selection on proteins, rather than the number of mutations that occur in a single generation, as has been assumed by previous authors. We thereby establish that selection for mutational load minimization acts at the level of an individual in a single generation. We conclude with comments on the shortcomings and advantages of load minimization over other hypotheses for the origin of the Standard Code.

We study a model in which cooperation and defection coexist in a dynamical steady state. In our model, subpopulations of cooperators and defectors inhabit sites on a lattice. The interactions among the individuals at a site, in the form of a prisoner's dilemma (PD) game, determine their fitnesses. The chosen PD payoff allows cooperators, but not defectors, to maintain a homogeneous population. Individuals mutate between types and migrate to neighboring sites with low probabilities. We consider both density-dependent and density-independent versions of the model. The persistence of cooperation in this model can be explained in terms of the life cycle of a population at a site. This life cycle starts when one cooperator establishes a population. Then defectors invade and eventually take over, resulting finally in the death of the population. During this life cycle, single cooperators migrate to empty neighboring sites to found new cooperator populations. The system can reach a steady state where cooperation prevails if the global “birth” rate of populations is equal to their global “death” rate. The dynamic persistence of cooperation ranges over a large section of the model's parameter space. We compare these dynamics to those from other models for the persistence of altruism and to predator–prey models.

During the evolution of life, there have been several transitions in which individuals began to cooperate, forming higher levels of organization, and sometimes losing their independent reproductive identity. For example, multicellularity and insect societies evolved independently multiple times. Several factors that confer evolutionary advantages on higher levels of organization have been proposed. In this paper we highlight one additional factor: the sharing of information between individuals. Information sharing is not subject to the intrinsic conservation laws that characterize the sharing of physical resources. A simple model will illustrate how information sharing can result in aggregates in which the individuals both receive more information about their environment and pay less for it. This may have played a role in the evolution of higher levels of organization.