The clock-like accumulation of germline and somatic mutations can arise from the interplay of DNA damage and repair.

The rates at which mutations accumulate across human cell types vary. To identify causes of this variation, mutations are often decomposed into a combination of the single-base substitution (SBS) "signatures" observed in germline, soma, and tumors, with the idea that each signature corresponds to one or a small number of underlying mutagenic processes. Two such signatures turn out to be ubiquitous across cell types: SBS signature 1, which consists primarily of transitions at methylated CpG sites thought to be caused by spontaneous deamination, and the more diffuse SBS signature 5, which is of unknown etiology. In cancers, the number of mutations attributed to these 2 signatures accumulates linearly with age of diagnosis, and thus the signatures have been termed "clock-like." To better understand this clock-like behavior, we develop a mathematical model that includes DNA replication errors, unrepaired damage, and damage repaired incorrectly. We show that mutational signatures can exhibit clock-like behavior because cell divisions occur at a constant rate and/or because damage rates remain constant over time, and that these distinct sources can be teased apart by comparing cell lineages that divide at different rates. With this goal in mind, we analyze the rate of accumulation of mutations in multiple cell types, including soma as well as male and female germline. We find no detectable increase in SBS signature 1 mutations in neurons and only a very weak increase in mutations assigned to the female germline, but a significant increase with time in rapidly dividing cells, suggesting that SBS signature 1 is driven by rounds of DNA replication occurring at a relatively fixed rate. In contrast, SBS signature 5 increases with time in all cell types, including postmitotic ones, indicating that it accumulates independently of cell divisions; this observation points to errors in DNA repair as the key underlying mechanism. Thus, the two "clock-like" signatures observed across cell types likely have distinct origins, one set by rates of cell division, the other by damage rates.

Changes in life history and population size can explain the relative neutral diversity levels on X and autosomes in extant human populations.

In human populations, the relative levels of neutral diversity on the X and autosomes differ markedly from each other and from the naïve 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.

Thinking About the Evolution of Complex Traits in the Era of Genome-Wide Association Studies.

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.

A population genetic interpretation of GWAS findings for human quantitative traits.

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.

Interpreting the Dependence of Mutation Rates on Age and Time.

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.

Life history effects on the molecular clock of autosomes and sex chromosomes.

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.

A Genomic Map of the Effects of Linked Selection in Drosophila.

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 blood group is a trans-species polymorphism in primates.

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.

Pervasive adaptive protein evolution apparent in diversity patterns around amino acid substitutions in Drosophila simulans.

In Drosophila, multiple lines of evidence converge in suggesting that beneficial substitutions to the genome may be common. All suffer from confounding factors, however, such that the interpretation of the evidence-in particular, conclusions about the rate and strength of beneficial substitutions-remains tentative. Here, we use genome-wide polymorphism data in D. simulans and sequenced genomes of its close relatives to construct a readily interpretable characterization of the effects of positive selection: the shape of average neutral diversity around amino acid substitutions. As expected under recurrent selective sweeps, we find a trough in diversity levels around amino acid but not around synonymous substitutions, a distinctive pattern that is not expected under alternative models. This characterization is richer than previous approaches, which relied on limited summaries of the data (e.g., the slope of a scatter plot), and relates to underlying selection parameters in a straightforward way, allowing us to make more reliable inferences about the prevalence and strength of adaptation. Specifically, we develop a coalescent-based model for the shape of the entire curve and use it to infer adaptive parameters by maximum likelihood. Our inference suggests that ∼13% of amino acid substitutions cause selective sweeps. Interestingly, it reveals two classes of beneficial fixations: a minority (approximately 3%) that appears to have had large selective effects and accounts for most of the reduction in diversity, and the remaining 10%, which seem to have had very weak selective effects. These estimates therefore help to reconcile the apparent conflict among previously published estimates of the strength of selection. More generally, our findings provide unequivocal evidence for strongly beneficial substitutions in Drosophila and illustrate how the rapidly accumulating genome-wide data can be leveraged to address enduring questions about the genetic basis of adaptation.

Gene regulatory network structure informs the distribution of perturbation effects.

Gene regulatory networks (GRNs) govern many core developmental and biological processes underlying human complex traits. Even with broad-scale efforts to characterize the effects of molecular perturbations and interpret gene coexpression, it remains challenging to infer the architecture of gene regulation in a precise and efficient manner. Key properties of GRNs, like hierarchical structure, modular organization, and sparsity, provide both challenges and opportunities for this objective. Here, we seek to better understand properties of GRNs using a new approach to simulate their structure and model their function. We produce realistic network structures with a novel generating algorithm based on insights from small-world network theory, and we model gene expression regulation using stochastic differential equations formulated to accommodate modeling molecular perturbations. With these tools, we systematically describe the effects of gene knockouts within and across GRNs, finding a subset of networks that recapitulate features of a recent genome-scale perturbation study. With deeper analysis of these exemplar networks, we consider future avenues to map the architecture of gene expression regulation using data from cells in perturbed and unperturbed states, finding that while perturbation data are critical to discover specific regulatory interactions, data from unperturbed cells may be sufficient to reveal regulatory programs.

Shifts in the intensity of purifying selection: an analysis of genome-wide polymorphism data from two closely related yeast species.

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.

Modeling the effect of changing selective pressures on polymorphism and divergence.

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.

Down the Penrose stairs, or how selection for fewer recombination hotspots maintains their existence.

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. This assumption, however, does not align with current evidence. Recent experimental work indicates that PRDM9 binding on both homologs facilitates DSB repair, and that the absence of sufficient symmetric binding disrupts meiosis. We therefore consider an alternative hypothesis: that rapid PRDM9 evolution is driven by the need to restore symmetric binding because of 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 genetic processes that govern the evolution of the zinc finger array and its binding sites. We show that 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 turn, drives rapid PRDM9 evolutionary turnover. Our results therefore suggest that the advantage of new PRDM9 alleles is in limiting the number of binding sites used effectively, rather than in increasing net PRDM9 binding. 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.

Broad-scale variation in human genetic diversity levels is predicted by purifying selection on coding and non-coding elements.

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.

Disentangling sources of clock-like mutations in germline and soma.

The rates of mutations vary across cell types. To identify causes of this variation, mutations are often decomposed into a combination of the single base substitution (SBS) "signatures" observed in germline, soma and tumors, with the idea that each signature corresponds to one or a small number of underlying mutagenic processes. Two such signatures turn out to be ubiquitous across cell types: SBS signature 1, which consists primarily of transitions at methylated CpG sites caused by spontaneous deamination, and the more diffuse SBS signature 5, which is of unknown etiology. In cancers, the number of mutations attributed to these two signatures accumulates linearly with age of diagnosis, and thus the signatures have been termed "clock-like." To better understand this clock-like behavior, we develop a mathematical model that includes DNA replication errors, unrepaired damage, and damage repaired incorrectly. We show that mutational signatures can exhibit clock-like behavior because cell divisions occur at a constant rate and/or because damage rates remain constant over time, and that these distinct sources can be teased apart by comparing cell lineages that divide at different rates. With this goal in mind, we analyze the rate of accumulation of mutations in multiple cell types, including soma as well as male and female germline. We find no detectable increase in SBS signature 1 mutations in neurons and only a very weak increase in mutations assigned to the female germline, but a significant increase with time in rapidly-dividing cells, suggesting that SBS signature 1 is driven by rounds of DNA replication occurring at a relatively fixed rate. In contrast, SBS signature 5 increases with time in all cell types, including post-mitotic ones, indicating that it accumulates independently of cell divisions; this observation points to errors in DNA repair as the key underlying mechanism. Thus, the two "clock-like" signatures observed across cell types likely have distinct origins, one set by rates of cell division, the other by damage rates.

Pervasive natural selection in the Drosophila genome?

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.

Pervasive hitchhiking at coding and regulatory sites in humans.

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.

Polygenic adaptation after a sudden change in environment.

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.

The impact of genetic modifiers on variation in germline mutation rates within and among human populations.

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.

Impact of essential workers in the context of social distancing for epidemic control.

New emerging infectious diseases are identified every year, a subset of which become global pandemics like COVID-19. In the case of COVID-19, many governments have responded to the ongoing pandemic by imposing social policies that restrict contacts outside of the home, resulting in a large fraction of the workforce either working from home or not working. To ensure essential services, however, a substantial number of workers are not subject to these limitations, and maintain many of their pre-intervention contacts. To explore how contacts among such "essential" workers, and between essential workers and the rest of the population, impact disease risk and the effectiveness of pandemic control, we evaluated several mathematical models of essential worker contacts within a standard epidemiology framework. The models were designed to correspond to key characteristics of cashiers, factory employees, and healthcare workers. We find in all three models that essential workers are at substantially elevated risk of infection compared to the rest of the population, as has been documented, and that increasing the numbers of essential workers necessitates the imposition of more stringent controls on contacts among the rest of the population to manage the pandemic. Importantly, however, different archetypes of essential workers differ in both their individual probability of infection and impact on the broader pandemic dynamics, highlighting the need to understand and target intervention for the specific risks faced by different groups of essential workers. These findings, especially in light of the massive human costs of the current COVID-19 pandemic, indicate that contingency plans for future epidemics should account for the impacts of essential workers on disease spread.