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We present a geometry-based interpretation of the f -statistics framework, commonly used in population genetics to estimate phylogenetic relationships from genomic data. The focus is on the determination of the mixing coefficients in population admixture events subject to post-admixture drift. The interpretation takes advantage of the high dimension of the dataset and analyzes the problem as a dimensional reduction issue. We show that it is possible to think of the f -statistics technique as an implicit transformation of the genomic data from a phase space into a subspace where the mapped data structure is more similar to the ancestral admixture configuration. The 2-way mixing coefficient is, as a matter of fact, carried out implicitly in this subspace. In addition, we propose the admixture test to be evaluated in the subspace because the comparison with the conventional one provides an important assessment of the admixture model. The overarching geometric framework provides slightly more general formulas than the f -formalism by using a different rationale as a starting point. Explicitly addressed are 2- and 3-way admixtures. The mixture proportions are provided by suitable linear fits, in 2 or 3 dimensions, that can be easily visualized. The difficulties encountered with introgression and gene flow are also addressed. The developments and findings are illustrated with numerical simulations and real-world cases. [ABSTRACT FROM AUTHOR]

Sex and recombination can affect the dynamics of transposable elements (TEs) in various ways: while sex is expected to help TEs to spread within populations, the deleterious effect of ectopic recombination among transposons represents a possible source of purifying selection limiting their number. Furthermore, recombination may also increase the efficiency of selection against TEs by reducing selective interference among loci. In order to better understand the effects of recombination and reproductive systems on TE dynamics, this article provides analytical expressions for the linkage disequilibrium among TEs in a classical model in which TE number is stabilized by synergistic purifying selection. The results show that positive linkage disequilibrium is predicted in infinite populations despite negative epistasis, due to the effect of the transposition process. Positive linkage disequilibrium may substantially inflate the variance in the number of elements per genome in the case of partially selfing or partially clonal populations. Finite population size tends to generate negative linkage disequilibrium (Hill-Robertson effect), the relative importance of this effect increasing with the degree of linkage among loci. The model is then extended in order to explore how TEs may affect selection for recombination. While positive linkage disequilibrium generated by transposition generally disfavors recombination, the Hill-Robertson effect may represent a non-negligible source of indirect selection for recombination when TEs are abundant. However, the direct fitness cost imposed by ectopic recombination among elements generally drives the population towards low-recombination regimes, at which TEs cannot be maintained at a stable equilibrium. [ABSTRACT FROM AUTHOR]

Investigating gene expression evolution over micro- and macroevolutionary timescales will expand our understanding of the role of gene expression in adaptation and speciation. In this study, we characterized the evolutionary forces acting on gene expression levels in eye and brain tissue of five Heliconius butterflies with divergence times of ∼5-12 MYA. We developed and applied Brownian motion (BM) and Ornstein-Uhlenbeck (OU) models to identify genes whose expression levels are evolving through drift, stabilizing selection, or a lineage-specific shift. We found that 81% of the genes evolve under genetic drift. When testing for branch-specific shifts in gene expression, we detected 368 (16%) shift events. Genes showing a shift toward upregulation have significantly lower gene expression variance than those genes showing a shift leading toward downregulation. We hypothesize that directional selection is acting in shifts causing upregulation, since transcription is costly. We further uncovered through simulations that parameter estimation of OU models is biased when using small phylogenies and only becomes reliable with phylogenies having ≥ 50 taxa. Therefore, we developed a new statistical test based on BM to identify highly conserved genes (i.e., evolving under strong stabilizing selection), which comprised 3% of the orthoclusters. In conclusion, we found that drift is the dominant evolutionary force driving gene expression evolution in eye and brain tissue in Heliconius Nevertheless, the higher proportion of genes evolving under directional than under stabilizing selection might reflect species-specific selective pressures on vision and the brain that are necessary to fulfill species-specific requirements.

The advent of next generation sequencing technologies has made whole-genome and whole-population sampling possible, even for eukaryotes with large genomes. With this development, experimental evolution studies can be designed to observe molecular evolution in action via evolve-and-resequence (E&R) experiments. Among other applications, E&R studies can be used to locate the genes and variants responsible for genetic adaptation. Most existing literature on time-series data analysis often assumes large population size, accurate allele frequency estimates, or wide time spans. These assumptions do not hold in many E&R studies. In this article, we propose a method-composition of likelihoods for evolve-and-resequence experiments (Clear)-to identify signatures of selection in small population E&R experiments. Clear takes whole-genome sequences of pools of individuals as input, and properly addresses heterogeneous ascertainment bias resulting from uneven coverage. Clear also provides unbiased estimates of model parameters, including population size, selection strength, and dominance, while being computationally efficient. Extensive simulations show that Clear achieves higher power in detecting and localizing selection over a wide range of parameters, and is robust to variation of coverage. We applied the Clear statistic to multiple E&R experiments, including data from a study of adaptation of Drosophila melanogaster to alternating temperatures and a study of outcrossing yeast populations, and identified multiple regions under selection with genome-wide significance.

A strong reduction in diversity around a specific locus is often interpreted as a recent rapid fixation of a positively selected allele, a phenomenon called a selective sweep. Rapid fixation of neutral variants can however lead to a similar reduction in local diversity, especially when the population experiences changes in population size, e.g. bottlenecks or range expansions. The fact that demographic processes can lead to signals of nucleotide diversity very similar to signals of selective sweeps is at the core of an ongoing discussion about the roles of demography and natural selection in shaping patterns of neutral variation. Here, we quantitatively investigate the shape of such neutral valleys of diversity under a simple model of a single population size change, and we compare it to signals of a selective sweep. We analytically describe the expected shape of such "neutral sweeps" and show that selective sweep valleys of diversity are, for the same fixation time, wider than neutral valleys. On the other hand, it is always possible to parametrize our model to find a neutral valley that has the same width as a given selected valley. Our findings provide further insight into how simple demographic models can create valleys of genetic diversity similar to those attributed to positive selection. [ABSTRACT FROM AUTHOR]

The statistical associations between mutations, collectively known as linkage disequilibrium, encode important information about the evolutionary forces acting within a population. Yet in contrast to single-site analogues like the site frequency spectrum, our theoretical understanding of linkage disequilibrium remains limited. In particular, little is currently known about how mutations with different ages and fitness costs contribute to expected patterns of linkage disequilibrium, even in simple settings where recombination and genetic drift are the major evolutionary forces. Here, I introduce a forward-time framework for predicting linkage disequilibrium between pairs of neutral and deleterious mutations as a function of their present-day frequencies. I show that the dynamics of linkage disequilibrium become much simpler in the limit that mutations are rare, where they admit a simple heuristic picture based on the trajectories of the underlying lineages. I use this approach to derive analytical expressions for a family of frequency-weighted linkage disequilibrium statistics as a function of the recombination rate, the frequency scale, and the additive and epistatic fitness costs of the mutations. I find that the frequency scale can have a dramatic impact on the shapes of the resulting linkage disequilibrium curves, reflecting the broad range of time scales over which these correlations arise. I also show that the differences between neutral and deleterious linkage disequilibrium are not purely driven by differences in their mutation frequencies and can instead display qualitative features that are reminiscent of epistasis. I conclude by discussing the implications of these results for recent linkage disequilibrium measurements in bacteria. This forward-time approach may provide a useful framework for predicting linkage disequilibrium across a range of evolutionary scenarios. [ABSTRACT FROM AUTHOR]

The 1966 GENETICS papers by John Hubby and Richard Lewontin were a landmark in the study of genome-wide levels of variability. They used the technique of gel electrophoresis of enzymes and proteins to study variation in natural populations of Drosophila pseudoobscura, at a set of loci that had been chosen purely for technical convenience, without prior knowledge of their levels of variability. Together with the independent study of human populations by Harry Harris, this seminal study provided the first relatively unbiased picture of the extent of genetic variability in protein sequences within populations, revealing that many genes had surprisingly high levels of diversity. These papers stimulated a large research program that found similarly high electrophoretic variability in many different species and led to statistical tools for interpreting the data in terms of population genetics processes such as genetic drift, balancing and purifying selection, and the effects of selection on linked variants. The current use of whole-genome sequences in studies of variation is the direct descendant of this pioneering work.

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated ("pulled") waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.

Plant architecture is shaped by the production of new organs, most of which emerge postembryonically. This process includes the formation of new lateral branches along existing shoots. Current evidence supports a detached-meristem model as the cellular basis of lateral shoot initiation. In this model, a small number of undifferentiated cells are sampled from the periphery of the shoot apical meristem (SAM) to act as precursors for axillary buds, which eventually develop into new shoots. Repeated branching thus creates cellular bottlenecks (i.e. somatic drift) that affect how de novo (epi)genetic mutations propagate through the plant body during development. Somatic drift could be particularly relevant for stochastic DNA methylation gains and losses (i.e. spontaneous epimutations), as they have been shown to arise rapidly with each cell division. Here, we formalize a special case of the detached-meristem model, where precursor cells are randomly sampled from the SAM periphery in a way that maximizes cell lineage independence. We show that somatic drift during repeated branching gives rise to a mixture of cellular phylogenies within the SAM over time. This process is dependent on the number of branch points, the strength of drift as well as the epimutation rate. Our model predicts that cell-to-cell DNA methylation heterogeneity in the SAM converges to nonzero states during development, suggesting that epigenetic variation is an inherent property of the SAM cell population. Our insights have direct implications for empirical studies of somatic (epi)genomic diversity in long-lived perennial and clonal species using bulk or single-cell sequencing approaches., Competing Interests: Conflicts of interest The author(s) declare no conflicts of interest., (© The Author(s) 2024. Published by Oxford University Press on behalf of The Genetics Society of America. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.)

Although maize is naturally an outcrossing organism, modern breeding utilizes highly inbred lines in controlled crosses to produce hybrids. The U.S. Department of Agriculture's reciprocal recurrent selection experiment between the Iowa Stiff Stalk Synthetic (BSSS) and the Iowa Corn Borer Synthetic No. 1 (BSCB1) populations represents one of the longest running experiments to understand the response to selection for hybrid performance. To investigate the genomic impact of this selection program, we genotyped the progenitor lines and >600 individuals across multiple cycles of selection using a genome-wide panel of ∼40,000 SNPs. We confirmed previous results showing a steady temporal decrease in genetic diversity within populations and a corresponding increase in differentiation between populations. Thanks to detailed historical information on experimental design, we were able to perform extensive simulations using founder haplotypes to replicate the experiment in the absence of selection. These simulations demonstrate that while most of the observed reduction in genetic diversity can be attributed to genetic drift, heterozygosity in each population has fallen more than expected. We then took advantage of our high-density genotype data to identify extensive regions of haplotype fixation and trace haplotype ancestry to single founder inbred lines. The vast majority of regions showing such evidence of selection differ between the two populations, providing evidence for the dominance model of heterosis. We discuss how this pattern is likely to occur during selection for hybrid performance and how it poses challenges for dissecting the impacts of modern breeding and selection on the maize genome.

Over the past few years, new high-throughput DNA sequencing technologies have dramatically increased speed and reduced sequencing costs. However, the use of these sequencing technologies is often challenged by errors and biases associated with the bioinformatical methods used for analyzing the data. In particular, the use of naïve methods to identify polymorphic sites and infer genotypes can inflate downstream analyses. Recently, explicit modeling of genotype probability distributions has been proposed as a method for taking genotype call uncertainty into account. Based on this idea, we propose a novel method for quantifying population genetic differentiation from next-generation sequencing data. In addition, we present a strategy for investigating population structure via principal components analysis. Through extensive simulations, we compare the new method herein proposed to approaches based on genotype calling and demonstrate a marked improvement in estimation accuracy for a wide range of conditions. We apply the method to a large-scale genomic data set of domesticated and wild silkworms sequenced at low coverage. We find that we can infer the fine-scale genetic structure of the sampled individuals, suggesting that employing this new method is useful for investigating the genetic relationships of populations sampled at low coverage.

Inversions restrict recombination when heterozygous with standard arrangements, but often have few noticeable phenotypic effects. Nevertheless, there are several examples of inversions that can be maintained polymorphic by strong selection under laboratory conditions. A long-standing model for the source of such selection is divergence between arrangements with respect to recessive or partially recessive deleterious mutations, resulting in a selective advantage to heterokaryotypic individuals over homokaryotypes. This paper uses a combination of analytical and numerical methods to investigate this model, for the simple case of an autosomal inversion with multiple independent nucleotide sites subject to mildly deleterious mutations. A complete lack of recombination in heterokaryotypes is assumed, as well as constancy of the frequency of the inversion over space and time. It is shown that a significantly higher mutational load will develop for the less frequent arrangement. A selective advantage to heterokaryotypes is only expected when the two alternative arrangements are nearly equal in frequency, so that their mutational loads are very similar in size. The effects of some Drosophila pseudoobscura polymorphic inversions on fitness traits seem to be too large to be explained by this process, although it may contribute to some of the observed effects. Several population genomic statistics can provide evidence for signatures of a reduced efficacy of selection associated with the rarer of two arrangements, but there is currently little published data that are relevant to the theoretical predictions., Competing Interests: Conflicts of interest The author(s) declare no conflicts of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America.)

Genetic drift is an important evolutionary force of strength inversely proportional to Ne, the effective population size. The impact of drift on genome diversity and evolution is known to vary among species, but quantifying this effect is a difficult task. Here we assess the magnitude of variation in drift power among species of animals via its effect on the mutation load - which implies also inferring the distribution of fitness effects of deleterious mutations. To this aim, we analyze the nonsynonymous (amino-acid changing) and synonymous (amino-acid conservative) allele frequency spectra in a large sample of metazoan species, with a focus on the primates vs. fruit flies contrast. We show that a Gamma model of the distribution of fitness effects is not suitable due to strong differences in estimated shape parameters among taxa, while adding a class of lethal mutations essentially solves the problem. Using the Gamma + lethal model and assuming that the mean deleterious effects of nonsynonymous mutations is shared among species, we estimate that the power of drift varies by a factor of at least 500 between large-Ne and small-Ne species of animals, i.e., an order of magnitude more than the among-species variation in genetic diversity. Our results are relevant to Lewontin's paradox while further questioning the meaning of the Ne parameter in population genomics. [ABSTRACT FROM AUTHOR]

Experimental investigations into the rates and fitness effects of spontaneous mutations are fundamental to our understanding of the evolutionary process. To gain insights into the molecular and fitness consequences of spontaneous mutations, we conducted a mutation accumulation (MA) experiment at varying population sizes in the nematode Caenorhabditis elegans, evolving 35 lines in parallel for 409 generations at three population sizes (N = 1, 10, and 100 individuals). Here, we focus on nuclear SNPs and small insertion/deletions (indels) under minimal influence of selection, as well as their accrual rates in larger populations under greater selection efficacy. The spontaneous rates of base substitutions and small indels are 1.84 (95% C.I. ± 0.14) × 10-9 substitutions and 6.84 (95% C.I. ± 0.97) × 10-10 changes/site/generation, respectively. Small indels exhibit a deletion bias with deletions exceeding insertions by threefold. Notably, there was no correlation between the frequency of base substitutions, nonsynonymous substitutions, or small indels with population size. These results contrast with our previous analysis of mitochondrial DNA mutations and nuclear copy-number changes in these MA lines, and suggest that nuclear base substitutions and small indels are under less stringent purifying selection compared to the former mutational classes. A transition bias was observed in exons as was a near universal base substitution bias toward A/T. Strongly context-dependent base substitutions, where 5'-Ts and 3'-As increase the frequency of A/T → T/A transversions, especially at the boundaries of A or T homopolymeric runs, manifest as higher mutation rates in (i) introns and intergenic regions relative to exons, (ii) chromosomal cores vs. arms and tips, and (iii) germline-expressed genes. [ABSTRACT FROM AUTHOR]

The discrete-time Wright-Fisher (DTWF) model and its diffusion limit are central to population genetics. These models can describe the forward-in-time evolution of allele frequencies in a population resulting from genetic drift, mutation, and selection. Computing likelihoods under the diffusion process is feasible, but the diffusion approximation breaks down for large samples or in the presence of strong selection. Existing methods for computing likelihoods under the DTWF model do not scale to current exome sequencing sample sizes in the hundreds of thousands. Here, we present a scalable algorithm that approximates the DTWF model with provably bounded error. Our approach relies on two key observations about the DTWF model. The first is that transition probabilities under the model are approximately sparse. The second is that transition distributions for similar starting allele frequencies are extremely close as distributions. Together, these observations enable approximate matrix-vector multiplication in linear (as opposed to the usual quadratic) time. We prove similar properties for Hypergeometric distributions, enabling fast computation of likelihoods for subsamples of the population. We show theoretically and in practice that this approximation is highly accurate and can scale to population sizes in the tens of millions, paving the way for rigorous biobank-scale inference. Finally, we use our results to estimate the impact of larger samples on estimating selection coefficients for loss-of-function variants. We find that increasing sample sizes beyond existing large exome sequencing cohorts will provide essentially no additional information except for genes with the most extreme fitness effects., Competing Interests: Conflicts of interest The author(s) declare no conflict of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

We construct a reliable estimation method for evolutionary parameters within the Wright-Fisher model, which describes changes in allele frequencies due to selection and genetic drift, from time-series data. Such data exist for biological populations, for example via artificial evolution experiments, and for the cultural evolution of behavior, such as linguistic corpora that document historical usage of different words with similar meanings. Our method of analysis builds on a Beta-with-Spikes approximation to the distribution of allele frequencies predicted by the Wright-Fisher model. We introduce a self-contained scheme for estimating parameters in the approximation, and demonstrate its robustness with synthetic data, especially in the strong-selection and near-extinction regimes where previous approaches fail. We further apply the method to allele frequency data for baker's yeast (Saccharomyces cerevisiae), finding a significant signal of selection in cases where independent evidence supports such a conclusion. We further demonstrate the possibility of detecting time points at which evolutionary parameters change in the context of a historical spelling reform in the Spanish language., Competing Interests: Conflicts of interest The author(s) declare no conflicts of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America.)

One hundred years ago, the first population genetic calculations were made for two loci. They indicated that populations should settle down to a state where the frequency of an allele at one locus is independent of the frequency of an allele at a second locus, even if these loci are linked. Fifty years later it was realized what is obvious in retrospect, that these calculations ignored the effect of chance segregation of linked loci, an effect now widely recognized following the association of closely linked markers (SNPs) with rare genetic diseases. Linkage disequilibrium is now accepted as the norm for closely linked loci, leading to powerful applications in the mapping of disease alleles and quantitative trait loci, in the detection of sites of selection in the human genome, in the application of genomic prediction of quantitative traits in animal and plant breeding, in the estimation of population size, and in the dating of population divergence. [ABSTRACT FROM AUTHOR]

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. [ABSTRACT FROM AUTHOR]

Humans have colonized the planet through a series of range expansions, which deeply impacted genetic diversity in newly settled areas and potentially increased the frequency of deleterious mutations on expanding wave fronts. To test this prediction, we studied the genomic diversity of French Canadians who colonized Quebec in the 17th century. We used historical information and records from -4000 ascending genealogies to select individuals whose ancestors lived mostly on the colonizing wave front and individuals whose ancestors remained in the core of the settlement. Comparison of exomic diversity reveals that: (i) both new and lowfrequency variants are significantly more deleterious in front than in core individuals, (ii) equally deleterious mutations are at higher frequencies in front individuals, and (iii) front individuals are two times more likely to be homozygous for rare very deleterious mutations present in Europeans. These differences have emerged in the past six to nine generations and cannot be explained by differential inbreeding, but are consistent with relaxed selection mainly due to higher rates of genetic drift on the wave front. Demographic inference and modeling of the evolution of rare variants suggest lower effective size on the front, and lead to an estimation of selection coefficients that increase with conservation scores. Even though range expansions have had a relatively limited impact on the overall fitness of French Canadians, they could explain the higher prevalence of recessive genetic diseases in recently settled regions of Quebec. [ABSTRACT FROM AUTHOR]

Different factors can influence the evolution of the mutation rate of a species: costs associated with DNA replication fidelity, indirect selection caused by the mutations produced (that should generally favor lower mutation rates, given that most mutations affecting fitness are deleterious), and genetic drift, which may render selection acting on weak mutators inefficient. In this paper, we use a two-locus model to compute the strength of indirect selection acting on a modifier locus that affects the mutation rate toward a deleterious allele at a second, linked, locus, in a population undergoing partial selfing or partial clonality. The results show that uniparental reproduction increases the effect of indirect selection for lower mutation rates. Extrapolating to the case of a whole genome with many deleterious alleles, and introducing a direct cost to DNA replication fidelity, the results can be used to compute the evolutionarily stable mutation rate, U. In the absence of mutational bias toward higher U, the analytical prediction fits well with individual-based, multilocus simulation results. When such a bias is added into the simulations, however, genetic drift may lead to the maintenance of higher mutation rates, and this effect may be amplified in highly selfing or highly clonal populations due to their reduced effective population size. [ABSTRACT FROM AUTHOR]

Recent theory predicts that the fitness of pioneer populations can decline when species expand their range, due to high rates of genetic drift on wave fronts making selection less efficient at purging deleterious variants. To test these predictions, we studied the fate of mutator bacteria expanding their range for 1650 generations on agar plates. In agreement with theory, we find that growth abilities of strains with a high mutation rate (HMR lines) decreased significantly over time, unlike strains with a lower mutation rate (LMR lines) that present three to four times fewer mutations. Estimation of the distribution of fitness effect under a spatially explicit model reveals a mean negative effect for new mutations (20.38%), but it suggests that both advantageous and deleterious mutations have accumulated during the experiment. Furthermore, the fitness of HMR lines measured in different environments has decreased relative to the ancestor strain, whereas that of LMR lines remained unchanged. Contrastingly, strains with a HMR evolving in a wellmixed environment accumulated less mutations than agar-evolved strains and showed an increased fitness relative to the ancestor. Our results suggest that spatially expanding species are affected by deleterious mutations, leading to a drastic impairment of their evolutionary potential. [ABSTRACT FROM AUTHOR]

Evolutionary transitions between male and female heterogamety are common in both vertebrates and invertebrates. Theoretical studies of these transitions have found that, when all genotypes are equally fit, continuous paths of intermediate equilibria link the two sex chromosome systems. This observation has led to a belief that neutral evolution along these paths can drive transitions, and that arbitrarily small fitness differences among sex chromosome genotypes can determine the system to which evolution leads. Here, we study stochastic evolutionary dynamics along these equilibrium paths. We find non-neutrality, both in transitions retaining the ancestral pair of sex chromosomes, and in those creating a new pair. In fact, substitution rates are biased in favor of dominant sex determining chromosomes, which fix with higher probabilities than mutations of no effect. Using diffusion approximations, we show that this non-neutrality is a result of "drift-induced selection" operating at every point along the equilibrium paths: stochastic jumps off the paths return with, on average, a directional bias in favor of the dominant segregating sex chromosome. Our results offer a novel explanation for the observed preponderance of dominant sex determining genes, and hint that drift-induced selection may be a common force in standard population genetic systems. [ABSTRACT FROM AUTHOR]

Prophage sequences constitute a substantial fraction of the temperate virus gene pool. Although subject to mutational decay, prophage sequences can also be an important source of adaptive mutations for these viral populations. Here we develop a lifehistory model for temperate viruses, including both the virulent (lytic) and the temperate phases of the life cycle. We then examine the survival of mutations that increase fitness during the lytic phase (attachment rate, burst size), increase fitness in the temperate phase (increasing host survival), or affect transitions between the two phases (integration or induction probability). We find that beneficial mutations are much more likely to survive, ultimately, if they first occur in the prophage state. This conclusion applies even to traits that are only expressed during the lytic phase, and arises due to the substantially lower variance in the offspring distribution during the temperate cycle. This observation, however, is balanced by the fact that many more mutations can be generated during lytic replication. Overall we predict that the prophage state provides a refuge, relatively shielded from genetic drift, in which temperate viruses can explore possible adaptive steps. [ABSTRACT FROM AUTHOR]

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane's application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as a multitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination. We first study the lineage-contamination phenomenon in isolation, deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when U≳sb; where U is deleterious mutation rate and sb is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by ~ 1-U/sb. We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is never zero but is depressed below classical predictions by a factor bounded from below by e-εU/s¯b ; where s¯b is mean selective advantage of beneficial mutations, and ε = 1-e-1 ≈ 0:63: This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or (2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely. [ABSTRACT FROM AUTHOR]

CRISPR/Cas9 gene drive (CGD) promises to be a highly adaptable approach for spreading genetically engineered alleles throughout a species, even if those alleles impair reproductive success. CGD has been shown to be effective in laboratory crosses of insects, yet it remains unclear to what extent potential resistance mechanisms will affect the dynamics of this process in large natural populations. Here we develop a comprehensive population genetic framework for modeling CGD dynamics, which incorporates potential resistance mechanisms as well as random genetic drift. Using this framework, we calculate the probability that resistance against CGD evolves from standing genetic variation, de novo mutation of wild-type alleles, or cleavage repair by nonhomologous end joining (NHEJ) -- a likely by-product of CGD itself. We show that resistance to standard CGD approaches should evolve almost inevitably in most natural populations, unless repair of CGD-induced cleavage via NHEJ can be effectively suppressed, or resistance costs are on par with those of the driver. The key factor determining the probability that resistance evolves is the overall rate at which resistance alleles arise at the population level by mutation or NHEJ. By contrast, the conversion efficiency of the driver, its fitness cost, and its introduction frequency have only minor impact. Our results shed light on strategies that could facilitate the engineering of drivers with lower resistance potential, and motivate the possibility to embrace resistance as a possible mechanism for controlling a CGD approach. This study highlights the need for careful modeling of the population dynamics of CGD prior to the actual release of a driver construct into the wild. [ABSTRACT FROM AUTHOR]

Numerous organismal traits, particularly at the cellular level, are likely to be under persistent directional selection across phylogenetic lineages. Unless all mutations affecting such traits have large enough effects to be efficiently selected in all species, gradients in mean phenotypes are expected to arise as a consequence of differences in the power of random genetic drift, which varies by approximately five orders of magnitude across the Tree of Life. Prior theoretical work examining the conditions under which such gradients can arise focused on the simple situation in which all genomic sites affecting the trait have identical and constant mutational effects. Here, we extend this theory to incorporate the more biologically realistic situation in which mutational effects on a trait differ among nucleotide sites. Pursuit of such modifications leads to the development of semi-analytic expressions for the ways in which selective interference arises via linkage effects in single-effects models, which then extend to more complex scenarios. The theory developed clarifies the conditions under which mutations of different selective effects mutually interfere with each others' fixation and shows how variance in effects among sites can substantially modify and extend the expected scaling relationships between mean phenotypes and effective population sizes., Competing Interests: Conflicts of interest The authors declare no conflict of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Most variants identified in human genome-wide association studies and scans for selection are noncoding. Interpretation of their effects and the way in which they contribute to phenotypic variation and adaptation in human populations is therefore limited by our understanding of gene regulation and the difficulty of confidently linking noncoding variants to genes. To overcome this, we developed a gene-wise test for population-specific selection based on combinations of regulatory variants. Specifically, we use the QX statistic to test for polygenic selection on cis-regulatory variants based on whether the variance across populations in the predicted expression of a particular gene is higher than expected under neutrality. We then applied this approach to human data, testing for selection on 17,388 protein-coding genes in 26 populations from the Thousand Genomes Project. We identified 45 genes with significant evidence (FDR<0.1) for selection, including FADS1, KHK, SULT1A2, ITGAM, and several genes in the HLA region. We further confirm that these signals correspond to plausible population-level differences in predicted expression. While the small number of significant genes (0.2%) is consistent with most cis-regulatory variation evolving under genetic drift or stabilizing selection, it remains possible that there are effects not captured in this study. Our gene-level QX score is independent of standard genomic tests for selection, and may therefore be useful in combination with traditional selection scans to specifically identify selection on regulatory variation. Overall, our results demonstrate the utility of combining population-level genomic data with functional data to understand the evolution of gene expression., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America.)

Natural selection not only affects the actual loci under selection but also leaves "footprints" in patterns of genetic variation in linked genetic regions. This offers exciting opportunities for inferring selection and for understanding the processes shaping levels of genetic variation in natural populations. Here, we develop analytical approximations based on coalescent theory to characterize the genetic footprint of a complex, but potentially common type of natural selection: balancing selection with seasonally fluctuating allele frequencies. As we show analytically and confirm with stochastic simulations, seasonal allele frequency fluctuations can have important (and partly unexpected) consequences for the genetic footprint of balancing selection. Fluctuating balancing selection generally leads to an increase in genetic diversity close to the selected site, the effect of balancing selection, but reduces diversity further away from the selected site, which is a consequence of the allele-frequency fluctuations effectively producing recurrent bottlenecks of allelic backgrounds. This medium- and long-range reduction usually outweighs the short-range increase when averaging diversity levels across the entire chromosome. Strong fluctuating balancing selection even induces a loss of genetic variation in unlinked regions, e.g. on different chromosomes. If many loci in the genome are simultaneously under fluctuating balancing selection this can lead to substantial genome-wide reductions in genetic diversity, even when allele-frequency fluctuations are small and local footprints are difficult to detect. Thus, together with genetic drift, selective sweeps and background selection, fluctuating selection could be a major force shaping levels of genetic diversity in natural populations., Competing Interests: Conflicts of interest None declared., (© The Author(s) 2023. Published by Oxford University Press on behalf of the Genetics Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Mutation, genetic drift, and selection are considered the main factors shaping genetic variation in nature. There is a lack, however, of general predictions accounting for the mutual interrelation between these factors. In the context of the background selection model, we provide a set of equations for the joint prediction of the effective population size and the rate of fixation of deleterious mutations, which are applicable both to sexual and asexual species. For a population of N haploid individuals and a model of deleterious mutations with effect s appearing with rate U in a genome L Morgans long, the asymptotic effective population size (Ne) and the average number of generations (T) between consecutive fixations can be approximated by Ne ≈ N exp [-2U/(2s Ne (1-1/3 UT)3] and T ≈ [exp(2xpNe) - 1][2UsNe]. The solution is applicable to Muller's ratchet, providing satisfactory approximations to the rate of accumulation of mutations for a wide range of parameters. We also obtain predictions of the effective size accounting for the expected nucleotide diversity. Predictions for sexual populations allow for outlining the general conditions where mutational meltdown occurs. The equations can be extended to any distribution of mutational effects and the consideration of hotspots of recombination, showing that Ne is rather insensitive and not proportional to changes in N for many combinations of parameters. This could contribute to explain the observed small differences in levels of polymorphism between species with very different census sizes. [ABSTRACT FROM AUTHOR]

Mutation accumulation (MA) experiments employ the strategy of minimizing the population size of evolving lineages to greatly reduce effects of selection on newly arising mutations. Thus, most mutations fix within MA lines independently of their fitness effects. This approach, more recently combined with genome sequencing, has detailed the rates, spectra, and biases of different mutational processes. However, a quantitative understanding of the fitness effects of mutations virtually unseen by selection has remained an untapped opportunity. Here, we analyzed the fitness of 43 sequenced MA lines of the multi-chromosome bacterium Burkholderia cenocepacia that had each undergone 5554 generations of MA and accumulated an average of 6.73 spontaneous mutations. Most lineages exhibited either neutral or deleterious fitness in three different environments in comparison with their common ancestor. The only mutational class that was significantly overrepresented in lineages with reduced fitness was the loss of the plasmid, though nonsense mutations, missense mutations, and coding insertion-deletions were also overrepresented in MA lineages whose fitness had significantly declined. Although the overall distribution of fitness effects was similar between the three environments, the magnitude and even the sign of the fitness of a number of lineages changed with the environment, demonstrating that the fitness of some genotypes was environmentally dependent. These results present an unprecedented picture of the fitness effects of spontaneous mutations in a bacterium with multiple chromosomes and provide greater quantitative support for the theory that the vast majority of spontaneous mutations are neutral or deleterious. [ABSTRACT FROM AUTHOR]

The effective population size (Ne) is a major factor determining allele frequency changes in natural and experimental populations. Temporal methods provide a powerful and simple approach to estimate short-term Ne: They use allele frequency shifts between temporal samples to calculate the standardized variance, which is directly related to Ne: Here we focus on experimental evolution studies that often rely on repeated sequencing of samples in pools (Pool-seq). Pool-seq is cost-effective and often outperforms individual-based sequencing in estimating allele frequencies, but it is associated with atypical sampling properties: Additional to sampling individuals, sequencing DNA in pools leads to a second round of sampling, which increases the variance of allele frequency estimates. We propose a new estimator of Ne; which relies on allele frequency changes in temporal data and corrects for the variance in both sampling steps. In simulations, we obtain accurate Ne estimates, as long as the drift variance is not too small compared to the sampling and sequencing variance. In addition to genome-wide Ne estimates, we extend our method using a recursive partitioning approach to estimate Ne locally along the chromosome. Since the type I error is controlled, our method permits the identification of genomic regions that differ significantly in their Ne estimates. We present an application to Pool-seq data from experimental evolution with Drosophila and provide recommendations for whole-genome data. The estimator is computationally efficient and available as an R package at https://github.com/ThomasTaus/Nest. [ABSTRACT FROM AUTHOR]

In small populations, genetic linkage between a polymorphic neutral locus and loci subject to selection, either against partially recessive mutations or in favor of heterozygotes, may result in an apparent selective advantage to heterozygotes at the neutral locus (associative overdominance) and a retardation of the rate of loss of variability by genetic drift at this locus. In large populations, selection against deleterious mutations has previously been shown to reduce variability at linked neutral loci (background selection). We describe analytical, numerical, and simulation studies that shed light on the conditions under which retardation vs. acceleration of loss of variability occurs at a neutral locus linked to a locus under selection. We consider a finite, randomly mating population initiated from an infinite population in equilibrium at a locus under selection. With mutation and selection, retardation occurs only when S, the product of twice the effective population size and the selection coefficient, is of order 1. With S ⪢ 1, background selection always causes an acceleration of loss of variability. Apparent heterozygote advantage at the neutral locus is, however, always observed when mutations are partially recessive, even if there is an accelerated rate of loss of variability. With heterozygote advantage at the selected locus, loss of variability is nearly always retarded. The results shed light on experiments on the loss of variability at marker loci in laboratory populations and on the results of computer simulations of the effects of multiple selected loci on neutral variability. [ABSTRACT FROM AUTHOR]

Self-fertilizing species often present lower levels of neutral polymorphism than their outcrossing relatives. Indeed, selfing automatically increases the rate of coalescence per generation, but also enhances the effects of background selection and genetic hitchhiking by reducing the efficiency of recombination. Approximations for the effect of background selection in partially selfing populations have been derived previously, assuming tight linkage between deleterious alleles and neutral loci. However, loosely linked deleterious mutations may have important effects on neutral diversity in highly selfing populations. In this article, I use a general method based on multilocus population genetics theory to express the effect of a deleterious allele on diversity at a linked neutral locus in terms of moments of genetic associations between loci. Expressions for these genetic moments at equilibrium are then computed for arbitrary rates of selfing and recombination. An extrapolation of the results to the case where deleterious alleles segregate at multiple loci is checked using individual-based simulations. At high selfing rates, the tight linkage approximation underestimates the effect of background selection in genomes with moderate to high map length; however, another simple approximation can be obtained for this situation and provides accurate predictions as long as the deleterious mutation rate is not too high. [ABSTRACT FROM AUTHOR]

Deleterious alleles can reach high frequency in small populations because of random fluctuations in allele frequency. This may lead, over time, to reduced average fitness. In this sense, selection is more "effective" in larger populations. Recent studies have considered whether the different demographic histories across human populations have resulted in differences in the number, distribution, and severity of deleterious variants, leading to an animated debate. This article first seeks to clarify some terms of the debate by identifying differences in definitions and assumptions used in recent studies. We argue that variants of Morton, Crow, and Muller's "total mutational damage" provide the soundest and most practical basis for such comparisons. Using simulations, analytical calculations, and 1000 Genomes Project data, we provide an intuitive and quantitative explanation for the observed similarity in genetic load across populations. We show that recent demography has likely modulated the effect of selection and still affects it, but the net result of the accumulated differences is small. Direct observation of differential efficacy of selection for specific allele classes is nevertheless possible with contemporary data sets. By contrast, identifying average genome-wide differences in the efficacy of selection across populations will require many modeling assumptions and is unlikely to provide much biological insight about human populations. [ABSTRACT FROM AUTHOR]

Much of our knowledge about the fitness effects of new mutations has been gained from mutation accumulation (MA) experiments. Yet the fitness effect of single mutations is rarely measured in MA experiments. This raises several issues, notably for inferring epistasis for fitness. The acceleration of fitness decline in MA lines has been taken as evidence for synergistic epistasis, but establishing the role of epistasis requires measuring the fitness of genotypes carrying known numbers of mutations. Otherwise, accelerating fitness loss could be explained by increased genetic mutation rates. Here we segregated mutations accumulated over 4800 generations in haploid and diploid MA lines of the yeast Saccharomyces cerevisiae. We found no correspondence between an accelerated fitness decline and synergistic epistasis among deleterious mutations in haploid lines. Pairs of mutations showed no overall epistasis. Furthermore, several lines of evidence indicate that genetic mutation rates did not increase in the MA lines. Crucially, segregant fitness analyses revealed that MA accelerated in both haploid and diploid lines, even though the fitness of diploid lines was nearly constant during the MA experiment. This suggests that the accelerated fitness decline in haploids was caused by cryptic environmental factors that increased mutation rates in all lines during the last third of the lines' transfers. In addition, we provide new estimates of deleterious mutation rates, including lethal mutations, and highlight that nearly all the mutational load we observed was due to one or two mutations having a large effect on fitness. [ABSTRACT FROM AUTHOR]

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships.We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a "metafounder," a pseudo-individual included as founder of the pedigree and similar to an "unknown parent group." Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given. [ABSTRACT FROM AUTHOR]

The effective population size Ne is a key parameter in population genetics and evolutionary biology, as it quantifies the expected distribution of changes in allele frequency due to genetic drift. Several methods of estimating Ne have been described, the most direct of which uses allele frequencies measured at two or more time points. A new likelihood-based estimator ...B for contemporary effective population size using temporal data is developed in this article. The existing likelihood methods are computationally intensive and unable to handle the case when the underlying Ne is large. This article tries to work around this problem by using a hidden Markov algorithm and applying continuous approximations to allele frequencies and transition probabilities. Extensive simulations are run to evaluate the performance of the proposed estimator ...B; and the results show that it is more accurate and has lower variance than previous methods. The new estimator also reduces the computational time by at least 1000-fold and relaxes the upper bound of Ne to several million, hence allowing the estimation of larger Ne: Finally, we demonstrate how this algorithm can cope with nonconstant Ne scenarios and be used as a likelihood-ratio test to test for the equality of Ne throughout the sampling horizon. An R package "NB" is now available for download to implement the method described in this article. [ABSTRACT FROM AUTHOR]

The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ~16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed. [ABSTRACT FROM AUTHOR]

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 demonstrate that the shape of the reconstructed genealogical tree for a moderately large number of random genomic samples taken from a fitness diverse, but otherwise unstructured, asexual population can be used to predict the relative fitness of individuals within the sample. To achieve this we define a heuristic algorithm, which we test in silico, using simulations of a Wright-Fisher model for a realistic range of mutation rates and selection strength. Our inferred fitness ranking is based on a linear discriminator that identifies rapidly coalescing lineages in the reconstructed tree. Inferred fitness ranking correlates strongly with actual fitness, with a genome in the top 10% ranked being in the top 20% fittest with false discovery rate of 0.1-0.3, depending on the mutation/selection parameters. The ranking also enables us to predict the genotypes that future populations inherit from the present one. While the inference accuracy increases monotonically with sample size, samples of 200 nearly saturate the performance. We propose that our approach can be used for inferring relative fitness of genomes obtained in single-cell sequencing of tumors and in monitoring viral outbreaks. [ABSTRACT FROM AUTHOR]

We study the population genetics of two neutral alleles under reversible mutation in a model that features a skewed offspring distribution, called the Λ-Fleming-Viot process. We describe the shape of the equilibrium allele frequency distribution as a function of the model parameters. We show that the mutation rates can be uniquely identified from this equilibrium distribution, but the form of the offspring distribution cannot itself always be so identified. We introduce an estimator for the mutation rate that is consistent, independent of the form of reproductive skew. We also introduce a two-allele infinite-sites version of the Λ-Fleming--Viot process, and we use it to study how reproductive skew influences standing genetic diversity in a population. We derive asymptotic formulas for the expected number of segregating sites as a function of sample size and offspring distribution. We find that the Wright-Fisher model minimizes the equilibrium genetic diversity, for a given mutation rate and variance effective population size, compared to all other Λ-processes. [ABSTRACT FROM AUTHOR]

Transposable elements are often considered as selfish DNA sequences able to invade the genome of their host species. Their evolutive dynamics are complex, due to the interaction between their intrinsic amplification capacity, selection at the host level, transposition regulation, and genetic drift. Here, we propose modeling the first steps of TE invasion, i.e., just after a horizontal transfer, when a single copy is present in the genome of one individual. If the element has a constant transposition rate, it will disappear in most cases: the elements with low-transposition rate are frequently lost through genetic drift, while those with high-transposition rate may amplify, leading to the sterility of their host. Elements whose transposition rate is regulated are able to successfully invade the populations, thanks to an initial transposition burst followed by a strong limitation of their activity. Self-regulation or hybrid dysgenesis may thus represent some genome-invasion parasitic strategies.