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The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary – but fixed – spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings C = C t t = 0 ∞ from a finite set G to itself. The set G represents the "sites" (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, C t : G → G , maps each site g ∈ G to the site containing g 's ancestor, t time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio r , we find that measures of genetic dissimilarity, among any set of sites, are scaled by 4 r (1 − r) relative to the even sex ratio case. [ABSTRACT FROM AUTHOR]

With the availability of high-quality full genome polymorphism (SNPs) data, it becomes feasible to study the past demographic and selective history of populations in exquisite detail. However, such inferences still suffer from a lack of statistical resolution for recent, for example bottlenecks, events, and/or for populations with small nucleotide diversity. Additional heritable (epi)genetic markers, such as indels, transposable elements, microsatellites, or cytosine methylation, may provide further, yet untapped, information on the recent past population history. We extend the Sequential Markovian Coalescent (SMC) framework to jointly use SNPs and other hyper-mutable markers. We are able to (1) improve the accuracy of demographic inference in recent times, (2) uncover past demographic events hidden to SNP-based inference methods, and (3) infer the hyper-mutable marker mutation rates under a finite site model. As a proof of principle, we focus on demographic inference in Arabidopsis thaliana using DNA methylation diversity data from 10 European natural accessions. We demonstrate that segregating single methylated polymorphisms (SMPs) satisfy the modeling assumptions of the SMC framework, while differentially methylated regions (DMRs) are not suitable as their length exceeds that of the genomic distance between two recombination events. Combining SNPs and SMPs while accounting for site- and region-level epimutation processes, we provide new estimates of the glacial age bottleneck and post-glacial population expansion of the European A. thaliana population. Our SMC framework readily accounts for a wide range of heritable genomic markers, thus paving the way for next-generation inference of evolutionary history by combining information from several genetic and epigenetic markers.

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright–Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data. [ABSTRACT FROM AUTHOR]

Runs of homozygosity (ROH) and identity-by-descent (IBD) sharing can be studied in diploid coalescent models by noting that ROH and IBD-sharing at a genomic site are predicted to be inversely related to coalescence times—which in turn can be mathematically obtained in terms of parameters describing consanguinity rates. Comparing autosomal and X-chromosomal coalescent models, we consider ROH and IBD-sharing in relation to consanguinity that proceeds via multiple forms of first-cousin mating. We predict that across populations with different levels of consanguinity, (1) in a manner that is qualitatively parallel to the increase of autosomal IBD-sharing with autosomal ROH, X-chromosomal IBD-sharing increases with X-chromosomal ROH, owing to the dependence of both quantities on consanguinity levels; (2) even in the absence of consanguinity, X-chromosomal ROH and IBD-sharing levels exceed corresponding values for the autosomes, owing to the smaller population size and lower coalescence time for the X chromosome than for autosomes; (3) with matrilateral consanguinity, the relative increase in ROH and IBD-sharing on the X chromosome compared to the autosomes is greater than in the absence of consanguinity. Examining genome-wide SNPs in human populations for which consanguinity levels have been estimated, we find that autosomal and X-chromosomal ROH and IBD-sharing levels generally accord with the predictions. We find that each 1% increase in autosomal ROH is associated with an increase of 2.1% in X-chromosomal ROH, and each 1% increase in autosomal IBD-sharing is associated with an increase of 1.6% in X-chromosomal IBD-sharing. For each calculation, particularly for ROH, the estimate is reasonably close to the increase of 2% predicted by the population-size difference between autosomes and X chromosomes. The results support the utility of coalescent models for understanding patterns of genomic sharing and their dependence on sex-biased processes. [ABSTRACT FROM AUTHOR]

Multiple-merger coalescents, also known as Λ -coalescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure Λ , which describes the rates of the multiple-merger events, is key to understand these processes. So far, most inference methods only work for some particular families of Λ -coalescents that are described by only one parameter, but not for more general models. This article is devoted to the construction of a non-parametric estimator of the density of Λ that is based on the observation at a single time of the so-called Site Frequency Spectrum (SFS), which describes the allelic frequencies in a present population sample. First, we produce estimates of the multiple-merger rates by solving a linear system, whose coefficients are obtained by appropriately subsampling the SFS. Then, we use a technique that aggregates the information extracted from the previous step through a kernel type of re-construction to give a non-parametric estimation of the measure Λ. We give a consistency result of this estimator under mild conditions on the behavior of Λ around 0. We also show some numerical examples of how our method performs. [ABSTRACT FROM AUTHOR]

One of the main necessities for population geneticists is the availability of sensitive statistical tools that enable to accept or reject the standard Wright–Fisher model of neutral evolution. A number of statistical tests have been developed to detect specific deviations from the null frequency spectrum in different directions (e.g., Tajima's D, Fu and Li's F and D tests, Fay and Wu's H). A general framework exists to generate all neutrality tests that are linear functions of the frequency spectrum. In this framework, it is possible to develop a family of optimal tests with almost maximum power against a specific alternative evolutionary scenario. In this paper we provide a thorough discussion of the structure and properties of linear and nonlinear neutrality tests. First, we present the general framework for linear tests and emphasise the importance of the property of scalability with the sample size (that is, the interpretation of the tests should not depend on the sample size), which, if missing, can lead to errors in interpreting the data. After summarising the motivation and structure of linear optimal tests, we present a more general framework for the optimisation of linear tests, leading to a new family of tunable neutrality tests. In a further generalisation, we extend the framework to nonlinear neutrality tests and we derive nonlinear optimal tests for polynomials of any degree in the frequency spectrum. [ABSTRACT FROM AUTHOR]

Modern agricultural practices, climate change, and globalization foster the rapid spread of plant pathogens, such as the maize fungal pathogen Setosphaeria turcica , which causes Northern corn leaf blight and expanded into Central Europe during the twentieth century. To investigate the rapid expansion of S. turcica , we sequenced 121 isolates from Europe and Kenya. Population genomic inference revealed a single genetically diverse cluster in Kenya and three clonal lineages with low diversity, as well as one cluster of multiple clonal sublineages in Europe. Phylogenetic dating suggests that all European lineages originated through sexual reproduction outside Europe and were subsequently introgressed multiple times. Unlike isolates from Kenya, European isolates did not show sexual recombination, despite the presence of both MAT1-1 and MAT1-2 mating types. For the clonal lineages, coalescent model selection supported a selectively neutral model with strong exponential population growth, rather than models with pervasive positive selection caused by host defense resistance or environmental adaptation. Within clonal lineages, phenotypic variation in virulence to different monogenic resistances, which defines the pathogen races, suggests that these races may originate from repeated mutations in virulence genes. Association testing based on k -mers did not identify genomic regions linked to pathogen races, but it did uncover strongly differentiated genomic regions between clonal lineages, which harbor genes with putative roles in pathogenicity. In conclusion, the expansion and population growth of S. turcica in Europe are mainly driven by an expansion of the maize cultivation area and not by rapid adaptation. [ABSTRACT FROM AUTHOR]

Recurrent mutation produces multiple copies of the same allele which may be co-segregating in a population. Yet, most analyses of allele-frequency or site-frequency spectra assume that all observed copies of an allele trace back to a single mutation. We develop a sampling theory for the number of latent mutations in the ancestry of a rare variant, specifically a variant observed in relatively small count in a large sample. Our results follow from the statistical independence of low-count mutations, which we show to hold for the standard neutral coalescent or diffusion model of population genetics as well as for more general coalescent trees. For populations of constant size, these counts are distributed like the number of alleles in the Ewens sampling formula. We develop a Poisson sampling model for populations of varying size and illustrate it using new results for site-frequency spectra in an exponentially growing population. We apply our model to a large data set of human SNPs and use it to explain dramatic differences in site-frequency spectra across the range of mutation rates in the human genome. [ABSTRACT FROM AUTHOR]

Inferring the demographic history of species is a great challenge in population genetics. This history is classically represented as a history of size changes, ignoring population structure. We present here the work carried out over the last decade around the concept of IICR (Inverse Instantaneous Coalescence Rate), which makes it possible to link, on the one hand, the history of the true population size for a panmictic population, and the inferred size, sometimes called "effective size", when structure is taken into account. We show that population structure can lead to misinterpretations of some demographic history inference results, we propose a framework for inferring structure-specific demographic parameters (number and size of subpopulations, migration rates), and we analyze the link between IICR and some form of selection modeling on genetic sequences.

Principal component analysis (PCA) is one of the most frequently-used approach to describe population structure from multilocus genotype data. Regarding geographic range expansions of modern humans, interpretations of PCA have, however, been questioned, as there is uncertainty about the wave-like patterns that have been observed in principal components. It has indeed been argued that wave-like patterns are mathematical artifacts that arise generally when PCA is applied to data in which genetic differentiation increases with geographic distance. Here, we present an alternative theory for the observation of wave-like patterns in PCA. We study a coalescent model – the umbrella model – for the diffusion of genetic variants. The model is based on genetic drift without any particular geographical structure. In the umbrella model, splits from an ancestral population occur almost continuously in time, giving birth to small daughter populations at a regular pace. Our results provide detailed mathematical descriptions of eigenvalues and eigenvectors for the PCA of sampled genomic sequences under the model. When variants uniquely represented in the sample are removed, the PCA eigenvectors are defined as cosine functions of increasing periodicity, reproducing wave-like patterns observed in equilibrium isolation-by-distance models. Including singleton variants in the analysis, the eigenvectors corresponding to the largest eigenvalues exhibit complex wave shapes. The accuracy of our predictions is further investigated with coalescent simulations. Our analysis supports the hypothesis that highly structured wave-like patterns could arise from genetic drift only, and may not always be artificial outcomes of spatially structured data. Genomic data related to the peopling of the Americas are reanalyzed in the light of our new theory. [ABSTRACT FROM AUTHOR]

The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to zero or diverge to infinity, and show undesirable sensitivity to perturbations in the data. The goal of this article is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographies and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model, and generalize our intuition to arbitrary sample sizes using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only [Formula: see text] epochs, where [Formula: see text] is between [Formula: see text] and [Formula: see text] The set of expected SFS for piecewise-constant demographies with fewer than [Formula: see text] epochs is open and nonconvex, which causes the above phenomena for inference from data.

Geographically separated populations can convergently adapt to the same selection pressure. Convergent evolution at the level of a gene may arise via three distinct modes. The selected alleles can (1) have multiple independent mutational origins, (2) be shared due to shared ancestral standing variation, or (3) spread throughout subpopulations via gene flow. We present a model-based, statistical approach that utilizes genomic data to detect cases of convergent adaptation at the genetic level, identify the loci involved and distinguish among these modes. To understand the impact of convergent positive selection on neutral diversity at linked loci, we make use of the fact that hitchhiking can be modeled as an increase in the variance in neutral allele frequencies around a selected site within a population. We build on coalescent theory to show how shared hitchhiking events between subpopulations act to increase covariance in allele frequencies between subpopulations at loci near the selected site, and extend this theory under different models of migration and selection on the same standing variation. We incorporate this hitchhiking effect into a multivariate normal model of allele frequencies that also accounts for population structure. Based on this theory, we present a composite-likelihood-based approach that utilizes genomic data to identify loci involved in convergence, and distinguishes among alternate modes of convergent adaptation. We illustrate our method on genome-wide polymorphism data from two distinct cases of convergent adaptation. First, we investigate the adaptation for copper toxicity tolerance in two populations of the common yellow monkey flower, Mimulus guttatus We show that selection has occurred on an allele that has been standing in these populations prior to the onset of copper mining in this region. Lastly, we apply our method to data from four populations of the killifish, Fundulus heteroclitus, that show very rapid convergent adaptation for tolerance to industrial pollutants. Here, we identify a single locus at which both independent mutation events and selection on an allele shared via gene flow, either slightly before or during selection, play a role in adaptation across the species' range.

By providing additional opportunities for coalescence within families, the presence of consanguineous unions in a population reduces coalescence times relative to non-consanguineous populations. First-cousin consanguinity can take one of six forms differing in the configuration of sexes in the pedigree of the male and female cousins who join in a consanguineous union: patrilateral parallel, patrilateral cross, matrilateral parallel, matrilateral cross, bilateral parallel, and bilateral cross. Considering populations with each of the six types of first-cousin consanguinity individually and a population with a mixture of the four unilateral types, we examine coalescent models of consanguinity. We previously computed, for first-cousin consanguinity models, the mean coalescence time for X-chromosomal loci and the limiting distribution of coalescence times for autosomal loci. Here, we use the separation-of-time-scales approach to obtain the limiting distribution of coalescence times for X-chromosomal loci. This limiting distribution has an instantaneous coalescence probability that depends on the probability that a union is consanguineous; lineages that do not coalesce instantaneously coalesce according to an exponential distribution. We study the effects on the coalescence time distribution of the type of first-cousin consanguinity, showing that patrilateral-parallel and patrilateral-cross consanguinity have no effect on X-chromosomal coalescence time distributions and that matrilateral-parallel consanguinity decreases coalescence times to a greater extent than does matrilateral-cross consanguinity. [ABSTRACT FROM AUTHOR]

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds on rates of convergence for parametric estimators in migration models. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible. [ABSTRACT FROM AUTHOR]

Properties of gene genealogies such as tree height (H), total branch length (L), total lengths of external (E) and internal (I) branches, mean length of basal branches (B), and the underlying coalescence times (T) can be used to study population-genetic processes and to develop statistical tests of population-genetic models. Uses of tree features in statistical tests often rely on predictions that depend on pairwise relationships among such features. For genealogies under the coalescent, we provide exact expressions for Taylor approximations to expected values and variances of ratios Xn/Yn, for all 15 pairs among the variables {Hn; Ln; En; In; Bn; Tk}, considering n leaves and 2 ≤ k ≤ n. For expected values of the ratios, the approximations match closely with empirical simulation-based values. The approximations to the variances are not as accurate, but they generally match simulations in their trends as n increases. Although En has expectation 2 and Hn has expectation 2 in the limit as n → ∞, the approximation to the limiting expectation for En/Hn is not 1, instead equaling π²/3 - 2 ≈ 1.28987. The new approximations augment fundamental results in coalescent theory on the shapes of genealogical trees. [ABSTRACT FROM AUTHOR]

We study the time to the most recent common ancestor of a sample of finite size in a wide class of genealogical models for populations with variable size. This is made possible by recently developed results on inhomogeneous phase-type random variables, allowing us to obtain the density and the moments of the TMRCA of time-dependent coalescent processes in terms of matrix formulas. We also provide matrix simplifications permitting a more straightforward calculation. With these results, the TMRCA provides an explicative variable to distinguish different evolutionary scenarios.

With the availability of high-quality full genome polymorphism (SNPs) data, it becomes feasible to study the past demographic and selective history of populations in exquisite detail. However, such inferences still suffer from a lack of statistical resolution for recent, for example bottlenecks, events, and/or for populations with small nucleotide diversity. Additional heritable (epi)genetic markers, such as indels, transposable elements, microsatellites, or cytosine methylation, may provide further, yet untapped, information on the recent past population history. We extend the Sequential Markovian Coalescent (SMC) framework to jointly use SNPs and other hyper-mutable markers. We are able to (1) improve the accuracy of demographic inference in recent times, (2) uncover past demographic events hidden to SNP-based inference methods, and (3) infer the hyper-mutable marker mutation rates under a finite site model. As a proof of principle, we focus on demographic inference in Arabidopsis thaliana using DNA methylation diversity data from 10 European natural accessions. We demonstrate that segregating single methylated polymorphisms (SMPs) satisfy the modeling assumptions of the SMC framework, while differentially methylated regions (DMRs) are not suitable as their length exceeds that of the genomic distance between two recombination events. Combining SNPs and SMPs while accounting for site- and region-level epimutation processes, we provide new estimates of the glacial age bottleneck and post-glacial population expansion of the European A. thaliana population. Our SMC framework readily accounts for a wide range of heritable genomic markers, thus paving the way for next-generation inference of evolutionary history by combining information from several genetic and epigenetic markers., Competing Interests: TS, FJ, AT No competing interests declared, (© 2023, Sellinger et al.)

Many metagenomic and environmental DNA studies require the taxonomic assignment of individual reads or sequences by aligning reads to a reference database, known as taxonomic binning. When a read aligns to more than one reference sequence, it is often classified based on sequence similarity. This step can assign reads to incorrect taxa, at a rate which depends both on the assignment algorithm and on underlying population genetic and database parameters. In particular, as we move towards using environmental DNA to study eukaryotic taxa subject to regular recombination, we must take into account issues concerning gene tree discordance. Though accuracy is often compared across algorithms using a fixed data set, the relative impact of these population genetic and database parameters on accuracy has not yet been quantified. Here, we develop both a theoretical and simulation framework in the simplified case of two reference species, and compute binning accuracy over a wide range of parameters, including sequence length, species–query divergence time, divergence times of the reference species, reference database completeness, sample age and effective population size. We consider two assignment methods and contextualize our results using parameters from a recent ancient environmental DNA study, comparing them to the commonly used discriminative k‐mer‐based method Clark (Current Biology, 31, 2021, 2728; BMC Genomics, 16, 2015, 1). Our results quantify the degradation in assignment accuracy as the samples diverge from their closest reference sequence, and with incompleteness of reference sequences. We also provide a framework in which others can compute expected accuracy for their particular method or parameter set. Code is available at https://github.com/bdesanctis/binning‐accuracy. [ABSTRACT FROM AUTHOR]

Premise: Accurate species delimitation is essential for evolutionary biology, conservation, and biodiversity management. We studied species delimitation in North American pinyon pines, Pinus subsection Cembroides, a natural group with high levels of incomplete lineage sorting. Methods: We used coalescent‐based methods and multivariate analyses of low‐copy number nuclear genes and nearly complete high‐copy number plastomes generated with the Hyb‐Seq method. The three coalescent‐based species delimitation methods evaluated were the Generalized Mixed Yule Coalescent (GMYC), Poisson Tree Process (PTP), and Trinomial Distribution of Triplets (Tr2). We also measured admixture in populations with possible introgression. Results: Our results show inconsistencies among GMYC, PTP, and Tr2. The single‐locus based GMYC analysis of plastid DNA recovered a higher number of species (up to 24 entities, including singleton lineages and clusters) than PTP and the multi‐locus coalescent approach. The PTP analysis identified 10 species whereas Tr2 recovered 13, which agreed closely with taxonomic treatments. Conclusions: We found that PTP and GMYC identified species with low levels of ILS and high morphological divergence (P. maximartinezii, P. pinceana, and P. rzedowskii). However, GMYC method oversplit species by identification of more divergent samples as singletons. Moreover, both PTP and GMYC were incapable of identifying some species that are readily identified morphologically. We suggest that the divergence times between lineages within North American pinyon pines are so disparate that GMYC results are unreliable. Results of the Tr2 method coincided well with previous delimitations based on morphology, DNA, geography, and secondary chemistry. [ABSTRACT FROM AUTHOR]

Linear functions of the site frequency spectrum (SFS) play a major role for understanding and investigating genetic diversity. Estimators of the mutation rate (e.g. based on the total number of segregating sites or average of the pairwise differences) and tests for neutrality (e.g. Tajima’s D) are perhaps the most well-known examples. The distribution of linear functions of the SFS is important for constructing confidence intervals for the estimators, and to determine significance thresholds for neutrality tests. These distributions are often approximated using simulation procedures. In this paper we use multivariate phase-type theory to specify, characterize and calculate the distribution of linear functions of the site frequency spectrum. In particular, we show that many of the classical estimators of the mutation rate are distributed according to a discrete phase-type distribution. Neutrality tests, however, are generally not discrete phase-type distributed. For neutrality tests we derive the probability generating function using continuous multivariate phase-type theory, and numerically invert the function to obtain the distribution. A main result is an analytically tractable formula for the probability generating function of the SFS. Software implementation of the phase-type methodology is available in the R package PhaseTypeR, and R code for the reproduction of our results is available as an accompanying vignette. [ABSTRACT FROM AUTHOR]

Abstract Background Inferring phylogenetic relationships of polyploid species and their diploid ancestors (leading to reticulate phylogenies in the case of an allopolyploid origin) based on multi-locus sequence data is complicated by the unknown assignment of alleles found in polyploids to diploid subgenomes. A parsimony-based approach to this problem has been proposed by Oberprieler et al. (Methods Ecol Evol 8:835–849, 2017), however, its implementation is of limited practical value. In addition to previously identified shortcomings, it has been found that in some cases, the obtained results barely satisfy the applied criterion. To be of better use to other researchers, a reimplementation with methodological refinement appears to be indispensable. Results We present the AllCoPol package, which provides a heuristic method for assigning alleles from polyploids to diploid subgenomes based on the Minimizing Deep Coalescences (MDC) criterion in multi-locus sequence datasets. An additional consensus approach further allows to assess the confidence of phylogenetic reconstructions. Simulations of tetra- and hexaploids show that under simplifying assumptions such as completely disomic inheritance, the topological errors of reconstructed phylogenies are similar to those of MDC species trees based on the true allele partition. Conclusions AllCoPol is a Python package for phylogenetic reconstructions of polyploids offering enhanced functionality as well as improved usability. The included methods are supplied as command line tools without the need for prior programming knowledge.

The use of genetic polymorphism data to understand the dynamics of adaptation and identify the loci that are involved has become a major pursuit of modern evolutionary genetics. In addition to the classical "hard sweep" hitchhiking model, recent research has drawn attention to the fact that the dynamics of adaptation can play out in a variety of different ways and that the specific signatures left behind in population genetic data may depend somewhat strongly on these dynamics. One particular model for which a large number of empirical examples are already known is that in which a single derived mutation arises and drifts to some low frequency before an environmental change causes the allele to become beneficial and sweeps to fixation. Here, we pursue an analytical investigation of this model, bolstered and extended via simulation study. We use coalescent theory to develop an analytical approximation for the effect of a sweep from standing variation on the genealogy at the locus of the selected allele and sites tightly linked to it. We show that the distribution of haplotypes that the selected allele is present on at the time of the environmental change can be approximated by considering recombinant haplotypes as alleles in the infinite-alleles model. We show that this approximation can be leveraged to make accurate predictions regarding patterns of genetic polymorphism following such a sweep. We then use simulations to highlight which sources of haplotypic information are likely to be most useful in distinguishing this model from neutrality, as well as from other sweep models, such as the classic hard sweep and multiple-mutation soft sweeps. We find that in general, adaptation from a unique standing variant will likely be difficult to detect on the basis of genetic polymorphism data from a single population time point alone, and when it can be detected, it will be difficult to distinguish from other varieties of selective sweeps. Samples from multiple populations and/or time points have the potential to ease this difficulty.

Consanguineous unions increase the frequency at which identical genomic segments are inherited along separate paths of descent, decreasing coalescence times for pairs of alleles drawn from an individual who is the offspring of a consanguineous pair. For an autosomal locus, it has recently been shown that the mean time to the most recent common ancestor (T M R C A) for two alleles in the same individual and the mean T M R C A for two alleles in two separate individuals both decrease with increasing consanguinity in a population. Here, we extend this analysis to the X chromosome, considering X-chromosomal coalescence times under a coalescent model with diploid, male–female mating pairs. We examine four possible first-cousin mating schemes that are equivalent in their effects on autosomes, but that have differing effects on the X chromosome: patrilateral-parallel, patrilateral-cross, matrilateral-parallel, and matrilateral-cross. In each mating model, we calculate mean T M R C A for X-chromosomal alleles sampled either within or between individuals. We describe a consanguinity effect on X-chromosomal T M R C A that differs from the autosomal pattern under matrilateral but not under patrilateral first-cousin mating. For matrilateral first cousins, the effect of consanguinity in reducing T M R C A is stronger on the X chromosome than on the autosomes, with an increased effect of parallel-cousin mating compared to cross-cousin mating. The theoretical computations support the utility of the model in understanding patterns of genomic sharing on the X chromosome. [ABSTRACT FROM AUTHOR]

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.

Abstract Background Our current understanding of archaic admixture in humans relies on statistical methods with large biases, whose magnitudes depend on the sizes and separation times of ancestral populations. To avoid these biases, it is necessary to estimate these parameters simultaneously with those describing admixture. Genetic estimates of population histories also confront problems of statistical identifiability: different models or different combinations of parameter values may fit the data equally well. To deal with this problem, we need methods of model selection and model averaging, which are lacking from most existing software. Results The Legofit software package allows simultaneous estimation of parameters describing admixture, and the sizes and separation times of ancestral populations. It includes facilities for data manipulation, estimation, analysis of residuals, model selection, and model averaging. Conclusions Legofit uses genetic data to study the history of a subdivided population. It is unaffected by recent history and can therefore focus on the deep history of population size, subdivision, and admixture. It outperforms several statistical methods that have been widely used to study population history and should be useful in any species for which DNA sequence data is available from several populations.

As populations boom and bust, the accumulation of genetic diversity is modulated, encoding histories of living populations in present-day variation. Many methods exist to decode these histories, and all must make strong model assumptions. It is typical to assume that mutations accumulate uniformly across the genome at a constant rate that does not vary between closely related populations. However, recent work shows that mutational processes in human and great ape populations vary across genomic regions and evolve over time. This perturbs the mutation spectrum (relative mutation rates in different local nucleotide contexts). Here, we develop theoretical tools in the framework of Kingman's coalescent to accommodate mutation spectrum dynamics. We present mutation spectrum history inference (mushi), a method to perform nonparametric inference of demographic and mutation spectrum histories from allele frequency data. We use mushi to reconstruct trajectories of effective population size and mutation spectrum divergence between human populations, identify mutation signatures and their dynamics in different human populations, and calibrate the timing of a previously reported mutational pulse in the ancestors of Europeans. We show that mutation spectrum histories can be placed in a well-studied theoretical setting and rigorously inferred from genomic variation data, like other features of evolutionary history. [ABSTRACT FROM AUTHOR]

Genome studies of facultative sexual species, which can either reproduce sexually or asexually, are providing insight into the evolutionary consequences of mixed reproductive modes. It is currently unclear to what extent the evolutionary history of facultative sexuals' genomes can be approximated by the standard coalescent, and if a coalescent effective population size N e exists. Here, I determine if and when these approximations can be made. When sex is frequent (occurring at a frequency much greater than 1 / N per reproduction per generation, for N the actual population size), the underlying genealogy can be approximated by the standard coalescent, with a coalescent N e ≈ N ⁠. When sex is very rare (at frequency much lower than 1 / N ⁠), approximations for the pairwise coalescent time can be obtained, which is strongly influenced by the frequencies of sex and mitotic gene conversion, rather than N ⁠. However, these terms do not translate into a coalescent N e ⁠. These results are used to discuss the best sampling strategies for investigating the evolutionary history of facultative sexual species. [ABSTRACT FROM AUTHOR]

Phylogeography combines geographic information with phylogenetic and population genomic approaches to infer the evolutionary history of a 1. species or population in a geographic context. This approach has been instrumental in understanding the emergence, spread. and evolution of a range; of plant pathogens. In particular. phylogeography can address questions about where a pathogen originated, whether it is native or introduced, and when and how often introductions occurred. We review the theory, methods. and approaches underpinning phylogeographic inference and highlight applications providing novel insights into the emergence and spread of select pathogens. We hope that this review will be useful in assessing the power, pitfalls, and opportunities presented by various phylogeographic approaches. [ABSTRACT FROM AUTHOR]

Organisms from microbes to humans engage in a variety of social behaviors, which affect fitness in complex, often nonlinear ways. The question of how these behaviors evolve has consequences ranging from antibiotic resistance to human origins. However, evolution with nonlinear social interactions is challenging to model mathematically, especially in combination with spatial, group, and/or kin assortment. We derive a mathematical condition for natural selection with synergistic interactions among any number of individuals. This result applies to populations with arbitrary (but fixed) spatial or network structure, group subdivision, and/or mating patterns. In this condition, nonlinear fitness effects are ascribed to collectives, and weighted by a new measure of collective relatedness. For weak selection, this condition can be systematically evaluated by computing branch lengths of ancestral trees. We apply this condition to pairwise games between diploid relatives, and to dilemmas of collective help or harm among siblings and on spatial networks. Our work provides a rigorous basis for extending the notion of "actor", in the study of social evolution, from individuals to collectives., (© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

Computational evolutionary biology, statistical phylogenetics and coalescent-based population genetics are becoming increasingly central to the analysis and understanding of molecular sequence data. We present the Bayesian Evolutionary Analysis by Sampling Trees (BEAST) software package version 1.7, which implements a family of Markov chain Monte Carlo (MCMC) algorithms for Bayesian phylogenetic inference, divergence time dating, coalescent analysis, phylogeography and related molecular evolutionary analyses. This package includes an enhanced graphical user interface program called Bayesian Evolutionary Analysis Utility (BEAUti) that enables access to advanced models for molecular sequence and phenotypic trait evolution that were previously available to developers only. The package also provides new tools for visualizing and summarizing multispecies coalescent and phylogeographic analyses. BEAUti and BEAST 1.7 are open source under the GNU lesser general public license and available at http://beast-mcmc.googlecode.com and http://beast.bio.ed.ac.uk.

Molecular evolution offers an insightful theory to interpret the genomic consequences of thermal adaptation to previous events of climate change beyond range shifts. However, disentangling often mixed footprints of selective and demographic processes from those due to lineage sorting, recombination rate variation, and genomic constrains is not trivial. Therefore, here we condense current and historical population genomic tools to study thermal adaptation and outline key developments (genomic prediction, machine learning) that might assist their utilization for improving forecasts of populations’ responses to thermal variation. We start by summarizing how recent thermal-driven selective and demographic responses can be inferred by coalescent methods and in turn how quantitative genetic theory offers suitable multi-trait predictions over a few generations via the breeder’s equation. We later assume that enough generations have passed as to display genomic signatures of divergent selection to thermal variation and describe how these footprints can be reconstructed using genome-wide association and selection scans or, alternatively, may be used for forward prediction over multiple generations under an infinitesimal genomic prediction model. Finally, we move deeper in time to comprehend the genomic consequences of thermal shifts at an evolutionary time scale by relying on phylogeographic approaches that allow for reticulate evolution and ecological parapatric speciation, and end by envisioning the potential of modern machine learning techniques to better inform long-term predictions. We conclude that foreseeing future thermal adaptive responses requires bridging the multiple spatial scales of historical and predictive environmental change research under modern cohesive approaches such as genomic prediction and machine learning frameworks.

The process of species diversification is traditionally summarized by a single tree, the species tree, whose reconstruction from molecular data is hindered by frequent conflicts between gene genealogies. Here, we argue that instead of seeing these conflicts as nuisances, we can exploit them to inform the diversification process itself. We adopt a gene‐based view of diversification to model the ubiquitous presence of gene flow between diverging lineages, one of the most important processes explaining disagreements among gene trees. We propose a new framework for modelling the joint evolution of gene and species lineages relaxing the hierarchy between the species tree and gene trees inherent to the standard view, as embodied in a popular model known as the multispecies coalescent (MSC). We implement this framework in two alternative models called the gene‐based diversification models (GBD): (a) GBD‐forward following all evolving genomes through time and (b) GBD‐backward based on coalescent theory. They feature four parameters tuning colonization, gene flow, genetic drift and genetic differentiation. We propose an inference method based on differences between gene trees. Applied to two empirical data sets prone to gene flow, we find better support for the GBD‐backward model than for the MSC model. Along with the increasing awareness of the extent of gene flow, this work shows the importance of considering the richer signal contained in genomic histories, rather than in the mere species tree, to better apprehend the complex evolutionary history of species. [ABSTRACT FROM AUTHOR]

Molecular evolution offers an insightful theory to interpret the genomic consequences of thermal adaptation to previous events of climate change beyond range shifts. However, disentangling often mixed footprints of selective and demographic processes from those due to lineage sorting, recombination rate variation, and genomic constrains is not trivial. Therefore, here we condense current and historical population genomic tools to study thermal adaptation and outline key developments (genomic prediction, machine learning) that might assist their utilization for improving forecasts of populations' responses to thermal variation. We start by summarizing how recent thermal-driven selective and demographic responses can be inferred by coalescent methods and in turn how quantitative genetic theory offers suitable multi-trait predictions over a few generations via the breeder's equation. We later assume that enough generations have passed as to display genomic signatures of divergent selection to thermal variation and describe how these footprints can be reconstructed using genome-wide association and selection scans or, alternatively, may be used for forward prediction over multiple generations under an infinitesimal genomic prediction model. Finally, we move deeper in time to comprehend the genomic consequences of thermal shifts at an evolutionary time scale by relying on phylogeographic approaches that allow for reticulate evolution and ecological parapatric speciation, and end by envisioning the potential of modern machine learning techniques to better inform long-term predictions. We conclude that foreseeing future thermal adaptive responses requires bridging the multiple spatial scales of historical and predictive environmental change research under modern cohesive approaches such as genomic prediction and machine learning frameworks. [ABSTRACT FROM AUTHOR]

The sample frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, migrations, and other demographic events affecting a set of populations. The expected multipopulation SFS under a given demographic model can be efficiently computed when the populations in the model are related by a tree, scaling to hundreds of populations. Admixture, back-migration, and introgression are common natural processes that violate the assumption of a tree-like population history, however, and until now the expected SFS could be computed for only a handful of populations when the demographic history is not a tree. In this article, we present a new method for efficiently computing the expected SFS and linear functionals of it, for demographies described by general directed acyclic graphs. This method can scale to more populations than previously possible for complex demographic histories including admixture. We apply our method to an 8-population SFS to estimate the timing and strength of a proposed "basal Eurasian" admixture event in human history. We implement and release our method in a new open-source software package momi2. [ABSTRACT FROM AUTHOR]

Only 6% of known species have a conservation status. Methods that assess conservation statuses are often based on individual counts and are thus too laborious to be generalized to all species. Population genomics methods that infer past variations in population size are easy to use but limited to the relatively distant past. Here we propose a population genomics approach that tests for recent population decline and may be used to assess species conservation statuses. More specifically, we study Maximal Recombination Free (MRF) blocks, that are segments of a sequence alignment inherited from a common ancestor without recombination. MRF blocks are relatively longer in small than in large populations. We use the distribution of MRF block lengths rescaled by their mean to test for recent population decline. However, because MRF blocks are difficult to detect, we also consider Maximal Linkage Disequilibrium (MLD) blocks, which are runs of single nucleotide polymorphisms compatible with a single tree. We develop a new method capable of inferring a very recent decline (e.g. with a detection power of 50% for populations whose size was halved to N , 0.05 × N generations ago) from rescaled MLD block lengths. Our framework could serve as a basis for quantitative tools to assess conservation status in a wide range of species. [ABSTRACT FROM AUTHOR]

First inspired by the seminal work of Lewontin and Krakauer (1973. Distribution of gene frequency as a test of the theory of the selective neutrality of polymorphisms. Genetics 74(1):175–195.) and Maynard Smith and Haigh (1974. The hitch-hiking effect of a favourable gene. Genet Res. 23(1):23–35.), genomic scans for positive selection remain a widely utilized tool in modern population genomic analysis. Yet, the relative frequency and genomic impact of selective sweeps have remained a contentious point in the field for decades, largely owing to an inability to accurately identify their presence and quantify their effects—with current methodologies generally being characterized by low true-positive rates and/or high false-positive rates under many realistic demographic models. Most of these approaches are based on Wright–Fisher assumptions and the Kingman coalescent and generally rely on detecting outlier regions which do not conform to these neutral expectations. However, previous theoretical results have demonstrated that selective sweeps are well characterized by an alternative class of model known as the multiple-merger coalescent. Taken together, this suggests the possibility of not simply identifying regions which reject the Kingman, but rather explicitly testing the relative fit of a genomic window to the multiple-merger coalescent. We describe the advantages of such an approach, which owe to the branching structure differentiating selective and neutral models, and demonstrate improved power under certain demographic scenarios relative to a commonly used approach. However, regions of the demographic parameter space continue to exist in which neither this approach nor existing methodologies have sufficient power to detect selective sweeps. [ABSTRACT FROM AUTHOR]

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, such as the seminal work of Li and Durbin, attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure—the history of multiple subpopulations that merge, split, and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem. [ABSTRACT FROM AUTHOR]

Phylogeography has grown explosively in the two decades since the word was coined and the discipline was outlined in 1987. Here I summarize the many achievements and novel perspectives that phylogeography has brought to population genetics, phylogenetic biology and biogeography. I also address future directions for the field. From the introduction of mitochondrial DNA assays in the late 1970s, to the key distinction between gene trees and species phylogenies, to the ongoing era of multi-locus coalescent theory, phylogeographic perspectives have consistently challenged conventional genetic and evolutionary paradigms, and they have forged empirical and conceptual bridges between the formerly separate disciplines of population genetics (microevolutionary analysis) and phylogenetic biology (in macroevolution). © 2008 The Author.

Delineating Evolutionary Significant Units for conservation purposes is a crucial step in conservation. Across a distribution range, species frequently display population structure that drives the distribution of genetic diversity. These patterns of genetic structure and diversity result from intricate interactions between biogeographic history and demographic dynamics. Prior biogeographic knowledge, however, is scarcely available, a trend particularly pronounced in the tropics where the taxonomic impediment is hampering biogeographic studies and conservation efforts. DNA barcoding has been initially proposed to foster taxonomic studies through the development of an automated molecular system of species identification. While its utility for species identification is increasingly acknowledged, its usefulness for fast and large-scale delineation of ESU remains to be explored. If proved to be useful for that purpose, DNA barcoding may also open new perspectives in conservation by quickly providing preliminary information about population conservation status. The present study aims at assessing the utility of DNA barcoding for the delineation of ESUs among the most common freshwater fish species of Java and Bali through the comparison of population genetic structures and diversification patterns across multiple species. Substantial levels of cryptic diversity are discovered among the three widely distributed freshwater fish species analyzed with a total of 21 evolutionary independent mitochondrial lineages (BINs) observed in Barbodes binotatus, Channa gachua and Glyptothorax platypogon. The maximum genetic distance for each coalescent tree ranges from 6.78 to 7.76 K2P genetic distances for C. gachua and G. platypogon, respectively. Diversification and population genetic analyses support a scenario of allopatric differentiation. The analysis of the BINs spatial distribution indicates concordant distribution patterns among the three species that allow identifying 18 ESUs. Implications for the conservation genetics of these species are discussed at the light of the history of the region.

Abstract Background Genotypes not directly measured in genetic studies are often imputed to improve statistical power and to increase mapping resolution. The accuracy of standard imputation techniques strongly depends on the similarity of linkage disequilibrium (LD) patterns in the study and reference populations. Here we develop a novel approach for genotype imputation in low-recombination regions that relies on the coalescent and permits to explicitly account for population demographic factors. To test the new method, study and reference haplotypes were simulated and gene trees were inferred under the basic coalescent and also considering population growth and structure. The reference haplotypes that first coalesced with study haplotypes were used as templates for genotype imputation. Computer simulations were complemented with the analysis of real data. Genotype concordance rates were used to compare the accuracies of coalescent-based and standard (IMPUTE2) imputation. Results Simulations revealed that, in LD-blocks, imputation accuracy relying on the basic coalescent was higher and less variable than with IMPUTE2. Explicit consideration of population growth and structure, even if present, did not practically improve accuracy. The advantage of coalescent-based over standard imputation increased with the minor allele frequency and it decreased with population stratification. Results based on real data indicated that, even in low-recombination regions, further research is needed to incorporate recombination in coalescence inference, in particular for studies with genetically diverse and admixed individuals. Conclusions To exploit the full potential of coalescent-based methods for the imputation of missing genotypes in genetic studies, further methodological research is needed to reduce computer time, to take into account recombination, and to implement these methods in user-friendly computer programs. Here we provide reproducible code which takes advantage of publicly available software to facilitate further developments in the field.

Isolation-with-migration (IM) models have become popular for explaining population divergence in the presence of migrations. Bayesian methods are commonly used to estimate IM models, but they are limited to small data analysis or simple model inference. Recently three methods, IMa3, MIST, and AIM, resolved these limitations. Here, we describe the major problems addressed by these three software and compare differences among their inference methods, despite their use of the same standard likelihood function.