2BAD: an application to estimate the parental contributions during two independent admixture events

Several approaches have been developed to calculate the relative contributions of parental populations in single admixture event scenarios, including Bayesian methods. In many breeds and populations, it may be more realistic to consider multiple admixture events. However, no approach has been developed to date to estimate admixture in such cases. This report describes a program application, 2BAD (for 2-event Bayesian ADmixture), which allows the consideration of up to two independent admixture events involving two or three parental populations and a single admixed population, depending on the number of populations sampled. For each of these models, it is possible to estimate several parameters (admixture, effective sizes, etc.) using an approximate Bayesian computation approach. In addition, the program allows comparing pairs of admixture models, determining which is the most likely given data. The application was tested through simulations and was found to provide good estimates for the contribution of the populations at the two admixture events. We were also able to determine whether an admixture model was more likely than a simple split model.     

Evaluation of model fit of inferred admixture proportions

Model based methods for genetic clustering of individuals, such as those implemented in structure or ADMIXTURE, allow the user to infer individual ancestries and study population structure. The underlying model makes several assumptions about the demographic history that shaped the analysed genetic data. One assumption is that all individuals are a result of K homogeneous ancestral populations that are all well represented in the data, while another assumption is that no drift happened after the admixture event. The histories of many real world populations do not conform to that model, and in that case taking the inferred admixture proportions at face value might be misleading. We propose a method to evaluate the fit of admixture models based on estimating the correlation of the residual difference between the true genotypes and the genotypes predicted by the model. When the model assumptions are not violated, the residuals from a pair of individuals are not correlated. In the case of a bad fitting admixture model, individuals with similar demographic histories have a positive correlation of their residuals. Using simulated and real data, we show how the method is able to detect a bad fit of inferred admixture proportions due to using an insufficient number of clusters K or to demographic histories that deviate significantly from the admixture model assumptions, such as admixture from ghost populations, drift after admixture events and nondiscrete ancestral populations. We have implemented the method as an open source software that can be applied to both unphased genotypes and low depth sequencing data.     

Inferring Admixture Histories of Human Populations Using Linkage Disequilibrium

Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele frequency divergences or patterns of ancestry segments in chromosomes of admixed individuals. An emerging new approach harnesses the exponential decay of admixture-induced linkage disequilibrium (LD) as a function of genetic distance. Here, we comprehensively develop LD-based inference into a versatile tool for investigating admixture. We present a new weighted LD statistic that can be used to infer mixture proportions as well as dates with fewer constraints on reference populations than previous methods. We define an LD-based three-population test for admixture and identify scenarios in which it can detect admixture events that previous formal tests cannot. We further show that we can uncover phylogenetic relationships among populations by comparing weighted LD curves obtained using a suite of references. Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the calculations. We implement all of these advances in a software package, ALDER, which we validate in simulations and apply to test for admixture among all populations from the Human Genome Diversity Project (HGDP), highlighting insights into the admixture history of Central African Pygmies, Sardinians, and Japanese.     

Population divergence with or without admixture: selecting models using an ABC approach

Genetic data have been widely used to reconstruct the demographic history of populations, including the estimation of migration rates, divergence times and relative admixture contribution from different populations. Recently, increasing interest has been given to the ability of genetic data to distinguish alternative models. One of the issues that has plagued this kind of inference is that ancestral shared polymorphism is often difficult to separate from admixture or gene flow. Here, we applied an approximate Bayesian computation (ABC) approach to select the model that best fits microsatellite data among alternative splitting and admixture models. We performed a simulation study and showed that with reasonably large data sets (20 loci) it is possible to identify with a high level of accuracy the model that generated the data. This suggests that it is possible to distinguish genetic patterns due to past admixture events from those due to shared polymorphism (population split without admixture). We then apply this approach to microsatellite data from an endangered and endemic Iberian freshwater fish species, in which a clustering analysis suggested that one of the populations could be admixed. In contrast, our results suggest that the observed genetic patterns are better explained by a population split model without admixture.     

Assessing the performance of qpAdm: a statistical tool for studying population admixture

qpAdm is a statistical tool for studying the ancestry of populations with histories that involve admixture between two or more source populations. Using qpAdm, it is possible to identify plausible models of admixture that fit the population history of a group of interest and to calculate the relative proportion of ancestry that can be ascribed to each source population in the model. Although qpAdm is widely used in studies of population history of human (and nonhuman) groups, relatively little has been done to assess its performance. We performed a simulation study to assess the behavior of qpAdm under various scenarios in order to identify areas of potential weakness and establish recommended best practices for use. We find that qpAdm is a robust tool that yields accurate results in many cases, including when data coverage is low, there are high rates of missing data or ancient DNA damage, or when diploid calls cannot be made. However, we caution against co-analyzing ancient and present-day data, the inclusion of an extremely large number of reference populations in a single model, and analyzing population histories involving extended periods of gene flow. We provide a user guide suggesting best practices for the use of qpAdm.     

Population genetics models of local ancestry

Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population structure and gene flow and interpret genomes of individuals that have ancestry from multiple source populations as mosaics of segments originating from each population. This article describes general and tractable models for local ancestry patterns with a focus on the length distribution of continuous ancestry tracts and the variance in total ancestry proportions among individuals. The models offer improved agreement with Wright-Fisher simulation data when compared to the state-of-the art and can be used to infer time-dependent migration rates from multiple populations. Considering HapMap African-American (ASW) data, we find that a model with two distinct phases of "European" gene flow significantly improves the modeling of both tract lengths and ancestry variances.     

Testing for ancient admixture between closely related populations

One enduring question in evolutionary biology is the extent of archaic admixture in the genomes of present-day populations. In this paper, we present a test for ancient admixture that exploits the asymmetry in the frequencies of the two nonconcordant gene trees in a three-population tree. This test was first applied to detect interbreeding between Neandertals and modern humans. We derive the analytic expectation of a test statistic, called the D statistic, which is sensitive to asymmetry under alternative demographic scenarios. We show that the D statistic is insensitive to some demographic assumptions such as ancestral population sizes and requires only the assumption that the ancestral populations were randomly mating. An important aspect of D statistics is that they can be used to detect archaic admixture even when no archaic sample is available. We explore the effect of sequencing error on the false-positive rate of the test for admixture, and we show how to estimate the proportion of archaic ancestry in the genomes of present-day populations. We also investigate a model of subdivision in ancestral populations that can result in D statistics that indicate recent admixture.     

Bayesian identification of admixture events using multilocus molecular markers

Bayesian statistical methods for the estimation of hidden genetic structure of populations have gained considerable popularity in the recent years. Utilizing molecular marker data, Bayesian mixture models attempt to identify a hidden population structure by clustering individuals into genetically divergent groups, whereas admixture models target at separating the ancestral sources of the alleles observed in different individuals. We discuss the difficulties involved in the simultaneous estimation of the number of ancestral populations and the levels of admixture in studied individuals' genomes. To resolve this issue, we introduce a computationally efficient method for the identification of admixture events in the population history. Our approach is illustrated by analyses of several challenging real and simulated data sets. The software (baps), implementing the methods introduced here, is freely available at http://www.rni.helsinki.fi/~jic/bapspage.html.     

Likelihood‐based inference of population history from low‐coverage de novo genome assemblies

Short‐read sequencing technologies have in principle made it feasible to draw detailed inferences about the recent history of any organism. In practice, however, this remains challenging due to the difficulty of genome assembly in most organisms and the lack of statistical methods powerful enough to discriminate between recent, nonequilibrium histories. We address both the assembly and inference challenges. We develop a bioinformatic pipeline for generating outgroup‐rooted alignments of orthologous sequence blocks from de novo low‐coverage short‐read data for a small number of genomes, and show how such sequence blocks can be used to fit explicit models of population divergence and admixture in a likelihood framework. To illustrate our approach, we reconstruct the Pleistocene history of an oak‐feeding insect (the oak gallwasp Biorhiza pallida), which, in common with many other taxa, was restricted during Pleistocene ice ages to a longitudinal series of southern refugia spanning the Western Palaearctic. Our analysis of sequence blocks sampled from a single genome from each of three major glacial refugia reveals support for an unexpected history dominated by recent admixture. Despite the fact that 80% of the genome is affected by admixture during the last glacial cycle, we are able to infer the deeper divergence history of these populations. These inferences are robust to variation in block length, mutation model and the sampling location of individual genomes within refugia. This combination of de novo assembly and numerical likelihood calculation provides a powerful framework for estimating recent population history that can be applied to any organism without the need for prior genetic resources.     

Robust estimation of local genetic ancestry in admixed populations using a nonparametric bayesian approach

We present a new haplotype-based approach for inferring local genetic ancestry of individuals in an admixed population. Most existing approaches for local ancestry estimation ignore the latent genetic relatedness between ancestral populations and treat them as independent. In this article, we exploit such information by building an inheritance model that describes both the ancestral populations and the admixed population jointly in a unified framework. Based on an assumption that the common hypothetical founder haplotypes give rise to both the ancestral and the admixed population haplotypes, we employ an infinite hidden Markov model to characterize each ancestral population and further extend it to generate the admixed population. Through an effective utilization of the population structural information under a principled nonparametric Bayesian framework, the resulting model is significantly less sensitive to the choice and the amount of training data for ancestral populations than state-of-the-art algorithms. We also improve the robustness under deviation from common modeling assumptions by incorporating population-specific scale parameters that allow variable recombination rates in different populations. Our method is applicable to an admixed population from an arbitrary number of ancestral populations and also performs competitively in terms of spurious ancestry proportions under a general multiway admixture assumption. We validate the proposed method by simulation under various admixing scenarios and present empirical analysis results from a worldwide-distributed dataset from the Human Genome Diversity Project.     

Population admixture,biological invasions and the balance between local adaptation and inbreeding depression

When previously isolated populations meet and mix, the resulting admixed population can benefit from several genetic advantages, including increased genetic variation, the creation of novel genotypes and the masking of deleterious mutations. These admixture benefits are thought to play an important role in biological invasions. In contrast, populations in their native range often remain differentiated and frequently suffer from inbreeding depression owing to isolation. While the advantages of admixture are evident for introduced populations that experienced recent bottlenecks or that face novel selection pressures, it is less obvious why native range populations do not similarly benefit from admixture. Here we argue that a temporary loss of local adaptation in recent invaders fundamentally alters the fitness consequences of admixture. In native populations, selection against dilution of the locally adapted gene pool inhibits unconstrained admixture and reinforces population isolation, with some level of inbreeding depression as an expected consequence. We show that admixture is selected against despite significant inbreeding depression because the benefits of local adaptation are greater than the cost of inbreeding. In contrast, introduced populations that have not yet established a pattern of local adaptation can freely reap the benefits of admixture. There can be strong selection for admixture because it instantly lifts the inbreeding depression that had built up in isolated parental populations. Recent work in Silene suggests that reduced inbreeding depression associated with post-introduction admixture may contribute to enhanced fitness of invasive populations. We hypothesize that in locally adapted populations, the benefits of local adaptation are balanced against an inbreeding cost that could develop in part owing to the isolating effect of local adaptation itself. The inbreeding cost can be revealed in admixing populations during recent invasions.     

Autosomal Admixture Levels Are Informative About Sex Bias in Admixed Populations

Sex-biased admixture has been observed in a wide variety of admixed populations. Genetic variation in sex chromosomes and functions of quantities computed from sex chromosomes and autosomes have often been examined to infer patterns of sex-biased admixture, typically using statistical approaches that do not mechanistically model the complexity of a sex-specific history of admixture. Here, expanding on a model of Verdu and Rosenberg (2011) that did not include sex specificity, we develop a model that mechanistically examines sex-specific admixture histories. Under the model, multiple source populations contribute to an admixed population, potentially with their male and female contributions varying over time. In an admixed population descended from two source groups, we derive the moments of the distribution of the autosomal admixture fraction from a specific source population as a function of sex-specific introgression parameters and time. Considering admixture processes that are constant in time, we demonstrate that surprisingly, although the mean autosomal admixture fraction from a specific source population does not reveal a sex bias in the admixture history, the variance of autosomal admixture is informative about sex bias. Specifically, the long-term variance decreases as the sex bias from a contributing source population increases. This result can be viewed as analogous to the reduction in effective population size for populations with an unequal number of breeding males and females. Our approach suggests that it may be possible to use the effect of sex-biased admixture on autosomal DNA to assist with methods for inference of the history of complex sex-biased admixture processes.     

An Extended Admixture Pulse Model Reveals the Limitations to Human–Neandertal Introgression Dating

Neandertal DNA makes up 2–3% of the genomes of all non-African individuals. The patterns of Neandertal ancestry in modern humans have been used to estimate that this is the result of gene flow that occurred during the expansion of modern humans into Eurasia, but the precise dates of this event remain largely unknown. Here, we introduce an extended admixture pulse model that allows joint estimation of the timing and duration of gene flow. This model leads to simple expressions for both the admixture segment distribution and the decay curve of ancestry linkage disequilibrium, and we show that these two statistics are closely related. In simulations, we find that estimates of the mean time of admixture are largely robust to details in gene flow models, but that the duration of the gene flow can only be recovered if gene flow is very recent and the exact recombination map is known. These results imply that gene flow from Neandertals into modern humans could have happened over hundreds of generations. Ancient genomes from the time around the admixture event are thus likely required to resolve the question when, where, and for how long humans and Neandertals interacted.     

Genomewide analysis of admixture and adaptation in the Africanized honeybee

Genetic exchange by hybridization or admixture can make an important contribution to evolution, and introgression of favourable alleles can facilitate adaptation to new environments. A small number of honeybees (Apis mellifera) with African ancestry were introduced to Brazil ~60 years ago, which dispersed and hybridized with existing managed populations of European origin, quickly spreading across much of the Americas in an example of a massive biological invasion. Here, we analyse whole‐genome sequences of 32 Africanized honeybees sampled from throughout Brazil to study the effect of this process on genome diversity. By comparison with ancestral populations from Europe and Africa, we infer that these samples have 84% African ancestry, with the remainder from western European populations. However, this proportion varies across the genome and we identify signals of positive selection in regions with high European ancestry proportions. These observations are largely driven by one large gene‐rich 1.4‐Mbp segment on chromosome 11 where European haplotypes are present at a significantly elevated frequency and likely confer an adaptive advantage in the Africanized honeybee population. This region has previously been implicated in reproductive traits and foraging behaviour in worker bees. Finally, by analysing the distribution of ancestry tract lengths in the context of the known time of the admixture event, we are able to infer an average generation time of 2.0 years. Our analysis highlights the processes by which populations of mixed genetic ancestry form and adapt to new environments.     

Mixed signals from hybrid genomes

Admixture results from interbreeding between individuals from different populations or species that were previously genetically isolated from each other (Fig.  1 ). Identifying admixture events in the genome is not always a straightforward task, because the genetic signature left behind fades with time as recombination events fragment the genomic segments introduced during the interbreeding event. Additionally, when the genetic architecture of populations or species that admix is not very different (e.g. they coalesce to a common ancestor recently), admixture signatures may be difficult to detect. Ignoring the effects of admixture can, however, pose severe problems for population genetic analyses that rely on the distribution of polymorphic markers across the genome. In this issue of Molecular Ecology, Bosse et al. ( 2014 ) analyse genomic data from modern pigs to understand hybridization processes that occurred between domestic pigs from European and Asiatic origin, and between pigs and wild boars. Their results are interesting regarding the fine‐scale distribution of admixture across the pig genome, and the way in which this admixture biases estimates of the effective population size in European domestic pigs. The implications of these results are significant, as they serve as a cautionary note on genomic analyses that depend on the distribution of polymorphic variants in potentially admixed populations.     

Asymptotically robust variance estimation for person‐time incidence rates

Person‐time incidence rates are frequently used in medical research. However, standard estimation theory for this measure of event occurrence is based on the assumption of independent and identically distributed (iid) exponential event times, which implies that the hazard function remains constant over time. Under this assumption and assuming independent censoring, observed person‐time incidence rate is the maximum‐likelihood estimator of the constant hazard, and asymptotic variance of the log rate can be estimated consistently by the inverse of the number of events. However, in many practical applications, the assumption of constant hazard is not very plausible. In the present paper, an average rate parameter is defined as the ratio of expected event count to the expected total time at risk. This rate parameter is equal to the hazard function under constant hazard. For inference about the average rate parameter, an asymptotically robust variance estimator of the log rate is proposed. Given some very general conditions, the robust variance estimator is consistent under arbitrary iid event times, and is also consistent or asymptotically conservative when event times are independent but nonidentically distributed. In contrast, the standard maximum‐likelihood estimator may become anticonservative under nonconstant hazard, producing confidence intervals with less‐than‐nominal asymptotic coverage. These results are derived analytically and illustrated with simulations. The two estimators are also compared in five datasets from oncology studies.     

Bayesian analysis of an admixture model with mutations and arbitrarily linked markers

We introduce here a Bayesian analysis of a classical admixture model in which all parameters are simultaneously estimated. Our approach follows the approximate Bayesian computation (ABC) framework, relying on massive simulations and a rejection-regression algorithm. Although computationally intensive, this approach can easily deal with complex mutation models and partially linked loci, and it can be thoroughly validated without much additional computation cost. Compared to a recent maximum-likelihood (ML) method, the ABC approach leads to similarly accurate estimates of admixture proportions in the case of recent admixture events, but it is found superior when the admixture is more ancient. All other parameters of the admixture model such as the divergence time between parental populations, the admixture time, and the population sizes are also well estimated, unlike the ML method. The use of partially linked markers does not introduce any particular bias in the estimation of admixture, but ML confidence intervals are found too narrow if linkage is not specifically accounted for. The application of our method to an artificially admixed domestic bee population from northwest Italy suggests that the admixture occurred in the last 10-40 generations and that the parental Apis mellifera and A. ligustica populations were completely separated since the last glacial maximum.     

Estimating admixture pedigrees of recent hybrids without a contiguous reference genome

The genome of recently admixed individuals or hybrids has characteristic genetic patterns that can be used to learn about their recent admixture history. One of these are patterns of interancestry heterozygosity, which can be inferred from SNP data from either called genotypes or genotype likelihoods, without the need for information on genomic location. This makes them applicable to a wide range of data that are often used in evolutionary and conservation genomic studies, such as low-depth sequencing mapped to scaffolds and reduced representation sequencing. Here we implement maximum likelihood estimation of interancestry heterozygosity patterns using two complementary models. We furthermore develop apoh (Admixture Pedigrees of Hybrids), a software that uses estimates of paired ancestry proportions to detect recently admixed individuals or hybrids, and to suggest possible admixture pedigrees. It furthermore calculates several hybrid indices that make it easier to identify and rank possible admixture pedigrees that could give rise to the estimated patterns. We implemented apoh both as a command line tool and as a Graphical User Interface that allows the user to automatically and interactively explore, rank and visualize compatible recent admixture pedigrees, and calculate the different summary indices. We validate the performance of the method using admixed family trios from the 1000 Genomes Project. In addition, we show its applicability on identifying recent hybrids from RAD-seq data of Grant's gazelle (Nanger granti and Nanger petersii) and whole genome low-depth data of waterbuck (Kobus ellipsiprymnus) which shows complex admixture of up to four populations.     

Disentangling Signatures of Selection Before and After European Colonization in Latin Americans

Throughout human evolutionary history, large-scale migrations have led to intermixing (i.e., admixture) between previously separated human groups. Although classical and recent work have shown that studying admixture can yield novel historical insights, the extent to which this process contributed to adaptation remains underexplored. Here, we introduce a novel statistical model, specific to admixed populations, that identifies loci under selection while determining whether the selection likely occurred post-admixture or prior to admixture in one of the ancestral source populations. Through extensive simulations, we show that this method is able to detect selection, even in recently formed admixed populations, and to accurately differentiate between selection occurring in the ancestral or admixed population. We apply this method to genome-wide SNP data of ∼4,000 individuals in five admixed Latin American cohorts from Brazil, Chile, Colombia, Mexico, and Peru. Our approach replicates previous reports of selection in the human leukocyte antigen region that are consistent with selection post-admixture. We also report novel signals of selection in genomic regions spanning 47 genes, reinforcing many of these signals with an alternative, commonly used local-ancestry-inference approach. These signals include several genes involved in immunity, which may reflect responses to endemic pathogens of the Americas and to the challenge of infectious disease brought by European contact. In addition, some of the strongest signals inferred to be under selection in the Native American ancestral groups of modern Latin Americans overlap with genes implicated in energy metabolism phenotypes, plausibly reflecting adaptations to novel dietary sources available in the Americas.     

Ancient Admixture in Human History

Population mixture is an important process in biology. We present a suite of methods for learning about population mixtures, implemented in a software package called ADMIXTOOLS, that support formal tests for whether mixture occurred and make it possible to infer proportions and dates of mixture. We also describe the development of a new single nucleotide polymorphism (SNP) array consisting of 629,433 sites with clearly documented ascertainment that was specifically designed for population genetic analyses and that we genotyped in 934 individuals from 53 diverse populations. To illustrate the methods, we give a number of examples that provide new insights about the history of human admixture. The most striking finding is a clear signal of admixture into northern Europe, with one ancestral population related to present-day Basques and Sardinians and the other related to present-day populations of northeast Asia and the Americas. This likely reflects a history of admixture between Neolithic migrants and the indigenous Mesolithic population of Europe, consistent with recent analyses of ancient bones from Sweden and the sequencing of the genome of the Tyrolean “Iceman.”