A classical likelihood based approach for admixture mapping using EM algorithm

Several disease-mapping methods have been proposed recently, which use the information generated by recent admixture of populations from historically distinct geographic origins. These methods include both classic likelihood and Bayesian approaches. In this study we directly maximize the likelihood function from the hidden Markov Model for admixture mapping using the EM algorithm, allowing for uncertainty in model parameters, such as the allele frequencies in the parental populations. We determined the robustness of the proposed method by examining the ancestral allele frequency estimate and individual marker-location specific ancestry when the data were generated by different population admixture models and no learning sample was used. The proposed method outperforms a widely used Bayesian MCMC strategy for data generated from various population admixture models. The multipoint information content for ancestry was derived based on the map provided by Smith et al. (2004) and the associated statistical power was calculated. We examined the distribution of admixture LD across the genome for both real and simulated data and established a threshold for genome wide significance applicable to admixture mapping studies. The software ADMIXPROGRAM for performing admixture mapping is available from authors.     

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.     

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.     

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.     

Fast and accurate population admixture inference from genotype data from a few microsatellites to millions of SNPs

Model-based (likelihood and Bayesian) and non-model-based (PCA and K-means clustering) methods were developed to identify populations and assign individuals to the identified populations using marker genotype data. Model-based methods are favoured because they are based on a probabilistic model of population genetics with biologically meaningful parameters and thus produce results that are easily interpretable and applicable. Furthermore, they often yield more accurate structure inferences than non-model-based methods. However, current model-based methods either are computationally demanding and thus applicable to small problems only or use simplified admixture models that could yield inaccurate results in difficult situations such as unbalanced sampling. In this study, I propose new likelihood methods for fast and accurate population admixture inference using genotype data from a few multiallelic microsatellites to millions of diallelic SNPs. The methods conduct first a clustering analysis of coarse-grained population structure by using the mixture model and the simulated annealing algorithm, and then an admixture analysis of fine-grained population structure by using the clustering results as a starting point in an expectation maximisation algorithm. Extensive analyses of both simulated and empirical data show that the new methods compare favourably with existing methods in both accuracy and running speed. They can analyse small datasets with just a few multiallelic microsatellites but can also handle in parallel terabytes of data with millions of markers and millions of individuals. In difficult situations such as many and/or lowly differentiated populations, unbalanced or very small samples of individuals, the new methods are substantially more accurate than other methods.Subject terms: Population genetics, Evolutionary ecology     

An empirical assessment of individual-based population genetic statistical techniques: application to British pig breeds

Recently developed Bayesian genotypic clustering methods for analysing genetic data offer a powerful tool to evaluate the genetic structure of domestic farm animal breeds. The unit of study with these approaches is the individual instead of the population. We aimed to empirically evaluate various individual-based population genetic statistical methods for characterization of genetic diversity and structure of livestock breeds. Eighteen British pig populations, comprising 819 individuals, were genotyped at 46 microsatellite markers. Three Bayesian genotypic clustering approaches, principle component analysis (PCA) and phylogenetic reconstruction were applied to individual multilocus genotypes to infer the genetic structure and diversity of the British pig breeds. Comparisons of the three Bayesian genotypic clustering methods (, and ) revealed some broad similarities but also some notable differences. Overall, the methods agreed that majority of the British pig breeds are independent genetic units with little evidence of admixture. The three Bayesian genotypic clustering methods provided complementary, biologically credible clustering solutions but at different levels of resolution. detected finer genetic differentiation and in some cases, populations within breeds. Consequently, it estimated a greater number of underlying genetic populations (K, in the notation of Bayesian clustering methods). Two of the Bayesian methods ( and ) and phylogenetic reconstruction provided similar success in assignment of individuals, supporting the use of these methods for breed assignment.     

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.     

Distinguishing migration from isolation: a Markov chain Monte Carlo approach

A Markov chain Monte Carlo method for estimating the relative effects of migration and isolation on genetic diversity in a pair of populations from DNA sequence data is developed and tested using simulations. The two populations are assumed to be descended from a panmictic ancestral population at some time in the past and may (or may not) after that be connected by migration. The use of a Markov chain Monte Carlo method allows the joint estimation of multiple demographic parameters in either a Bayesian or a likelihood framework. The parameters estimated include the migration rate for each population, the time since the two populations diverged from a common ancestral population, and the relative size of each of the two current populations and of the common ancestral population. The results show that even a single nonrecombining genetic locus can provide substantial power to test the hypothesis of no ongoing migration and/or to test models of symmetric migration between the two populations. The use of the method is illustrated in an application to mitochondrial DNA sequence data from a fish species: the threespine stickleback (Gasterosteus aculeatus).     

The population genetic effects of ancestry and admixture in a subdivided cattle breed

The genetic structure of the Dexter, a minority cattle breed with complex demographic history, was investigated using microsatellite markers and a range of statistical approaches designed to detect both admixture and genetic drift. Modern representatives of two putative ancestral populations, the Devon and Kerry, together with the different populations of the Dexter, which have experienced different demographic histories, were analysed. Breed units showed comparatively high levels of genetic variability ( H _E = 0.63–0.68); however, distinct genetic subgroups were detected within the Dexter, which could be attributed to known demographic events. Much lower diversity was identified in three small, isolated Dexter populations ( H _E = 0.52–0.55) and higher differentiation ( F _ST > 0.13) was found. For one of these populations, where strong selection has taken place, we also found evidence of a demographic bottleneck. Three methods for quantifying breed admixture were applied and substantial method-based variation in estimates for the genetic contribution of the two proposed ancestral populations for each subdivision of the Dexter was found. Results were consistent only in the case of a group consisting of selected Traditional Dexter animals, where the ancestor of the modern Kerry breed was also determined as the greater parental contributor to the Dexter. The inconsistency of estimation of admixture proportions between the methods highlights the potentially confounding role of genetic drift in shaping small population structure, and the consequences of accurately describing population histories from contemporary genetic data.     

Estimating mutation parameters,population history and genealogy simultaneously from temporally spaced sequence data

Molecular sequences obtained at different sampling times from populations of rapidly evolving pathogens and from ancient subfossil and fossil sources are increasingly available with modern sequencing technology. Here, we present a Bayesian statistical inference approach to the joint estimation of mutation rate and population size that incorporates the uncertainty in the genealogy of such temporally spaced sequences by using Markov chain Monte Carlo (MCMC) integration. The Kingman coalescent model is used to describe the time structure of the ancestral tree. We recover information about the unknown true ancestral coalescent tree, population size, and the overall mutation rate from temporally spaced data, that is, from nucleotide sequences gathered at different times, from different individuals, in an evolving haploid population. We briefly discuss the methodological implications and show what can be inferred, in various practically relevant states of prior knowledge. We develop extensions for exponentially growing population size and joint estimation of substitution model parameters. We illustrate some of the important features of this approach on a genealogy of HIV-1 envelope (env) partial sequences.     

Applications of the Dirichlet distribution to forensic match probabilities

The Dirichlet distribution provides a convenient conjugate prior for Bayesian analyses involving multinomial proportions. In particular, allele frequency estimation can be carried out with a Dirichlet prior. If data from several distinct populations are available, then the parameters characterizing the Dirichlet prior can be estimated by maximum likelihood and then used for allele frequency estimation in each of the separate populations. This empirical Bayes procedure tends to moderate extreme multinomial estimates based on sample proportions. The Dirichlet distribution can also be employed to model the contributions from different ancestral populations in computing forensic match probabilities. If the ancestral populations are in genetic equilibrium, then the product rule for computing match probabilities is valid conditional on the ancestral contributions to a typical person of the reference population. This fact facilitates computation of match probabilities and tight upper bounds to match probabilities.Editor's commentsThe author continues the formal Bayesian analysis introduced by Gjertson & Morris in this voluem. He invokes Dirichlet distributions, and so brings rigor to the discussion of the effects of population structure on match probabilities. The increased computational burden this approach entails should not be regarded as a hindrance.     

Comparison of three methods to estimate genetic ancestry and control for stratification in genetic association studies among admixed populations

Population stratification may confound the results of genetic association studies among unrelated individuals from admixed populations. Several methods have been proposed to estimate the ancestral information in admixed populations and used to adjust the population stratification in genetic association tests. We evaluate the performances of three different methods: maximum likelihood estimation, ADMIXMAP and Structure through various simulated data sets and real data from Latino subjects participating in a genetic study of asthma. All three methods provide similar information on the accuracy of ancestral estimates and control type I error rate at an approximately similar rate. The most important factor in determining accuracy of the ancestry estimate and in minimizing type I error rate is the number of markers used to estimate ancestry. We demonstrate that approximately 100 ancestry informative markers (AIMs) are required to obtain estimates of ancestry that correlate with correlation coefficients more than 0.9 with the true individual ancestral proportions. In addition, after accounting for the ancestry information in association tests, the excess of type I error rate is controlled at the 5% level when 100 markers are used to estimate ancestry. However, since the effect of admixture on the type I error rate worsens with sample size, the accuracy of ancestry estimates also needs to increase to make the appropriate correction. Using data from the Latino subjects, we also apply these methods to an association study between body mass index and 44 AIMs. These simulations are meant to provide some practical guidelines for investigators conducting association studies in admixed populations.     

mStruct: Inference of Population Structure in Light of Both Genetic Admixing and Allele Mutations

Traditional methods for analyzing population structure, such as the Structure program, ignore the influence of the effect of allele mutations between the ancestral and current alleles of genetic markers, which can dramatically influence the accuracy of the structural estimation of current populations. Studying these effects can also reveal additional information about population evolution such as the divergence time and migration history of admixed populations. We propose mStruct, an admixture of population-specific mixtures of inheritance models that addresses the task of structure inference and mutation estimation jointly through a hierarchical Bayesian framework, and a variational algorithm for inference. We validated our method on synthetic data and used it to analyze the Human Genome Diversity Project–Centre d''Etude du Polymorphisme Humain (HGDP–CEPH) cell line panel of microsatellites and HGDP single-nucleotide polymorphism (SNP) data. A comparison of the structural maps of world populations estimated by mStruct and Structure is presented, and we also report potentially interesting mutation patterns in world populations estimated by mStruct.THE deluge of genomic polymorphism data, such as the genomewide multilocus genotype profiles of variable numbers of tandem repeats (i.e., microsatellites) and single-nucleotide polymorphisms (SNPs), has fueled the long-standing interest in analyzing patterns of genetic variations to reconstruct the ancestral structures of modern human populations. Genetic ancestral information can shed light on the evolutionary history and migrations of modern populations (Bowcock et al. 1994; Rosenberg et al. 2002; Conrad et al. 2006). It also provides guidelines for more accurate association studies (Roeder et al. 1998) and is useful for many other population genetics problems (Queller et al. 1993; Hammer et al. 1998; Templeton 2002).Various methods have been proposed for stratifying population structures on the basis of multilocus genotype information from a set of individuals. For example, Pritchard et al. (2000) proposed a model-based approach implemented in the program Structure, which uses a statistical methodology known as the allele-frequency admixture model to stratify population structures. This model, and admixture models in general arising in genetic and other contexts (Blei et al. 2003), belongs to a more general class of hierarchical Bayesian models known as the mixed membership models (Erosheva et al. 2004). Such a model postulates that an empirical multiple-instance sample, such as the ensemble of genetic markers of an individual, is made up of either independently and identically distributed (iid) instantiations (Pritchard et al. 2000) or spatially coupled (Falush et al. 2003) instantiations, from multiple population-specific fixed-dimensional multinomial distributions of marker alleles [known as allele-frequency profiles, AP (Falush et al. 2003)]. Under this assumption, the admixture model identifies each ancestral population by a specific AP (that defines a unique vector of allele frequencies of each marker in each ancestral population) and displays the fraction of contributions from each AP in a modern individual genome as an admixing vector (also known as an ancestral proportion vector or structure vector) in a structural map over the population sample in question. Figure 1 shows an example of a structural map of four modern populations inferred from a portion of the HapMap multipopulation data set by Structure. In this population structural map, the admixing vector underlying each individual is represented as a thin vertical line of unit length and multiple colors, with the height of each color reflecting the fraction of the individual''s genome originated from a certain ancestral population denoted by that color and formally represented by a unique AP. This method has been applied to the Human Genome Diversity Project–Centre d''Etude du Polymorphisme Humain (HGDP–CEPH) Human Genome Diversity Cell Line Panel in Rosenberg et al. (2002) and many other studies, and has unraveled interesting patterns in the genetic structures of the world population. However, even though Structure was originally built on a genetic admixture model, in reality the structural patterns derived by Structure in various studies often turn out to be distinct clusters among the study populations (e.g., Figure 1), which has led many to think of it as a clustering program rather than a tool for uncovering genetic admixing as it was supposed to do. The design limitation of the Structure model behind this issue motivated us to develop a new approach in this article to analyze admixed genetic samples.Open in a separate windowFigure 1.—Population structural map inferred by Structure on HapMap data consisting of four populations.A recent extension of Structure, known as Structurama (Pella and Masuda 2006; Huelsenbeck and Andolfatto 2007), relaxes the finite dimensional assumption on ancestral populations in the admixture model by employing a Dirichlet process prior over the ancestral allele-frequency profiles. This allows automatic estimation of the maximum a posteriori probable number of ancestral populations. This extension is a useful improvement since it eliminates the need for manual selection of the number of ancestral populations. Anderson and Thompson (2002) address the problem of classifying species hybrids into categories, using a model-based Bayesian clustering approach implemented in the NewHybrid program. While this problem is not exactly identical to the problem of stratifying the structure of highly admixed populations, it is useful for structural analysis of populations that were recently admixed. The BAPS program (Corander et al. 2003) also uses a Bayesian approach to find the best partition of a set of individuals into subpopulations on the basis of genotypes. Parallel to the aforementioned model-based approaches for genomic structural analysis, direct algebraic eigen-decomposition and dimensionality reduction methods, such as the Eigensoft program (Patterson et al. 2006) based on principal components analysis (PCA), offer an alternative approach to explore and visualize the ancestral composition of modern populations and facilitate formal statistical tests for significance of population differentiation. However, unlike the model-based methods such as Structure, where each inferred ancestral population bears a concrete genetic meaning as a population-specific allele-frequency profile, the eigenvectors computed by Eigensoft represent the mutually orthogonal directions in an abstract low-dimensional ancestral space, in which population samples can be embedded and visualized; these eigenvectors can be understood as mathematical surrogates of independent genetic sources underlying a population sample, but lack a concrete interpretation under a generative genetic inheritance model (from here on, we use the term “inheritance model” to describe the process by which a descendant allele is derived from an ancestral allele). Analyses based on Eigensoft are usually limited to two-dimensional ancestral spaces, offering limited power in stratifying highly admixed populations.This progress notwithstanding, an important aspect of population admixing that is largely missing in the existing methods is the effect of allele mutations between the ancestral and current alleles of genetic markers, which can dramatically influence the accuracy of the structural estimation of current populations. It can also reveal additional information about population evolution, such as the relative divergence time and migration history of admixed populations.Consider, for example, the Structure model. Since an AP merely represents the frequency of alleles in an ancestral population rather than the actual allelic content or haplotypes of the alleles themselves, the admixture models developed so far on the basis of APs do not model genetic changes due to mutations from the ancestral alleles. Indeed, a serious pitfall of the model underlying Structure, as pointed out in Excoffier and Hamilton (2003), is that there is no mutation model for modern individual alleles with respect to hypothetical common prototypes in the ancestral populations. That means every unique allele in the modern population is assumed to have a distinct ancestral proportion, rather than allowing the possibility of it just being a descendant of some common ancestral allele that can also give rise to other closely related alleles at the same locus of other individuals in the modern population. Thus, while Structure aims to provide ancestry information for each individual and each locus, there is no explicit representation of the “ancestors” as a physical set of “founding alleles.” Therefore, the inferred population structural map emphasizes revealing the contributions of abstract population-specific ancestral proportion profiles, which does not necessarily reflect individual diversity or the extent of genetic changes with respect to the founders. Due to this limitation, Structure does not enable inference of the founding genetic patterns, the age of the founding alleles, or the population divergence time (Excoffier and Hamilton 2003).The lack of an appropriate allele mutation model in a structural inference program can also compromise our ability to reliably assess the amount or level of genetic admixing in different populations. The Structure model, like several other related models (Blei et al. 2003), is based on the fundamental assumption of the presence of genetic admixing among multiple founding populations. However, as we shall see later, on real population data such as the HGDP–CEPH panel, it produces results that favor clustering individuals into predominantly one allele-frequency profile or another, thus leading us to conclude that there was little or no admixing between the ancestral human populations. We believe that this occurs due to the absence of a mutation model in Structure. While a partitioning of individuals would be desirable for clustering them into groups, it does not offer enough biological insight into the intermixing of the populations.In this article, we present mStruct (which stands for Structure under mutations), based on a new model: an admixture of population-specific mixtures of inheritance models (AdMim). Statistically, AdMim is an admixture of mixture models, which represents each ancestral population as a mixture of ancestral alleles each with its own inheritance process and each modern individual as an “ancestry vector” (or structure vector) that reflects membership proportions of the ancestral populations. As we explain shortly, mStruct facilitates estimation of both the structural map of populations and the mutation parameters of either SNP or microsatellite alleles under various contexts. A new variational inference algorithm, which is much faster than the MCMC algorithm used for Structure, was developed for estimating the structure vectors and other genetic parameters of interest. We compare our method with Structure on simulated genotype data and on the microsatellite and SNP genotype data of world populations (Rosenberg et al. 2002; Conrad et al. 2006). Our results using microsatellite data reveal the presence of significant levels of genetic admixing among the founding populations underlying the HGDP–CEPH cell line panel, as well as consequences of expansion of humans out of Africa. Our results suggest that the inability of Structure to model mutations during genetic admixing could have caused it to detect correct clustering but very low levels of genetic admixing in each modern population in the HGDP–CEPH data. We also report interesting visualizations of genetic divergence in world populations revealed by the mutation patterns estimated by mStruct. The mStruct software has been implemented in C++ and is available for download at http://www.sailing.cs.cmu.edu/mstruct.html.     

Estimation of admixture proportions: a likelihood-based approach using Markov chain Monte Carlo.

When populations are separated for long periods and then brought into contact for a brief episode in part of their range, this can result in genetic admixture. To analyze this type of event we considered a simple model under which two parental populations (P1 and P2) mix and create a hybrid population (H). After that event, the three populations evolve under pure drift without exchange during T generations. We developed a new method, which allows the simultaneous estimation of the time since the admixture event (scaled by the population size t(i) = T/N(i), where N(i) is the effective population size of population i) and the contribution of one of two parental populations (which we call p1). This method takes into account drift since the admixture event, variation caused by sampling, and uncertainty in the estimation of the ancestral allele frequencies. The method is tested on simulated data sets and then applied to a human data set. We find that (i) for single-locus data, point estimates are poor indicators of the real admixture proportions even when there are many alleles; (ii) biallelic loci provide little information about the admixture proportion and the time since admixture, even for very small amounts of drift, but can be powerful when many loci are used; (iii) the precision of the parameters' estimates increases with sample size n = 50 vs. n = 200 but this effect is larger for the t(i)'s than for p1; and (iv) the increase in precision provided by multiple loci is quite large, even when there is substantial drift (we found, for instance, that it is preferable to use five loci than one locus, even when drift is 100 times larger for the five loci). Our analysis of a previously studied human data set illustrates that the joint estimation of drift and p1 can provide additional insights into the data.     

Inferring weak population structure with the assistance of sample group information

Genetic clustering algorithms require a certain amount of data to produce informative results. In the common situation that individuals are sampled at several locations, we show how sample group information can be used to achieve better results when the amount of data is limited. New models are developed for the structure program, both for the cases of admixture and no admixture. These models work by modifying the prior distribution for each individual's population assignment. The new prior distributions allow the proportion of individuals assigned to a particular cluster to vary by location. The models are tested on simulated data, and illustrated using microsatellite data from the CEPH Human Genome Diversity Panel. We demonstrate that the new models allow structure to be detected at lower levels of divergence, or with less data, than the original structure models or principal components methods, and that they are not biased towards detecting structure when it is not present. These models are implemented in a new version of structure which is freely available online at http://pritch.bsd.uchicago.edu/structure.html.     

The genetic structure of Drosophila ananassae populations from Asia, Australia and Samoa

Information about genetic structure and historical demography of natural populations is central to understanding how natural selection changes genomes. Drosophila ananassae is a widespread species occurring in geographically isolated or partially isolated populations and provides a unique opportunity to investigate population structure and molecular variation. We assayed microsatellite repeat-length variation among 13 populations of D. ananassae to assess the level of structure among the populations and to make inferences about their ancestry and historic biogeography. High levels of genetic structure are apparent among all populations, particularly in Australasia and the South Pacific, and patterns are consistent with the hypothesis that the ancestral populations are from Southeast Asia. Analysis of population structure and use of F-statistics and Bayesian analysis suggest that the range expansion of the species into the Pacific is complex, with multiple colonization events evident in some populations represented by lineages that show no evidence of recent admixture. The demographic patterns show isolation by distance among populations and population expansion within all populations. A morphologically distinct sister species, D. pallidosa, collected in Malololelei, Samoa, appears to be more closely related to some of the D. ananassae populations than many of the D. ananassae populations are to one another. The patterns of genotypic diversity suggest that many of the individuals that we sampled may be morphologically indistinguishable nascent species.     

Spatially explicit Bayesian clustering models in population genetics

This article reviews recent developments in Bayesian algorithms that explicitly include geographical information in the inference of population structure. Current models substantially differ in their prior distributions and background assumptions, falling into two broad categories: models with or without admixture. To aid users of this new generation of spatially explicit programs, we clarify the assumptions underlying the models, and we test these models in situations where their assumptions are not met. We show that models without admixture are not robust to the inclusion of admixed individuals in the sample, thus providing an incorrect assessment of population genetic structure in many cases. In contrast, admixture models are robust to an absence of admixture in the sample. We also give statistical and conceptual reasons why data should be explored using spatially explicit models that include admixture.     

North African Populations Carry the Signature of Admixture with Neandertals

One of the main findings derived from the analysis of the Neandertal genome was the evidence for admixture between Neandertals and non-African modern humans. An alternative scenario is that the ancestral population of non-Africans was closer to Neandertals than to Africans because of ancient population substructure. Thus, the study of North African populations is crucial for testing both hypotheses. We analyzed a total of 780,000 SNPs in 125 individuals representing seven different North African locations and searched for their ancestral/derived state in comparison to different human populations and Neandertals. We found that North African populations have a significant excess of derived alleles shared with Neandertals, when compared to sub-Saharan Africans. This excess is similar to that found in non-African humans, a fact that can be interpreted as a sign of Neandertal admixture. Furthermore, the Neandertal''s genetic signal is higher in populations with a local, pre-Neolithic North African ancestry. Therefore, the detected ancient admixture is not due to recent Near Eastern or European migrations. Sub-Saharan populations are the only ones not affected by the admixture event with Neandertals.     

Inferring Demographic History from a Spectrum of Shared Haplotype Lengths

There has been much recent excitement about the use of genetics to elucidate ancestral history and demography. Whole genome data from humans and other species are revealing complex stories of divergence and admixture that were left undiscovered by previous smaller data sets. A central challenge is to estimate the timing of past admixture and divergence events, for example the time at which Neanderthals exchanged genetic material with humans and the time at which modern humans left Africa. Here, we present a method for using sequence data to jointly estimate the timing and magnitude of past admixture events, along with population divergence times and changes in effective population size. We infer demography from a collection of pairwise sequence alignments by summarizing their length distribution of tracts of identity by state (IBS) and maximizing an analytic composite likelihood derived from a Markovian coalescent approximation. Recent gene flow between populations leaves behind long tracts of identity by descent (IBD), and these tracts give our method power by influencing the distribution of shared IBS tracts. In simulated data, we accurately infer the timing and strength of admixture events, population size changes, and divergence times over a variety of ancient and recent time scales. Using the same technique, we analyze deeply sequenced trio parents from the 1000 Genomes project. The data show evidence of extensive gene flow between Africa and Europe after the time of divergence as well as substructure and gene flow among ancestral hominids. In particular, we infer that recent African-European gene flow and ancient ghost admixture into Europe are both necessary to explain the spectrum of IBS sharing in the trios, rejecting simpler models that contain less population structure.     

Control of confounding of genetic associations in stratified populations

To control for hidden population stratification in genetic-association studies, statistical methods that use marker genotype data to infer population structure have been proposed as a possible alternative to family-based designs. In principle, it is possible to infer population structure from associations between marker loci and from associations of markers with the trait, even when no information about the demographic background of the population is available. In a model in which the total population is formed by admixture between two or more subpopulations, confounding can be estimated and controlled. Current implementations of this approach have limitations, the most serious of which is that they do not allow for uncertainty in estimations of individual admixture proportions or for lack of identifiability of subpopulations in the model. We describe methods that overcome these limitations by a combination of Bayesian and classical approaches, and we demonstrate the methods by using data from three admixed populations--African American, African Caribbean, and Hispanic American--in which there is extreme confounding of trait-genotype associations because the trait under study (skin pigmentation) varies with admixture proportions. In these data sets, as many as one-third of marker loci show crude associations with the trait. Control for confounding by population stratification eliminates these associations, except at loci that are linked to candidate genes for the trait. With only 32 markers informative for ancestry, the efficiency of the analysis is 70%. These methods can deal with both confounding and selection bias in genetic-association studies, making family-based designs unnecessary.