A coalescent-based estimator of admixture from DNA sequences

A variety of estimators have been developed to use genetic marker information in inferring the admixture proportions (parental contributions) of a hybrid population. The majority of these estimators used allele frequency data, ignored molecular information that is available in markers such as microsatellites and DNA sequences, and assumed that mutations are absent since the admixture event. As a result, these estimators may fail to deliver an estimate or give rather poor estimates when admixture is ancient and thus mutations are not negligible. A previous molecular estimator based its inference of admixture proportions on the average coalescent times between pairs of genes taken from within and between populations. In this article I propose an estimator that considers the entire genealogy of all of the sampled genes and infers admixture proportions from the numbers of segregating sites in DNA sequence samples. By considering the genealogy of all sequences rather than pairs of sequences, this new estimator also allows the joint estimation of other interesting parameters in the admixture model, such as admixture time, divergence time, population size, and mutation rate. Comparative analyses of simulated data indicate that the new coalescent estimator generally yields better estimates of admixture proportions than the previous molecular estimator, especially when the parental populations are not highly differentiated. It also gives reasonably accurate estimates of other admixture parameters. A human mtDNA sequence data set was analyzed to demonstrate the method, and the analysis results are discussed and compared with those from previous studies.     

Maximum-likelihood estimation of admixture proportions from genetic data

For an admixed population, an important question is how much genetic contribution comes from each parental population. Several methods have been developed to estimate such admixture proportions, using data on genetic markers sampled from parental and admixed populations. In this study, I propose a likelihood method to estimate jointly the admixture proportions, the genetic drift that occurred to the admixed population and each parental population during the period between the hybridization and sampling events, and the genetic drift in each ancestral population within the interval between their split and hybridization. The results from extensive simulations using various combinations of relevant parameter values show that in general much more accurate and precise estimates of admixture proportions are obtained from the likelihood method than from previous methods. The likelihood method also yields reasonable estimates of genetic drift that occurred to each population, which translate into relative effective sizes (N(e)) or absolute average N(e)'s if the times when the relevant events (such as population split, admixture, and sampling) occurred are known. The proposed likelihood method also has features such as relatively low computational requirement compared with previous ones, flexibility for admixture models, and marker types. In particular, it allows for missing data from a contributing parental population. The method is applied to a human data set and a wolflike canids data set, and the results obtained are discussed in comparison with those from other estimators and from previous 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.     

Genetic drift and anthropometric variation in Ireland

The effect of genetic drift on the genetic structure of seven Irish populations was investigated using anthropometric data collected during the 1890s on 259 adult males. These populations ranged in size from 769 to 3757, were relatively stable over time, and were located within 119 km of one another. Two populations are known to have experienced considerable English admixture. Data on ten anthropometric variables (three body measures and seven craniofacial measures) were adjusted for age and used to compute a relationship (R) matrix. The R matrix was converted into a distance measure and compared with a potential genetic drift distance measure, defined as (1/Ni + 1/Nj), where Ni and Nj are the effective population sizes of groups i and j (derivation of this formula is presented). Distances were rank-transformed, and the correlation between their pairwise elements was computed using matrix permutation methods to assess significance. Under the hypothesis that drift affects anthropometric variation, these correlations are expected to be positive. The correlation between anthropometric distance and potential genetic drift distance is 0.123, which is not significantly different from 0 (P = 0.368). When a multiple regression model is used to adjust for geographic distance and English admixture, the partial correlation (0.369) is significant (p = 0.021). As part of further analysis of the genetic structure of these populations, the same analyses were repeated using a distance matrix derived from surname frequencies. The correlation of surname distance and potential genetic drift distance is 0.164, which is not significant (p = 0.264). When the multiple regression model is applied, the correlation is 0.401, which is borderline significant (p = 0.055). These results show the influence of genetic drift, local migration, and admixture on Irish population structure.     

Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies

We describe extensions to the method of Pritchard et al. for inferring population structure from multilocus genotype data. Most importantly, we develop methods that allow for linkage between loci. The new model accounts for the correlations between linked loci that arise in admixed populations ("admixture linkage disequilibium"). This modification has several advantages, allowing (1) detection of admixture events farther back into the past, (2) inference of the population of origin of chromosomal regions, and (3) more accurate estimates of statistical uncertainty when linked loci are used. It is also of potential use for admixture mapping. In addition, we describe a new prior model for the allele frequencies within each population, which allows identification of subtle population subdivisions that were not detectable using the existing method. We present results applying the new methods to study admixture in African-Americans, recombination in Helicobacter pylori, and drift in populations of Drosophila melanogaster. The methods are implemented in a program, structure, version 2.0, which is available at http://pritch.bsd.uchicago.edu.     

A powerful regression-based method for admixture mapping of isolation across the genome of hybrids

We propose a novel method that uses natural admixture between divergent lineages (hybridization) to investigate the genetic architecture of reproductive isolation and adaptive introgression. Our method employs multinomial regression to estimate genomic clines and to quantify introgression for individual loci relative to the genomic background (clines in genotype frequency along a genomic admixture gradient). Loci with patterns of introgression that deviate significantly from null expectations based on the remainder of the genome are potentially subject to selection and thus of interest to understanding adaptation and the evolution of reproductive isolation. Using simulations, we show that different forms of selection modify these genomic clines in predictable ways and that our method has good power to detect moderate to strong selection for multiple forms of selection. Using individual-based simulations, we demonstrate that our method generally has a low false positive rate, except when genetic drift is particularly pronounced (e.g. low population size, low migration rates from parental populations, and substantial time since initial admixture). Additional individual-based simulations reveal that moderate selection against heterozygotes can be detected as much as 50 c m away from the focal locus directly experiencing selection, but is not detected at unlinked loci. Finally, we apply our analytical method to previously published data sets from a mouse ( Mus musculus and M. domesticus ) and two sunflower ( Helianthus petiolaris and H. annuus ) hybrid zones. This method should be applicable to numerous species that are currently the focus of research in evolution and ecology and should help bring about new insights regarding the processes underlying the origin and maintenance of biological diversity.     

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.     

lea (likelihood‐based estimation of admixture): a program to estimate simultaneously admixture and time since the admixture event

We consider an admixture event, T generations in the past, where two ‘parental’ populations, P₁ and P₂, of size N₁ and N₂, contribute different proportions into the gene pool of an admixed population, H of size N_h. lea (likelihood‐based estimator of admixture) is a program which allows the user to obtain the posterior distribution of the parameters of the model. This includes p₁, the contribution of P₁, and t₁, t₂ and t_h, the time since the admixture event (scaled by the population size) for the three populations. lea allows the user to stop and restart the analyses at any time.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Admixture and Genetic Diversity Distribution Patterns of Non-Recombining Lineages of Native American Ancestry in Colombian Populations

Genetic diversity of present American populations results from very complex demographic events involving different types and degrees of admixture. Through the analysis of lineage markers such as mtDNA and Y chromosome it is possible to recover the original Native American haplotypes, which remained identical since the admixture events due to the absence of recombination. However, the decrease in the effective population sizes and the consequent genetic drift effects suffered by these populations during the European colonization resulted in the loss or under-representation of a substantial fraction of the Native American lineages. In this study, we aim to clarify how the diversity and distribution of uniparental lineages vary with the different demographic characteristics (size, degree of isolation) and the different levels of admixture of extant Native groups in Colombia. We present new data resulting from the analyses of mtDNA whole control region, Y chromosome SNP haplogroups and STR haplotypes, and autosomal ancestry informative insertion-deletion polymorphisms in Colombian individuals from different ethnic and linguistic groups. The results demonstrate that populations presenting a high proportion of non-Native American ancestry have preserved nevertheless a substantial diversity of Native American lineages, for both mtDNA and Y chromosome. We suggest that, by maintaining the effective population sizes high, admixture allowed for a decrease in the effects of genetic drift due to Native population size reduction and thus resulting in an effective preservation of the Native American non-recombining lineages.     

Divergence at neutral and non-neutral loci in Drosophila buzzatii populations and their hybrids

The impact of intraspecific hybridisation on fitness and morphological traits depends on the history of natural selection and genetic drift, which may have led to differently coadapted gene-complexes in the parental populations. The divergence at neutral and non-neutral loci between populations can be evaluated by estimating F_ST and Q_ST respectively, and hence give an estimate of drift and selection in the populations. Here we investigate (1) whether divergence between populations in quantitative traits (wing size and shape) can be attributed to selection or drift alone, (2) The impact of intraspecific hybridisation on estimators for divergence at neutral (F_ST) and non-neutral loci (Q_ST) in hybrids, (3) If measurement of shape is more informative than size in order to detect divergence in quantitative traits between populations. The aims were addressed by performing two hybridisations between three populations of Drosophila buzzatii, one between populations from Argentina and the Canary Islands (separated for 200 years), and the other between populations from Argentina and Australia (separated for 80 years). We observed the highest divergence at neutral loci between the Argentinean and Canary Island populations, but highest morphological divergence between the Argentinean and Australian populations, indicating that natural selection is acting on the wings. Divergence based on Q_ST measures in the hybrids was sensitive towards increased phenotypic variance (σ²p) within groups and should be used with care when σ²p of populations differ. Our results indicate that measures of shape give a better estimate of divergence at the underlying quantitative traits loci than measures of size.     

Detecting adaptive trait loci in nonmodel systems: divergence or admixture mapping?

Mapping adaptive trait loci (ATL) underlying ecological divergence is an essential step towards understanding the processes that generate phenotypic diversity. Technological advances have made it possible to sequence exomes in nonmodel systems, providing an efficient means of analysing functional genetic variants. Divergence scans of genetic markers for outlier loci, or ‘divergence mapping’, have been used to map locally adapted genes, but this approach is likely to be underpowered when background divergence is elevated. Genotype–phenotype association tests in admixed populations, or ‘admixture mapping’, may provide a useful approach for mapping locally adapted loci when neutral divergence is high. To determine the power and limits of divergence mapping, we simulated exomes containing a single ATL across two parental populations of varying neutral divergence, estimated divergence and quantified the power to identify the ATL. We found that divergence mapping had very high power when background F_ST is <0.2, but decreased dramatically above this level. To evaluate the utility of admixture mapping, we simulated exomes from admixed populations, then simulated phenotypes, conducted genotype–phenotype association tests and found that even two generations of random mating after admixture could provide high mapping power in scenarios where pure divergence mapping was ineffective (F_ST = 0.35). Moreover, admixture mapping had high power across all levels of divergence after 20 generations since admixture. Together with high‐throughput exome sequencing, admixture mapping could be used to map ATL in systems such as Heliconius butterflies or Gryllus crickets when experimental design and analytical approach are chosen accordingly.     

Selection for recombination in structured populations

In finite populations, linkage disequilibria generated by the interaction of drift and directional selection (Hill-Robertson effect) can select for sex and recombination, even in the absence of epistasis. Previous models of this process predict very little advantage to recombination in large panmictic populations. In this article we demonstrate that substantial levels of linkage disequilibria can accumulate by drift in the presence of selection in populations of any size, provided that the population is subdivided. We quantify (i) the linkage disequilibrium produced by the interaction of drift and selection during the selective sweep of beneficial alleles at two loci in a subdivided population and (ii) the selection for recombination generated by these disequilibria. We show that, in a population subdivided into n demes of large size N, both the disequilibrium and the selection for recombination are equivalent to that expected in a single population of a size intermediate between the size of each deme (N) and the total size (nN), depending on the rate of migration among demes, m. We also show by simulations that, with small demes, the selection for recombination is stronger than both that expected in an unstructured population (m = 1 - 1/n) and that expected in a set of isolated demes (m = 0). Indeed, migration maintains polymorphisms that would otherwise be lost rapidly from small demes, while population structure maintains enough local stochasticity to generate linkage disequilibria. These effects are also strong enough to overcome the twofold cost of sex under strong selection when sex is initially rare. Overall, our results show that the stochastic theories of the evolution of sex apply to a much broader range of conditions than previously expected.     

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.     

Mathematical properties of Fst between admixed populations and their parental source populations

We consider the properties of the F(st) measure of genetic divergence between an admixed population and its parental source populations. Among all possible populations admixed among an arbitrary set of parental populations, we show that the value of F(st) between an admixed population and a specific source population is maximized when the admixed population is simply the most distant of the other source populations. For the case with only two parental populations, as a function of the admixture fraction, we further demonstrate that this F(st) value is monotonic and convex, so that F(st) is informative about the admixture fraction. We illustrate our results using example human population-genetic data, showing how they provide a framework in which to interpret the features of F(st) in admixed populations.     

Linkage disequilibrium in a population undergoing periodic fragmentation and admixture

Glacial and interglacial cycles are considered to have caused the fragmentation and admixture of populations in many organisms. A simple model incorporating such periodic changes of the population structure is analysed in order to investigate the behaviour of neutral genetic variation at one and two loci. The equilibrium is reached very quickly in terms of cycles if the length of a cycle is long, as would be expected of the glaciation cycles. Heterozygosity and linkage disequilibrium are shown to depend on the length of time of the fragmented and admixed phases, population sizes, and number (n) of subpopulations in the fragmented phase. If the population size is small in the fragmented phase and its duration is long, the squared correlation coefficient of two loci (a measure of linkage disequilibrium) just after the admixture is approximated by 1/(n-1) for n > 1. After admixture, the correlation decays at a rate of approximately twice the recombination rate. Therefore, if post-glaciation admixture created linkage disequilibrium, we expect to observe linkage disequilibrium even between moderately linked loci, and its decay pattern along the chromosome is very different from that in a random mating population at equilibrium. This is especially true in organisms with long generation times such as trees.     

Mapping genes that underlie ethnic differences in disease risk: methods for detecting linkage in admixed populations, by conditioning on parental admixture.

Genes that underlie ethnic differences in disease risk can be mapped in affected individuals of mixed descent if the ancestry of the alleles at each marker locus can be assigned to one of the two founding populations. Linkage can be detected by testing for association of the disease with the ancestry of alleles at the marker locus, by conditioning on the admixture (defined as the proportion of genes that have ancestry from the high-risk population) of both parents. With regard to exploiting the effects of admixture, this test is more flexible and powerful than the transmission-disequilibrium test. Under the assumption of a multiplicative model, the statistical power for a given sample size depends only on parental admixture and the risk ratio r between populations that is generated by the locus. The most informative families are those in which mean parental admixture is .2-.7 and in which admixture is similar in both parents. The number of markers required for a genome search depends on the number of generations since admixture and on the information content for ancestry (f) of the markers, defined as a function of allele frequencies in the two founding populations. Simulations using a hidden Markov model suggest that, when admixture has occurred 2-10 generations earlier, a multipoint analysis using 2,000 biallelic markers, with f values of 30%, can extract 70%-90% of the ancestry information for each locus. Sets of such markers could be selected from libraries of single-nucleotide polymorphisms, when these become available.     

Assessing introgression of Sahelian zebu genes into native Bos taurus breeds in Burkina Faso

A total of 350 samples were analyzed to estimate zebu gene proportions into two different taurine cattle breeds of Burkina Faso (Lobi and N’Dama) using 38 microsatellites and various statistical methodologies. West African and East African zebu samples were sequentially used as reference parental populations. Furthermore, N’Dama cattle from Congo, the composite South African Bonsmara cattle breed and a pool of European cattle were used successively as second parental populations. Independently of the methodology applied: (a) the use of West African zebu samples gave higher admixture coefficients than the East African zebu; (b) the higher zebu proportions were estimated when the European cattle was used as parental population 2; and (c) the use of the N’Dama population from Congo as parental population 2 gave the more consistent zebu proportion estimates for both the Lobi and the N’Dama breeds. In any case, the zebu admixture proportions estimated were not negligible and were always higher in the N’Dama cattle than in the Lobi cattle of Burkina Faso. This suggested that the introgression of Sahelian zebu genes into the taurine cattle of Southern West Africa can follow a complex pattern that can depend on local agro-ecological features. The current research pointed out that the estimation of admixture coefficients is highly dependent on both the assumptions underlying the methodologies applied and the selection of parental populations. Our analyses suggest that either too high or nil genetic identity between the parental and the expectedly derived populations must be avoided.     

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.