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Measuring inbreeding and its consequences on fitness is central for many areas in biology including human genetics and the conservation of endangered species. However, there is no consensus on the best method, neither for quantification of inbreeding itself nor for the model to estimate its effect on specific traits. We simulated traits based on simulated genomes from a large pedigree and empirical whole-genome sequences of human data from populations with various sizes and structures (from the 1,000 Genomes project). We compare the ability of various inbreeding coefficients (F) to quantify the strength of inbreeding depression: allele-sharing, two versions of the correlation of uniting gametes which differ in the weight they attribute to each locus and two identical-by-descent segments-based estimators. We also compare two models: the standard linear model and a linear mixed model (LMM) including a genetic relatedness matrix (GRM) as random effect to account for the nonindependence of observations. We find LMMs give better results in scenarios with population or family structure. Within the LMM, we compare three different GRMs and show that in homogeneous populations, there is little difference among the different F and GRM for inbreeding depression quantification. However, as soon as a strong population or family structure is present, the strength of inbreeding depression can be most efficiently estimated only if i) the phenotypes are regressed on F based on a weighted version of the correlation of uniting gametes, giving more weight to common alleles and ii) with the GRM obtained from an allele-sharing relatedness estimator. [ABSTRACT FROM AUTHOR]

Being able to properly quantify genetic differentiation is key to understanding the evolutionary potential of a species. One central parameter in this context is FST, the mean coancestry within populations relative to the mean coancestry between populations. Researchers have been estimating FST globally or between pairs of populations for a long time. More recently, it has been proposed to estimate population-specific FST values, and population-pair mean relative coancestry. Here, we review the several definitions and estimation methods of FST, and stress that they provide values relative to a reference population. We show the good statistical properties of an allele-sharing, method of moments based estimator of FST (global, population-specific and population-pair) under a very general model of population structure. We point to the limitation of existing likelihood and Bayesian estimators when the populations are not independent. Last, we show that recent attempts to estimate absolute, rather than relative, mean coancestry fail to do so. Author summary: We present a general model for the evolution of coancestries within and among populations possibly of different sizes and connected by migration, allowing for any type of mating pattern. We describe a moment-based, allele-sharing estimator of global, population-specific and population-pair FST, the coancestries within or between pairs of populations relative to the average mean coancestry between populations and show its good statistical properties using both simulated and real, published data from the 1,000 genomes project. As few as 10 individuals per population with 104 independent SNPs are sufficient to obtain accurate estimates. We evaluate statistically how our estimate compares to others, and discuss how population-pair (as opposed to pairwise) FST could become a useful metric in molecular ecology and conservation genetics. [ABSTRACT FROM AUTHOR]

In the Funding section, the grant number from the funder Swiss National Science Foundation for Research support is listed incorrectly. The correct grant number is: 31003A-179358.By Jerome Goudet and Bruce S. WeirReported by Author; Author [Extracted from the article]

Abstract: Statistical tests for Hardy–Weinberg equilibrium are important elementary tools in genetic data analysis. X‐chromosomal variants have long been tested by applying autosomal test procedures to females only, and gender is usually not considered when testing autosomal variants for equilibrium. Recently, we proposed specific X‐chromosomal exact test procedures for bi‐allelic variants that include the hemizygous males, as well as autosomal tests that consider gender. In this study, we present the extension of the previous work for variants with multiple alleles. A full enumeration algorithm is used for the exact calculations of tri‐allelic variants. For variants with many alternate alleles, we use a permutation test. Some empirical examples with data from the 1,000 genomes project are discussed. [ABSTRACT FROM AUTHOR]

Many population genetic activities, ranging from evolutionary studies to association mapping, to forensic identification, rely on appropriate estimates of population structure or relatedness. All applications require recognition that quantities with an underlying meaning of allelic dependence are not defined in an absolute sense, but instead are made “relative to” some set of alleles other than the target set. The 1984 Weir and Cockerham FST estimate made explicit that the reference set of alleles was across populations, whereas standard kinship estimates do not make the reference explicit. Weir and Cockerham stated that their FST estimates were for independent populations, and standard kinship estimates have an implicit assumption that pairs of individuals in a study sample, other than the target pair, are unrelated or are not inbred. However, populations lose independence when there is migration between them, and dependencies between pairs of individuals in a population exist for more than one target pair. We have therefore recast our treatments of population structure, relatedness, and inbreeding to make explicit that the parameters of interest involve the differences in degrees of allelic dependence between the target and the reference sets of alleles, and so can be negative. We take the reference set to be the population from which study individuals have been sampled. We provide simple moment estimates of these parameters, phrased in terms of allelic matching within and between individuals for relatedness and inbreeding, or within and between populations for population structure. A multi-level hierarchy of alleles within individuals, alleles between individuals within populations, and alleles between populations, allows a unified treatment of relatedness and population structure. We expect our new measures to have a wide range of applications, but we note that their estimates are sensitive to rare or private variants: some population-characterization applications suggest exploiting those sensitivities, whereas estimation of relatedness may best use all genetic markers without filtering on minor allele frequency. [ABSTRACT FROM AUTHOR]

The article focuses on the 2019 Elizabeth W. Jones award for excellence in education. Topics include the recognition of the success of the Summer Institute in Statistical Genetics (SISG), focus on statistical genetics, and progress through the lens of testing for Hardy–Weinberg equilibrium (HWE), and application of methods for detection of selection.

Principal component analysis (PCA) is widely used in genome-wide association studies (GWAS), and the principal component axes often represent perpendicular gradients in geographic space. The explanation of PCA results is of major interest for geneticists to understand fundamental demographic parameters. Here, we provide an interpretation of PCA based on relatedness measures, which are described by the probability that sets of genes are identical-by-descent (IBD). An approximately linear transformation between ancestral proportions (AP) of individuals with multiple ancestries and their projections onto the principal components is found. In addition, a new method of eigenanalysis “EIGMIX” is proposed to estimate individual ancestries. EIGMIX is a method of moments with computational efficiency suitable for millions of SNP data, and it is not subject to the assumption of linkage equilibrium. With the assumptions of multiple ancestries and their surrogate ancestral samples, EIGMIX is able to infer ancestral proportions (APs) of individuals. The methods were applied to the SNP data from the HapMap Phase 3 project and the Human Genome Diversity Panel. The APs of individuals inferred by EIGMIX are consistent with the findings of the program ADMIXTURE. In conclusion, EIGMIX can be used to detect population structure and estimate genome-wide ancestral proportions with a relatively high accuracy. [ABSTRACT FROM AUTHOR]

Characterizing the genetic structure of populations is of importance to evolutionary biology, to human disease gene mapping, and to forensic science. Sewall Wright introduced a set of F-statistics to describe population structure in 1951, and he emphasized that these quantities were ratios of variances. Responding to uncertainty over the best way to estimate F-statistics, Weir and Cockerham published a method-of-moments set of estimators in 1984. This paper continues to be widely cited, with over 7,000 citations to date. Some background to the publishing history of the Weir and Cockerham paper is given here, along with subsequent developments and a discussion of current uses of Wright's F-statistics. [ABSTRACT FROM AUTHOR]

Likelihood ratios are necessary to properly interpret mixed stain DNA evidence. They can flexibly consider alternate hypotheses and can account for population substructure. The likelihood ratio should be seen as an estimate and not a fixed value, because the calculations are functions of allelic frequency estimates that were estimated from a small portion of the population. Current methods do not account for uncertainty in the likelihood ratio estimates and are therefore an incomplete picture of the strength of the evidence. We propose the use of a confidence interval to report the consequent variation of likelihood ratios. The confidence interval is calculated using the standard forensic likelihood ratio formulae and a variance estimate derived using the Taylor expansion. The formula is explained, and a computer program has been made available. Numeric work shows that the evidential strength of DNA profiles decreases as the variation among populations increases. [ABSTRACT FROM AUTHOR]

Genotyping technology now allows the rapid and affordable generation of million-SNP profiles for humans, leading to considerable activity in association mapping. Similar activity is anticipated for many plant species, including Brassica. These plant association mapping activities will require the same care in quality control and quality assurance as for humans. The subsequent analyses may draw upon the same body of theory that is described here in the language of quantitative genetics. [ABSTRACT FROM AUTHOR]

We propose a multilocus version of FST and a measure of haplotype diversity using localized haplotype clusters. Specifically, we use haplotype clusters identified with BEAGLE, which is a program implementing a hidden Markov model for localized haplotype clustering and performing several functions including inference of haplotype phase. We apply this methodology to HapMap phase 3 data. With this haplotypecluster approach, African populations have highest diversity and lowest divergence from the ancestral population, East Asian populations have lowest diversity and highest divergence, and other populations (European, Indian, and Mexican) have intermediate levels of diversity and divergence. These relationships accord with expectation based on other studies and accepted models of human history. In contrast, the population-specific FST estimates obtained directly from single-nucleotide polymorphisms (SNPs) do not reflect such expected relationships. We show that ascertainment bias of SNPs has less impact on the proposed haplotype-cluster-based FST than on the SNP-based version, which provides a potential explanation for these results. Thus, these new measures of FST and haplotype-cluster diversity provide an important new tool for population genetic analysis of high-density SNP data. [ABSTRACT FROM AUTHOR]

Wright's F-statistics, and especially F(ST), provide important insights into the evolutionary processes that influence the structure of genetic variation within and among populations, and they are among the most widely used descriptive statistics in population and evolutionary genetics. Estimates of F(ST) can identify regions of the genome that have been the target of selection, and comparisons of F(ST) from different parts of the genome can provide insights into the demographic history of populations. For these reasons and others, F(ST) has a central role in population and evolutionary genetics and has wide applications in fields that range from disease association mapping to forensic science. This Review clarifies how F(ST) is defined, how it should be estimated, how it is related to similar statistics and how estimates of F(ST) should be interpreted. [ABSTRACT FROM AUTHOR]

Abstract: An algorithm to predict the level of identity by descent simultaneously at multiple loci is presented, which can in principle be extended to any number of loci. The model assumes a random mating population, with random association of haplotypes. The relationship is shown between coefficients of multi-locus identity or non-identity by descent and moments of multi-locus linkage disequilibrium. Thus, these moments can be computed from the multilocus identity or, using algorithms derived previously to predict the disequilibria moments, vice-versa. The results can be applied to predict multi-locus identity in, for example, gene mapping. [Copyright &y& Elsevier]

A maximum-likelihood estimator for pairwise relatedness is presented for the situation in which the individuals under consideration come from a large outbred subpopulation of the population for which allele frequencies are known. We demonstrate via simulations that a variety of commonly used estimators that do not take this kind of misspecification of allele frequencies into account will systematically overestimate the degree of relatedness between two individuals from a subpopulation. A maximum-likelihood estimator that includes FST as a parameter is introduced with the goal of producing the relatedness estimates that would have been obtained if the subpopulation allele frequencies had been known. The estimator is shown to work quite well, even when the value FST is misspecified. Bootstrap confidence intervals are also examined and shown to exhibit close to nominal coverage when FST is correctly specified. [ABSTRACT FROM AUTHOR]

Individuals who belong to the same family or the same population are related because of their shared ancestry. Population and quantitative genetics theory is built with parameters that describe relatedness, and the estimation of these parameters from genetic markers enables progress in fields as disparate as plant breeding, human disease gene mapping and forensic science. The large number of multiallelic microsatellite loci and biallelic SNPs that are now available have markedly increased the precision with which relationships can be estimated, although they have also revealed unexpected levels of genomic heterogeneity of relationship measures. [ABSTRACT FROM AUTHOR]

A population-based latent variable approach is proposed for association mapping of quantitative trait loci (QTL), using multiple closely linked genetic markers within a small candidate region in the genome. By incorporating QTL as latent variables into a penetrance model, the QTL are flexible to characterize either alleles at putative trait loci or potential risk haplotypes/sub-haplotypes of the markers. Under a general likelihood framework, we develop an EM-based algorithm to estimate genetic effects of the QTL and haplotype frequencies of the QTL and markers jointly. Closed form solutions derived in the maximization step of the EM procedure for updating the joint haplotype frequencies of QTL and markers can effectively reduce the computational intensity. Various association measures between QTL and markers can then be derived from the haplotype frequencies of markers and used to infer QTL positions. The likelihood ratio statistic also provides a joint test for association between a quantitative trait and marker genotypes without requiring adjustment for the multiple testing. Extensive simulation studies are performed to evaluate the approach. [ABSTRACT FROM AUTHOR]

Estimates of genetic population structure (FST) were constructed from all autosomes in two large SNP data sets. The Perlegen data set contains genotypes on ∼1 million SNPs segregating in all three samples of Americans of African, Asian, and European descent; and the Phase I HapMap data set contains genotypes on ∼0.6 million SNPs segregating in all four samples from specific Caucasian, Chinese, Japanese, and Yoruba populations. Substantial heterogeneity of FST values was found between segments within chromosomes, although there was similarity between the two data sets. There was also substantial heterogeneity among population-specific FST values, with the relative sizes of these values often changing along each chromosome. Population-structure estimates are often used as indicators of natural selection, but the analyses presented here show that individual-marker estimates are too variable to be useful. There is inherent variation in these statistics because of variation in genealogy even among neutral loci, and values at pairs of loci are correlated to an extent that reflects the linkage disequilibrium between them. Furthermore, it may be that the best indications of selection will come from population-specific FST values rather than the usually reported population-average values. [ABSTRACT FROM AUTHOR]

Quantitative geneticists have become interested in the heritability of transcription and detection of expression quantitative trait loci (eQTLs). Linkage mapping methods have identified major-effect eQTLs for some transcripts and have shown that regulatory polymorphisms in cis and in trans affect expression. It is also clear that these mapping strategies have little power to detect polygenic factors, and some new statistical approaches are emerging that paint a more complex picture of transcriptional heritability. Several studies imply pervasive non-additivity of transcription, transgressive segregation and epistasis, and future studies will soon document the extent of genotype–environment interaction and population structure at the transcriptional level. The implications of these findings for genotype–phenotype mapping and modeling the evolution of transcription are discussed. [Copyright &y& Elsevier]

Explores the identical in state probabilities for pairs of individuals said to have matching DNA profiles in Australia. Methods for linkage mapping of human disease genes; Growth of the number of loci used for forensic profiling; Number of profile pair matching of the loci.

Reports on results from a study done on hybrids between Drosophilia simulans and D. mauritana males. Differences between males and females of these hybrids; Percentage of sterile hemizygous X chromosomal introgressions; More.

Presents several charts depicting the allele frequency for Profiler Plus data collected from forensic agencies in Australia.

An editorial is presented which discusses on the studies of monozygotic twins. in forensic settings. It expresses concern on the potential risks of personally identifying the subjects in the studies, the autonomy, and vulnerability of those whom the framework in the manuscript was applied. It also emphasizes the reason behind presenting the studies after the proof-of-principle cases had been removed.

The article recognizes the contributions of biologists Masatoshi Neri in the field of genetics. The Thomas Hunt Morgan Medal is given to Neri for his contributions in population and evolutionary genetics theory. He most widely cited work involves the presentation of the neighbor-joining method for phylogeny reconstruction. He also formulated a birth-and-death evolution model for the fate of the members of a multigene family after gene duplication.

Reports on the receipt of researcher Trudy F. C. Mackay of the 2004 "Genetics Society of America Medal" from the Genetics Society of America. Rationale behind the receipt of Mackay of the award; Contributions of Mackay on the science of genetics; Bases of her work on the characterization of the genetic basis of quantitative genetic variation.

The concept of kinship permeates many domains of fundamental and applied biology ranging from social evolution to conservation science to quantitative and human genetics. Until recently, pedigrees were the gold standard to infer kinship, but the advent of next‐generation sequencing and the availability of dense genetic markers in many species make it a good time to (re)evaluate the usefulness of genetic markers in this context. Using three published data sets where both pedigrees and markers are available, we evaluate two common and a new genetic estimator of kinship. We show discrepancies between pedigree values and marker estimates of kinship and explore via simulations the possible reasons for these. We find these discrepancies are attributable to two main sources: pedigree errors and heterogeneity in the origin of founders. We also show that our new marker‐based kinship estimator has very good statistical properties and behaviour and is particularly well suited for situations where the source population is of small size, as will often be the case in conservation biology, and where high levels of kinship are expected, as is typical in social evolution studies. [ABSTRACT FROM AUTHOR]

Statistical tests for Hardy-Weinberg equilibrium have been an important tool for detecting genotyping errors in the past, and remain important in the quality control of next generation sequence data. In this paper, we analyze complete chromosomes of the 1000 genomes project by using exact test procedures for autosomal and X-chromosomal variants. We find that the rate of disequilibrium largely exceeds what might be expected by chance alone for all chromosomes. Observed disequilibrium is, in about 60% of the cases, due to heterozygote excess. We suggest that most excess disequilibrium can be explained by sequencing problems, and hypothesize mechanisms that can explain exceptional heterozygosities. We report higher rates of disequilibrium for the MHC region on chromosome 6, regions flanking centromeres and p-arms of acrocentric chromosomes. We also detected long-range haplotypes and areas with incidental high disequilibrium. We report disequilibrium to be related to read depth, with variants having extreme read depths being more likely to be out of equilibrium. Disequilibrium rates were found to be 11 times higher in segmental duplications and simple tandem repeat regions. The variants with significant disequilibrium are seen to be concentrated in these areas. For next generation sequence data, Hardy-Weinberg disequilibrium seems to be a major indicator for copy number variation. [ABSTRACT FROM AUTHOR]

An obituary for professor James F. Crow is presented.

Genealogical inference from genetic data is essential for a variety of applications in human genetics. In genome-wide and sequencing association studies, for example, accurate inference on both recent genetic relatedness, such as family structure, and more distant genetic relatedness, such as population structure, is necessary for protection against spurious associations. Distinguishing familial relatedness from population structure with genotype data, however, is difficult because both manifest as genetic similarity through the sharing of alleles. Existing approaches for inference on recent genetic relatedness have limitations in the presence of population structure, where they either (1) make strong and simplifying assumptions about population structure, which are often untenable, or (2) require correct specification of and appropriate reference population panels for the ancestries in the sample, which might be unknown or not well defined. Here, we propose PC-Relate, a model-free approach for estimating commonly used measures of recent genetic relatedness, such as kinship coefficients and IBD sharing probabilities, in the presence of unspecified structure. PC-Relate uses principal components calculated from genome-screen data to partition genetic correlations among sampled individuals due to the sharing of recent ancestors and more distant common ancestry into two separate components, without requiring specification of the ancestral populations or reference population panels. In simulation studies with population structure, including admixture, we demonstrate that PC-Relate provides accurate estimates of genetic relatedness and improved relationship classification over widely used approaches. We further demonstrate the utility of PC-Relate in applications to three ancestrally diverse samples that vary in both size and genealogical complexity. [ABSTRACT FROM AUTHOR]

A simple tandem repeat (STR) PCR-based typing system developed for the genetic individualization of domestic cat samples has been used to generate a population genetic database of domestic cat breeds. A panel of 10 tetranucleotide STR loci and a gender-identifying sequence tagged site (STS) were co-amplified in genomic DNA of 1043 individuals representing 38 cat breeds. The STR panel exhibits relatively high heterozygosity in cat breeds, with an average 10-locus heterozygosity of 0.71, which represents an average of 38 breed-specific heterozygosities for the 10-member panel. When the entire set of breed individuals was analyzed as a single population, a heterozygosity of 0.87 was observed. Heterozygosities obtained for the 10 loci range from 0.72 to 0.96. The power for genetic individualization of domestic cat samples of the multiplex is high, with a probability of match ( pm) of 6.2E-14, using a conservative θ = 0.05. [ABSTRACT FROM AUTHOR]

With the expansion of offender/arrestee DNA profile databases, genetic forensic identification has become commonplace in the United States criminal justice system. Implementation of familial searching has been proposed to extend forensic identification to family members of individuals with profiles in offender/arrestee DNA databases. In familial searching, a partial genetic profile match between a database entrant and a crime scene sample is used to implicate genetic relatives of the database entrant as potential sources of the crime scene sample. In addition to concerns regarding civil liberties, familial searching poses unanswered statistical questions. In this study, we define confidence intervals on estimated likelihood ratios for familial identification. Using these confidence intervals, we consider familial searching in a structured population. We show that relatives and unrelated individuals from population samples with lower gene diversity over the loci considered are less distinguishable. We also consider cases where the most appropriate population sample for individuals considered is unknown. We find that as a less appropriate population sample, and thus allele frequency distribution, is assumed, relatives and unrelated individuals become more difficult to distinguish. In addition, we show that relationship distinguishability increases with the number of markers considered, but decreases for more distant genetic familial relationships. All of these results indicate that caution is warranted in the application of familial searching in structured populations, such as in the United States. INSET: 13. [ABSTRACT FROM AUTHOR]

Coevolving interacting genes undergo complementary mutations to maintain their interaction. Distinct combinations of alleles in coevolving genes interact differently, conferring varying degrees of fitness. If this fitness differential is adequately large, the resulting selection for allele matching could maintain allelic association, even between physically unlinked loci. Allelic association is often observed in a population with the use of gametic linkage disequilibrium. However, because the coevolving genes are not necessarily in physical linkage, this is not an appropriate measure of coevolution-induced allelic association. Instead, we propose using both composite linkage disequilibrium (CLD) and a measure of association between genotypes, which we call genotype association (GA). Using a simple selective model, we simulated loci and calculated power for tests of CLD and GA, showing that the tests can detect the allelic association expected under realistic selective pressure. We apply CLD and GA tests to the polymorphic, physically unlinked, and putatively coevolving human gamete-recognition genes ZP3 and ZP3R. We observe unusual allelic association, not attributable to population structure, between ZP3 and ZP3R. This study shows that selection for allele matching can drive allelic association between unlinked loci in a contemporary human population, and that selection can be detected with the use of CLD and GA tests. The observation of this selection is surprising, but reasonable in the highly selected system of fertilization. If confirmed, this sort of selection provides an exception to the paradigm of chromosomal independent assortment. [ABSTRACT FROM AUTHOR]

Abstract: The coancestry coefficient, also known as the population structure parameter, is of great interest in population genetics. It can be thought of as the intraclass correlation of pairs of alleles within populations and it can serve as a measure of genetic distance between populations. For a general class of evolutionary models it determines the distribution of allele frequencies among populations. Under more restrictive models it can be regarded as the probability of identity by descent of any pair of alleles at a locus within a random mating population. In this paper we review estimation procedures that use the method of moments or are maximum likelihood under the assumption of normally distributed allele frequencies. We then consider the problem of testing hypotheses about this parameter. In addition to parametric and non-parametric bootstrap tests we present an asymptotically-distributed chi-square test. This test reduces to the contingency-table test for equal sample sizes across populations. Our new test appears to be more powerful than previous tests, especially for loci with multiple alleles. We apply our methods to HapMap SNP data to confirm that the coancestry coefficient for humans is strictly positive. [Copyright &y& Elsevier]

The correlation between alleles at a pair of genetic loci is a measure of linkage disequilibrium. The square of the sample correlation multiplied by sample size provides the usual test statistic for the hypothesis of no disequilibrium for loci with two alleles and this relation has proved useful for study design and marker selection. Nevertheless, this relation holds only in a diallelic case, and an extension to multiple alleles has not been made. Here we introduce a similar statistic, R², which leads to a correlation-based test for loci with multiple alleles: for a pair of loci with k and m alleles, and a sample of n individuals, the approximate distribution of n(k- 1) (m-1)/(km)R² under independence between loci is X²(k-1)(m-1). One advantage of this statistic is thatitcan he interpreted as the total correlation between a pair of loci. When the phase of two-locus genotypes is known, the approach is equivalent to a test for the overall correlation between rows and columns in a contingency table. In the phase-known case, R² is the sum of the squared sample correlations for all km 2 X 2 subtables formed by collapsing to one allele vs. the rest at each locus. We examine the approximate distribution under the null of independence for R² and report its close agreement with the exact distribution obtained by permutation. The test for independence using R² is a strong competitor to approaches such as Pearson's chi square, Fisher's exact test, and a test based on Cressie and Read's power divergence statistic. We combine this approach with our previous composite-disequilibrium measures to address the case when the genotypic phase is unknown. Calculation of the new multiallele test statistic and its P-value is very simple and utilizes the approximate distribution of R². We provide a computer program that evaluates approximate as well as "exact" permutational P-values. [ABSTRACT FROM AUTHOR]

In his 1972 paper ‘The apportionment of human diversity’, Lewontin showed that, when averaged over loci, genetic diversity is predominantly attributable to differences among individuals within populations. However, selection can alter the apportionment of diversity of specific genes or genomic regions. We examine genetic diversity at the human leucocyte antigen (HLA) loci, located within the major histocompatibility complex (MHC) region. HLA genes code for proteins that are critical to adaptive immunity and are well-documented targets of balancing selection. The single-nucleotide polymorphisms (SNPs) within HLA genes show strong signatures of balancing selection on large timescales and are broadly shared among populations, displaying low FST values. However, when we analyse haplotypes defined by these SNPs (which define ‘HLA alleles’), we find marked differences in frequencies between geographic regions. These differences are not reflected in the FST values because of the extreme polymorphism at HLA loci, illustrating challenges in interpreting FST. Differences in the frequency of HLA alleles among geographic regions are relevant to bone-marrow transplantation, which requires genetic identity at HLA loci between patient and donor. We discuss the case of Brazil's bone marrow registry, where a deficit of enrolled volunteers with African ancestry reduces the chance of finding donors for individuals with an MHC region of African ancestry. [ABSTRACT FROM AUTHOR]

The linkage disequilibrium coefficient r 2 is a measure of statistical dependence of the alleles possessed by an individual at different genetic loci. It is widely used in association studies to search for the locations of disease-causing genes on chromosomes. Most studies to date treat r 2 as a fixed property of two loci in a finite population, and investigate the sampling distribution of estimators due to the statistical sampling of individuals from the population. Here, we instead consider the distribution of r 2 itself under a process of genetic sampling through the generations. Using a classical two-locus model for genetic drift, mutation, and recombination, we investigate the probability density function of r 2 at stationarity. This density function provides a tool for inference on evolutionary parameters such as mutation and recombination rates. We reconstruct the approximate stationary density of r 2 by calculating a finite sequence of the distribution's moments and applying the maximum entropy principle. Our approach is based on the diffusion approximation, under which we demonstrate that for certain models in population genetics, moments of the stationary distribution can be obtained without knowing the probability distribution itself. To illustrate our approach, we show how the stationary probability density of r 2 can be used in a maximum likelihood framework to estimate mutation and recombination rates from sample data of r 2. [ABSTRACT FROM AUTHOR]