Correction: An allele-sharing, moment-based estimator of global, population-specific and population-pair FST under a general model of population structure.

[This corrects the article DOI: 10.1371/journal.pgen.1010871.].

Detecting inbreeding depression in structured populations.

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 ([Formula: see text]) 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 [Formula: see text] 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 [Formula: see text] 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.

An allele-sharing, moment-based estimator of global, population-specific and population-pair FST under a general model of population structure.

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.

Rank-invariant estimation of inbreeding coefficients.

The two alleles an individual carries at a locus are identical by descent (ibd) if they have descended from a single ancestral allele in a reference population, and the probability of such identity is the inbreeding coefficient of the individual. Inbreeding coefficients can be predicted from pedigrees with founders constituting the reference population, but estimation from genetic data is not possible without data from the reference population. Most inbreeding estimators that make explicit use of sample allele frequencies as estimates of allele probabilities in the reference population are confounded by average kinships with other individuals. This means that the ranking of those estimates depends on the scope of the study sample and we show the variation in rankings for common estimators applied to different subdivisions of 1000 Genomes data. Allele-sharing estimators of within-population inbreeding relative to average kinship in a study sample, however, do have invariant rankings across all studies including those individuals. They are unbiased with a large number of SNPs. We discuss how allele sharing estimates are the relevant quantities for a range of empirical applications.

Detection and quantification of inbreeding depression for complex traits from SNP data.

Quantifying the effects of inbreeding is critical to characterizing the genetic architecture of complex traits. This study highlights through theory and simulations the strengths and shortcomings of three SNP-based inbreeding measures commonly used to estimate inbreeding depression (ID). We demonstrate that heterogeneity in linkage disequilibrium (LD) between causal variants and SNPs biases ID estimates, and we develop an approach to correct this bias using LD and minor allele frequency stratified inference (LDMS). We quantified ID in 25 traits measured in [Formula: see text] participants of the UK Biobank, using LDMS, and confirmed previously published ID for 4 traits. We find unique evidence of ID for handgrip strength, waist/hip ratio, and visual and auditory acuity (ID between -2.3 and -5.2 phenotypic SDs for complete inbreeding; [Formula: see text]). Our results illustrate that a careful choice of the measure of inbreeding combined with LDMS stratification improves both detection and quantification of ID using SNP data.

On the testing of Hardy-Weinberg proportions and equality of allele frequencies in males and females at biallelic genetic markers.

Standard statistical tests for equality of allele frequencies in males and females and tests for Hardy-Weinberg equilibrium are tightly linked by their assumptions. Tests for equality of allele frequencies assume Hardy-Weinberg equilibrium, whereas the usual chi-square or exact test for Hardy-Weinberg equilibrium assume equality of allele frequencies in the sexes. In this paper, we propose ways to break this interdependence in assumptions of the two tests by proposing an omnibus exact test that can test both hypotheses jointly, as well as a likelihood ratio approach that permits these phenomena to be tested both jointly and separately. The tests are illustrated with data from the 1000 Genomes project.

Model-free Estimation of Recent Genetic Relatedness.

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.

Genetic Diversity and Association Studies in US Hispanic/Latino Populations: Applications in the Hispanic Community Health Study/Study of Latinos.

US Hispanic/Latino individuals are diverse in genetic ancestry, culture, and environmental exposures. Here, we characterized and controlled for this diversity in genome-wide association studies (GWASs) for the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). We simultaneously estimated population-structure principal components (PCs) robust to familial relatedness and pairwise kinship coefficients (KCs) robust to population structure, admixture, and Hardy-Weinberg departures. The PCs revealed substantial genetic differentiation within and among six self-identified background groups (Cuban, Dominican, Puerto Rican, Mexican, and Central and South American). To control for variation among groups, we developed a multi-dimensional clustering method to define a "genetic-analysis group" variable that retains many properties of self-identified background while achieving substantially greater genetic homogeneity within groups and including participants with non-specific self-identification. In GWASs of 22 biomedical traits, we used a linear mixed model (LMM) including pairwise empirical KCs to account for familial relatedness, PCs for ancestry, and genetic-analysis groups for additional group-associated effects. Including the genetic-analysis group as a covariate accounted for significant trait variation in 8 of 22 traits, even after we fit 20 PCs. Additionally, genetic-analysis groups had significant heterogeneity of residual variance for 20 of 22 traits, and modeling this heteroscedasticity within the LMM reduced genomic inflation for 19 traits. Furthermore, fitting an LMM that utilized a genetic-analysis group rather than a self-identified background group achieved higher power to detect previously reported associations. We expect that the methods applied here will be useful in other studies with multiple ethnic groups, admixture, and relatedness.

Genome-wide Association Study of Platelet Count Identifies Ancestry-Specific Loci in Hispanic/Latino Americans.

Platelets play an essential role in hemostasis and thrombosis. We performed a genome-wide association study of platelet count in 12,491 participants of the Hispanic Community Health Study/Study of Latinos by using a mixed-model method that accounts for admixture and family relationships. We discovered and replicated associations with five genes (ACTN1, ETV7, GABBR1-MOG, MEF2C, and ZBTB9-BAK1). Our strongest association was with Amerindian-specific variant rs117672662 (p value = 1.16 × 10(-28)) in ACTN1, a gene implicated in congenital macrothrombocytopenia. rs117672662 exhibited allelic differences in transcriptional activity and protein binding in hematopoietic cells. Our results underscore the value of diverse populations to extend insights into the allelic architecture of complex traits.