Interpreting population- and family-based genome-wide association studies in the presence of confounding.

A central aim of genome-wide association studies (GWASs) is to estimate direct genetic effects: the causal effects on an individual's phenotype of the alleles that they carry. However, estimates of direct effects can be subject to genetic and environmental confounding and can also absorb the "indirect" genetic effects of relatives' genotypes. Recently, an important development in controlling for these confounds has been the use of within-family GWASs, which, because of the randomness of mendelian segregation within pedigrees, are often interpreted as producing unbiased estimates of direct effects. Here, we present a general theoretical analysis of the influence of confounding in standard population-based and within-family GWASs. We show that, contrary to common interpretation, family-based estimates of direct effects can be biased by genetic confounding. In humans, such biases will often be small per-locus, but can be compounded when effect-size estimates are used in polygenic scores (PGSs). We illustrate the influence of genetic confounding on population- and family-based estimates of direct effects using models of assortative mating, population stratification, and stabilizing selection on GWAS traits. We further show how family-based estimates of indirect genetic effects, based on comparisons of parentally transmitted and untransmitted alleles, can suffer substantial genetic confounding. We conclude that, while family-based studies have placed GWAS estimation on a more rigorous footing, they carry subtle issues of interpretation that arise from confounding.

A Spatial Framework for Understanding Population Structure and Admixture.

Geographic patterns of genetic variation within modern populations, produced by complex histories of migration, can be difficult to infer and visually summarize. A general consequence of geographically limited dispersal is that samples from nearby locations tend to be more closely related than samples from distant locations, and so genetic covariance often recapitulates geographic proximity. We use genome-wide polymorphism data to build "geogenetic maps," which, when applied to stationary populations, produces a map of the geographic positions of the populations, but with distances distorted to reflect historical rates of gene flow. In the underlying model, allele frequency covariance is a decreasing function of geogenetic distance, and nonlocal gene flow such as admixture can be identified as anomalously strong covariance over long distances. This admixture is explicitly co-estimated and depicted as arrows, from the source of admixture to the recipient, on the geogenetic map. We demonstrate the utility of this method on a circum-Tibetan sampling of the greenish warbler (Phylloscopus trochiloides), in which we find evidence for gene flow between the adjacent, terminal populations of the ring species. We also analyze a global sampling of human populations, for which we largely recover the geography of the sampling, with support for significant histories of admixture in many samples. This new tool for understanding and visualizing patterns of population structure is implemented in a Bayesian framework in the program SpaceMix.

Inferring Continuous and Discrete Population Genetic Structure Across Space.

A classic problem in population genetics is the characterization of discrete population structure in the presence of continuous patterns of genetic differentiation. Especially when sampling is discontinuous, the use of clustering or assignment methods may incorrectly ascribe differentiation due to continuous processes (e.g., geographic isolation by distance) to discrete processes, such as geographic, ecological, or reproductive barriers between populations. This reflects a shortcoming of current methods for inferring and visualizing population structure when applied to genetic data deriving from geographically distributed populations. Here, we present a statistical framework for the simultaneous inference of continuous and discrete patterns of population structure. The method estimates ancestry proportions for each sample from a set of two-dimensional population layers, and, within each layer, estimates a rate at which relatedness decays with distance. This thereby explicitly addresses the "clines versus clusters" problem in modeling population genetic variation, and remedies some of the overfitting to which nonspatial models are prone. The method produces useful descriptions of structure in genetic relatedness in situations where separated, geographically distributed populations interact, as after a range expansion or secondary contact. We demonstrate the utility of this approach using simulations and by applying it to empirical datasets of poplars and black bears in North America.

Disentangling the effects of geographic and ecological isolation on genetic differentiation.

Populations can be genetically isolated both by geographic distance and by differences in their ecology or environment that decrease the rate of successful migration. Empirical studies often seek to investigate the relationship between genetic differentiation and some ecological variable(s) while accounting for geographic distance, but common approaches to this problem (such as the partial Mantel test) have a number of drawbacks. In this article, we present a Bayesian method that enables users to quantify the relative contributions of geographic distance and ecological distance to genetic differentiation between sampled populations or individuals. We model the allele frequencies in a set of populations at a set of unlinked loci as spatially correlated Gaussian processes, in which the covariance structure is a decreasing function of both geographic and ecological distance. Parameters of the model are estimated using a Markov chain Monte Carlo algorithm. We call this method Bayesian Estimation of Differentiation in Alleles by Spatial Structure and Local Ecology (BEDASSLE), and have implemented it in a user-friendly format in the statistical platform R. We demonstrate its utility with a simulation study and empirical applications to human and teosinte data sets.