A Note on the Relations Between Spatio-Genetic Models

Novel probabilistic models of spatial genetic ancestry with applications to stratification correction in genome-wide association studies

Motivation

Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequency evolution. We develop a general probabilistic model and an associated inference algorithm that unify the model-based and data-driven approaches to visualizing and inferring population structure. Our spatial inference algorithm can also be effectively applied to the problem of population stratification in genome-wide association studies (GWAS), where hidden population structure can create fictitious associations when population ancestry is correlated with both the genotype and the trait.

Results

Our algorithm Geographic Ancestry Positioning (GAP) relates local genetic distances between samples to their spatial distances, and can be used for visually discerning population structure as well as accurately inferring the spatial origin of individuals on a two-dimensional continuum. On both simulated and several real datasets from diverse human populations, GAP exhibits substantially lower error in reconstructing spatial ancestry coordinates compared to PCA. We also develop an association test that uses the ancestry coordinates inferred by GAP to accurately account for ancestry-induced correlations in GWAS. Based on simulations and analysis of a dataset of 10 metabolic traits measured in a Northern Finland cohort, which is known to exhibit significant population structure, we find that our method has superior power to current approaches.

Availability and Implementation

Our software is available at https://github.com/anand-bhaskar/gap .

Contacts

abhaskar@stanford.edu or ajavanma@usc.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Population Structure of UK Biobank and Ancient Eurasians Reveals Adaptation at Genes Influencing Blood Pressure

Analyzing genetic differences between closely related populations can be a powerful way to detect recent adaptation. The very large sample size of the UK Biobank is ideal for using population differentiation to detect selection and enables an analysis of the UK population structure at fine resolution. In this study, analyses of 113,851 UK Biobank samples showed that population structure in the UK is dominated by five principal components (PCs) spanning six clusters: Northern Ireland, Scotland, northern England, southern England, and two Welsh clusters. Analyses of ancient Eurasians revealed that populations in the northern UK have higher levels of Steppe ancestry and that UK population structure cannot be explained as a simple mixture of Celts and Saxons. A scan for unusual population differentiation along the top PCs identified a genome-wide-significant signal of selection at the coding variant rs601338 in FUT2 (p = 9.16 × 10-9). In addition, by combining evidence of unusual differentiation within the UK with evidence from ancient Eurasians, we identified genome-wide-significant (p = 5 × 10-8) signals of recent selection at two additional loci: CYP1A2-CSK and F12. We detected strong associations between diastolic blood pressure in the UK Biobank and both the variants with selection signals at CYP1A2-CSK (p = 1.10 × 10-19) and the variants with ancient Eurasian selection signals at the ATXN2-SH2B3 locus (p = 8.00 × 10-33), implicating recent adaptation related to blood pressure.

Isolation-by-distance-and-time in a stepping-stone model

With the great advances in ancient DNA extraction, genetic data are now obtained from geographically separated individuals from both present and past. However, population genetics theory about the joint effect of space and time has not been thoroughly studied. Based on the classical stepping-stone model, we develop the theory of Isolation by distance and time. We derive the correlation of allele frequencies between demes in the case where ancient samples are present, and investigate the impact of edge effects with forward-in-time simulations. We also derive results about coalescent times in circular and toroidal models. As one of the most common ways to investigate population structure is principal components analysis (PCA), we evaluate the impact of our theory on PCA plots. Our results demonstrate that time between samples is an important factor. Ancient samples tend to be drawn to the center of a PCA plot.