Evolutionary Influences on Local Patterns of Genetic Relatedness

Dimensionality reduction methods, such as Principal Components Analysis (PCA) or Multi-dimensional Scaling (MDS), when applied to genomic data, help to visualize the relatedness of individuals in lower dimensional space and are ubiquitous in population-genetic studies. These analyses use genome-wide patterns of variation to provide an "average" picture of genetic structure and relatedness. However, evolutionary processes result in different patterns of relationship among samples in local genomic regions as compared to the genome-wide aggregate. Recently, these local patterns of relatedness have been used to identify regions under selection and inverted segments. Here, we propose a unifying method to dissect these local deviations in genetic relatedness. Our method, Local Decomposition and Similarity to All Regions (LODESTAR), uses Procrustes Analysis to assess the similarity between local MDS results computed using pairwise allele sharing distances or a set of user-defined points. Given two sets of points, Procrustes Analysis computes the optimal rotation and scaling that fits one set of points onto the other, while maintaining the relative relationship between points within both sets. We use the Procrustes statistic to measure the similarity between the two sets of points. We show how this method can be used to explore local relatedness patterns that mirror sampling geography or population stratification by performing Procrustes analysis between local relatedness plots and coordinates representing sampling geography or between local relatedness plots and the genome-wide relatedness plot, respectively. In addition, we show how the variance of samples in lower-dimensional space can capture regions lacking population structure and inverted segments.