Relationships among evolutionary distance, the variance–covariance matrix, multidimensional scaling, and principal component analysis

Abstract

AbstractPrincipal component analyses (PCAs) are often used to visualize patterns of genetic variation in human populations. Previous studies showed a close correspondence between genetic and geographic distances. In such PCAs, the principal components are eigenvectors of the data’s variance-covariance matrix, which is obtained by a genetic relationship matrix (GRM). However, it is difficult to apply GRM to multiallelic sites. In this paper, I showed that a PCA from GRM is equivalent to multidimensional scaling (MDS) from nucleotide differences. Therefore, a PCA can be conducted using nucleotide differences. The new method provided in this study provides a straightforward method to predict the effects of different demographic processes on genetic diversity.