A joint framework for studying population structure using principal component analysis and F-statistics

Principal component analysis (PCA) and F-statistics are routinely used in population genetic and archaeogenetic studies. Here, we present a statistical framework to combine them into a joint analysis, showing where they coincide, and where slightly different assumptions made can lead to different outcomes. In particular, we discuss the differences of probabilistic PCA, Latent Subspace Estimation and classical PCA, and show that F-statistics are more naturally interpreted in a probabilistic PCA framework. We also show that individual-based F-statistics can be accurately estimated from probabilistic PCA in the presence of large amounts of missing data. We compare estimates from probabilistic PCA-based framework to ADMIXTOOLS 2 using simulations and published data, and show that this joint estimation framework addresses limitations of estimating F-statistics and PCA independently.