Exploring the Biological Meaning for Mathematically Synthesized Principal Component in Population Genetics

Principal Component Analysis (PCA) is widely applied in population genetics to reveal the hidden population structure. Through PCA, a few of variables (PCs) synthesized from high dimensional SNP matrix can capture the major variations. However, why PCs have such power to reveal population structure is not clear because reducing dimensions inevitably accompanies with reducing interpretability. We discovered striking correlation between PC1 (the most important PC variable capturing the highest variation) and Base composition across SNPs (BCS) from empirical datasets. Theoretical derivation further formulates the relationship between BCS and PC1. Therefore, we proposed BCS is an ideal indicator for exploring the biological meaning for invisible PCs. By analyzing the 3D geometric object formed by SNPs, subset of SNPs mainly contributing to PC1, PC2, and PC3 were able to be isolated, respectively. BCS developed from each subset is highly correlated with corresponding PC, which is developed from the whole SNPs. The biological meaning of each PC is further elucidated as such subset of SNPs has unique allele frequency for the group from which the corresponding PC separates. Therefore, our analysis suggests that PC variable highly concentrates information from the signature genome sequences possessed by subpopulation.