A logratio approach to the analysis of autosomal genotype frequencies across multiple samples

John Aitchison has shown that the logratio principal component analysis of multiple samples of a biallelic polymorphism can evidentiate the Hardy-Weinberg law. This article extends Aitchison’s work to multiallelic polymorphisms showing how the Hardy-Weinberg law manifests itself in a logratio based statistical analysis of larger genotypic compositions. Some fundamental relationships between allelic and genotypic compositions are derived, and the close relationships between the logratio principal component analysis of allelic and genotypic compositions and the corresponding compositional biplots are established. We perform simulations and practical genetic data analysis to explore the implications of Hardy-Weinberg equilibrium for the logratio principal component analysis of genotypic compositions. A general multiallelic compositional measure for disequilibrium is presented, and shown to relate to the classical inbreeding coefficient. The proposed compositional analysis is illustrated with biallelic glyoxalase genotypes and multiallelic forensic STRs from the 1,000 Genomes project.