A Logratio Approach to the Analysis of Autosomal Genotype Frequencies Across Multiple Samples

Area of Science:

• Population Genetics
• Statistical Genetics
• Bioinformatics

Background:

• The Hardy-Weinberg law is a cornerstone of population genetics.
• Compositional data analysis (logratio approach) has been underexplored in population genetics.
• Aitchison previously demonstrated logratio PCA for biallelic polymorphisms and Hardy-Weinberg law.

Purpose of the Study:

• Extend Aitchison's work to multiallelic polymorphisms.
• Demonstrate how Hardy-Weinberg law manifests in logratio-based statistical analysis.
• Develop visual tools for genetic equilibrium and disequilibrium analysis.

Main Methods:

• Logratio principal component analysis (PCA) of allele and genotype frequencies.
• Compositional biplots for visualization.
• Simulations and analysis of real genetic data (e.g., glyoxalase, D2S441, ABO loci).

Main Results:

• Established relationships between allelic and genotypic compositions.
• Demonstrated excellent visualizations of genetic equilibrium and disequilibrium using compositional biplots.
• Presented a general multiallelic compositional measure for disequilibrium, related to the inbreeding coefficient.

Conclusions:

• Logratio PCA provides powerful insights into Hardy-Weinberg equilibrium for multiallelic systems.
• Compositional data analysis offers a valuable framework for population genetic studies.
• The developed methods facilitate the analysis of complex genetic data, including haplotype-based predictions.