Pairwise Kinship Data Do Not Determine Multi-Way Admixture Diversity: A Group-Theoretic Illustration

Abstract

Pairwise kinship data Fst is widely used to measure genetic diversity, but it fails for admixtures of three or more populations. This paper proves why using group theory: two different genetic scenarios can have identical pairwise overlaps but produce different admixture diversities (8 vs 4 in Z2,3). Simulations confirm this limitation. The lesson: use three-population f3-statistics instead of pairwise Fst for accurate admixture detection.