The BBP phase change is not just a phenomenon of the eigenvector-based analysis we are discussing here. We suspect that at least for biallelic unlinked markers, no methods for detecting structure will do much better than our TW-based techniques. This implies that no method will have any significant success rate if population divergence is below the BBP threshold, while above threshold, reasonable methods will succeed. To test this we made a series of simulations, each with 1,600 biallelic markers and two populations each of size 50. We varied FST and ran both our eigenanalysis and STRUCTURE. (See Methods for more detail about the simulations and analysis.) We were not successful in using STRUCTURE to produce a higher likelihood for the existence of two clusters rather than one except for the very largest FST levels. We wanted to place our methods and STRUCTURE on a “level playing field.” Our PCA methods return a leading eigenvector, while running STRUCTURE with K = 2 clusters, returns for each individual the probability of belonging to cluster 1. We used a nonparametric idea, applying a
