The theory shows that the methods are sensitive, so that on large datasets, population structure will often be detectable. Moreover, the novel result on the phase change is not limited just to PCA, but turns out to reflect a deep property about the ability to discover structure in genetic data. For example, in the paper we present simulations that show the ability to detect structure occurs with the same dataset size when STRUCTURE and PCA are used; that is, the phase change manifests itself in the same place.
