Our implementation of PCA has three major features. 1) It runs extremely quickly on large datasets (within a few hours on datasets with hundreds of thousands of markers and thousands of samples), whereas methods such as STRUCTURE can be impractical. This makes it possible to extract the powerful information about population structure that we will show is present in large datasets. 2) Our PCA framework provides the first formal tests for the presence of population structure in genetic data. 3) The PCA method does not attempt to classify all individuals into discrete populations or linear combinations of populations, which may not always be the correct model for population history. Instead, PCA outputs each individual's coordinates along axes of variation. An algorithm could in principle be used as a post-processing step to cluster individuals based on their coordinates along these axes, but we have not implemented this.
