In addition to single nucleotide polymorphisms (SNPs) and microsatellites, PCA has been applied to haplotype frequencies [6,7] and the distribution of ALU insertion polymorphisms [8] in order to study population structure. Most of the literature on PCA in genetics is applied, not methodological, and we know of no paper that concentrates as we do here on the statistical significance of the components. Data with hundreds or thousands of individuals and hundreds of thousands of markers are now becoming available, so that small but real effects will be detectable, and it is important to develop rigorous tests for population structure that will be practical, even on the largest datasets. This is our main aim in this paper.
