Two important results emerge from this study. First, we show that application of PCA to genetic data is statistically appropriate, and provide a formal set of statistical tests for population structure. Second, we describe a “phase change” phenomenon about the ability to detect structure that emerges from our analysis: for a fixed dataset size, divergence between two populations (as measured, for example, by a statistic like FST) that is below a threshold is essentially undetectable, but a little above threshold detection will be easy. Based on these results, we are able to give an estimate of how much data will be required to find population structure given a level of genetic divergence such as FST (as defined by Cavalli-Sforza, [15, p. 26, Equation 3].)
