We do not review in detail older methods for testing for significance. One technique is the “broken stick” model [27,28], used, for instance, in a recent population genetics analysis [5]. In this model, one normalizes the m′ nonzero eigenvalues to sum to 1, then sorts them in decreasing order, and compares the k-th eigenvalue with the expected size of the k-th largest subinterval of the unit interval, partitioned by “breaking” the interval at m′ − 1 uniformly chosen points. This method does not use the number of markers in any way, thus it cannot be making optimum use of the data. In particular for datasets with large numbers of markers, real population structure may go undetected.
