An Efficient and Accurate Graph-Based Approach to Detect Population Substructure

Currently, large-scale projects are underway to perform whole genome disease association studies. Such studies involve the genotyping of hundreds of thousands of SNP markers. One of the main obstacles in performing such studies is that the underlying population substructure could artificially inflate the p-values, thereby generating a lot of false positives. Although existing tools cope well with very distinct sub-populations, closely related population groups remain a major cause of concern. In this work, we present a graph based approach to detect population substructure. Our method is based on a distance measure between individuals. We show analytically that when the allele frequency differences between the two populations are large enough (in the l2-norm sense), our algorithm is guaranteed to find the correct classification of individuals to sub-populations. We demonstrate the empirical performance of our algorithms on simulated and real data and compare it against existing methods, namely the widely used software method STRUCTURE and the recent method EIGENSTRAT. Our new technique is highly efficient (in particular it is hundreds of times faster than STRUCTURE), and overall it is more accurate than the two other methods in classifying individuals into sub-populations. We demonstrate empirically that unlike the other two methods, the accuracy of our algorithm consistently increases with the number of SNPs genotyped. Finally, we demonstrate that the efficiency of our method can be used to assess the significance of the resulting clusters. Surprisingly, we find that the different methods find population sub-structure in each of the homogeneous populations of the HapMap project. We use our significance score to demonstrate that these substructures are probably due to over-fitting.