Mathieson and McVean reply:

Listgarten and colleagues demonstrate that their recently reported FaST-LMM-Select method for controlling for population structure in association studies1 can correct the inflation in test statistics for rare variants described in our study of structured populations2 while still retaining power to detect causal variants that are not spatially clustered. However, as they note, their method will inevitably lose power to detect rare causal variants that are spatially clustered (as most rare variants are likely to be), and the problem of how to reliably detect such associations remains open. Simple association studies are fundamentally limited in this way, and we believe that different study designs may be required to reliably detect rare causal variants. Family based studies can correct for population structure and retain power when effect sizes are large, but, for more modest effects, perhaps the most promising approach comes from large studies in isolated populations. Many of these populations have extended pedigree information, and transmission-style tests using these pedigrees or local genomic relatedness information (for example, regions of shared identity by descent, IBD) may be able to combine the robustness of family based tests with the sample sizes and consequent power of association studies.