It is not straightforward to compare these results to those of Huang et al. (2009a) because our experimental design is somewhat different. Nonetheless, we believe that our basic conclusions align with theirs. For example, we observed that the imputation accuracy with a worldwide reference panel (khap = 2020) was never much lower than the accuracy with the optimal khap (peaks of black curves in Figure 2), and the Huang et al. (2009a) results show a similar trend for cosmopolitan vs. optimal mixtures of HapMap 2 panels. In this sense, our khap approximation can be viewed as a flexible and automatic way of implementing the Huang et al. (2009a) panel selection approach with an arbitrarily large number of reference populations.