Background Though a variety of linkage disequilibrium tests have recently been introduced to measure the signal of recent positive selection, the statistical properties of the various methods have not been directly compared. While most applications of these tests have suggested that positive selection has played an important role in recent human history, the results of these tests have varied dramatically. Results Here, we evaluate the performance of three statistics designed to detect incomplete selective sweeps, LRH and iHS, and ALnLH. To analyze the properties of these tests, we introduce a new computational method that can model complex population histories with migration and changing population sizes to simulate gene trees influenced by recent positive selection. We demonstrate that iHS performs substantially better than the other two statistics, with power of up to 0.74 at the 0.01 level for the variation best suited for full genome scans and a power of over 0.8 at the 0.01 level for the variation best suited for candidate gene tests. The performance of the iHS statistic was robust to complex demographic histories and variable recombination rates. Genome scans involving the other two statistics suffer from low power and high false positive rates, with false discovery rates of up to 0.96 for ALnLH. The difference in performance between iHS and ALnLH, did not result from the properties of the statistics, but instead from the different methods for mitigating the multiple comparison problem inherent in full genome scans. Conclusions We introduce a new method for simulating genealogies influenced by positive selection with complex demographic scenarios. In a power analysis based on this method, iHS outperformed LRH and ALnLH in detecting incomplete selective sweeps. We also show that the single-site iHS statistic is more powerful in a candidate gene test than the multi-site statistic, but that the multi-site statistic maintains a low false discovery rate with only a minor loss of power when applied to a scan of the entire genome. Our results highlight the need for careful consideration of multiple comparison problems when evaluating and interpreting the results of full genome scans for positive selection.
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