Huff et al. BMC Genomics 2010, 11:8 http://www.biomedcentral.com/1471-2164/11/8 better choice, providing an average power of 0.81 at the 0.01 level according to our estimates (Figure 3). There are two other considerations when comparing the power analysis from Voight et al. [5] with the results from this study. First, Voight et al. [5] established criti- cal values from models with histories of population bottlenecks, but tested those values against selection models where the population size was constant. Because population bottlenecks also introduce LD, this resulted in conservative critical regions and lower power. Second, our strategy for simulating ascertainment bias resulted in higher SNP density and more low frequency alleles compared to Voight et al. [5], which probably elevated the power of the test in our analysis when the favored allele was relatively rare. As pointed out by Przeworski et al., empirical scans for selection will miss many selection events when they are applied to genomes that have been heavily influ- enced by recent positive selection [13]. This is evident in Figure 4a, where the power of iHS is 0.74 when selec- tive sweeps are very rare, 0.69 when 1% of the genome is influenced by positive selection, and drops to 0.33 when just 5% of the genome influenced by selection. This effect could be mitigated by choosing critical values from a subset of the genome that has a smaller propor- tion of recent selection events. We expect a priori that nongenic regions are less likely to be targeted by selec- tion. This expectation is supported in Voight et al. [5], where they demonstrated a highly significant enrichment for genic regions within the group of loci identified as potential targets of positive selection (p < 1E-20). By establishing critical regions from nongenic regions, it may be possible to substantially improve the power of genome scans for recent positive selection with only a small increase in false positives. Conclusions In agreement with previous findings, our results demon- strate that the multi-site iHS test is an excellent test for detecting incomplete selective sweeps in full genome scans, with power between 0.33 and 0.74 and false dis- covery rate between 0 and 0.53 at the 0.01 level. In comparison, the power of the ALnLH test in full gen- ome scans was approximately 25% lower with a false discovery rate between 0.74 and 0.96. However, the sta- tistical properties of the two statistics are quite similar when applied to a single site in a candidate gene test, with power of over 0.8 at the 0.01 level, demonstrating the importance differences in the adjustments made for multiple tests in full genome scans. Our results highlight the need for careful consideration of multiple compari- son problems when evaluating and interpreting the results of full genome scans for positive selection. The algorithm we present for simulating genealogies Page 6 of 9 influenced by positive selection will allow for more thor- ough exploration of complex demographic scenarios when evaluating methods for detecting positive selection. Methods Simulating the allele trajectory To simulate positive selection, we employed the coales- cent framework first proposed by Kaplan et al. [14], where the selected and neutral alleles are treated as two subdivided populations. In this method, the trajectory of the favored allele is determined separately through model or simulation, which provides the population sizes of the two allelic classes throughout the coalescent simulation. Though there are a variety of existing meth- ods for generating the trajectory of the favored allele, most are limited to simple models of demography and selection. The original method of Kaplan et al. [14] models strong balancing selection by assuming that allele frequencies remain constant. Braverman et al. [15] introduced a model of directional selection, but the tra- jectory path is deterministic. Stochastic simulations of the trajectory have generally been limited to backward time Moran models, which require a single population of fixed size [13,16-18]. Slatkin proposed an importance- sampling method that weights realizations of a reversed Wright-Fisher model according to the conditional prob- ability of the trajectory path in forward time given the observed genetic data [19]. This model allows for vari- able population size, and could be extended to include population subdivision and migration. However, the method is computationally intensive and the introduc- tion of n subpopulations with migration would increase computational complexity by a factor of n2+n. Pickrell et al. [7] adopt a hybrid approach, where a single popu- lation is initialized by coalescent simulation until the first population split. From that point on, the simulation occurs in forward time using Wright-Fisher drift [7]. While this method can model complex demography, it does not allow for conditioning on the desired allele fre- quency of the favored allele. It also requires the simula- tion to track each recombinant haplotype in each subpopulation, and as such is computationally intensive even for relatively small genomic regions. In the interest of developing a more flexible method, we introduce a new importance-sampling method based on forward Wright-Fisher drift. Consider a sample of n sequences from a single subpopulation, x of which carry a favored allele that originated t generations ago with a selection coefficient of s. We would like to draw ran- domly from the trajectories that produce x modern copies of the favored allele in a sample of size n. To accomplish this, we simulate the forward trajectory of the favored allele, continuing until the allele is lost,