As additional mammalian genomes become available, the statistical power to detect positive selection will improve. However, most forthcoming genomes are being sequenced at low coverage, and will inevitably exhibit increased levels of error in base calls, genome assemblies, ortholog identification (due to short contigs), and alignment-all of which can lead to spurious signals for positive selection. (The same errors tend to produce false negatives, rather than false positives, in the identification of conserved elements.) Thus, careful data quality controls will be needed to take advantage of these data. In addition, when considering the impact of additional sequences on statistical power, it is useful to distinguish between positive selection that acts continuously (or in recurrent episodes) over a long evolutionary period, and positive selection that acts transiently or in a lineagespecific manner. Deep phylogenetic sequencing should generally improve detection power for continuous or recurrent positive selection, but power for transient selection depends strongly on the sequenced species and the lineages of interest. For example, the genome sequences of a dozen non-primate mammals will likely have little effect on the power to detect human-specific selection, while the gorilla and neanderthal genomes could help considerably. There are fundamental limitations in the detection of weak, transient, or highly localized positive selection that will not be overcome by any amount of genome sequencing. Nevertheless, the availability of several new primate genomes, including those of the orangutan, marmoset, and gorilla, may significantly improve power for PSGs in primates.