The McDonald-Kreitman test and slightly deleterious mutations

It is possible to estimate the proportion of substitutions that are due to adaptive evolution using the numbers of silent and nonsilent polymorphisms and substitutions in a McDonald and Kreitman-type analysis. Unfortunately, this estimate of adaptive evolution is biased downward by the segregation of slightly deleterious mutations. It has been suggested that 1 way to cope with the effects of these slightly deleterious mutations is to remove low-frequency polymorphisms from the analysis. We investigate the performance of this method theoretically. We show that although removing low-frequency polymorphisms does indeed reduce the bias in the estimate of adaptive evolution, the estimate is always downwardly biased, often to the extent that one would not be able to detect adaptive evolution, even if it existed. The method is reasonably satisfactory, only if the rate of adaptive evolution is high and the distribution of fitness effects for slightly deleterious mutations is very leptokurtic. Our analysis suggests that adaptive evolution could be quite prevalent in humans (> 8%) and still not be detectable using current methodologies. Our analysis also suggests that the level of adaptive evolution has probably been underestimated, possibly substantially, in both bacteria and Drosophila.