Lineage effects and the index of dispersion of molecular evolution

Recent efforts to estimate the index of dispersion [R(t)] of molecular evolution-i.e., the ratio of the variance in the number of substitutions on a lineage to the mean number-have suffered from an inability to adjust the data for lineage effects. These effects may include the generation-time dependency of the rate of evolution or improper assumptions about the branching pattern of a phylogenetic tree. In the present paper a method for correcting for lineage effects in the estimation of R(t) is presented for trees made up of three species. The recent data published by Li et al. for 20 loci in three orders of mammals is examined, and the average R(t), corrected for lineage effects, is shown to be 7.75 for replacement substitutions and 3.3 for silent substitutions. Thus the high values reported earlier may not be dismissed as due to generation-time effects or improper assumptions about phylogenies. Computer simulations are presented to give confidence in the estimate for replacement substitutions but also to demonstrate that the estimate for silent substitutions is sensitive to corrections for multiple substitutions and is not as reliable. This work's implications for our understanding of the mechanism of molecular evolution are discussed, and the arguments in favor of the hypothesis that replacement substitutions are mostly selected while silent substitutions are mostly neutral is presented.