Multiple substitutions create biased estimates of divergence times and small increases in the variance to mean ratio

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Abstract
Analysis of mutational processes has demonstrated that mutations usually occur as non-random events with many factors that influence the fidelity of DNA replication. One such unusual pattern of mutation shows that some mutational events will create more than one sequence alteration. This possibility is not generally considered in estimates of sequence divergence and yet affects both the mean and variance of these estimates. Theoretical results and simulation results are presented to examine how extensive the effects of multiple alterations resulting from single mutational events may be on sequence divergence. It is shown that estimates of the divergence times are biased but that this bias is not large unless the number of sequence alterations per event are unrealistically large. The number of alterations per event required to achieve a given bias is determined. The variance is increased by multiple alterations above the variance expected for the same mean number of single alterations, but not up to the levels that are observed in nature. The resulting increase in the variance to mean ratio changes with the amount of divergence, from an initially high ratio followed by a slow decline to one.