Letter to the Editor

Clusters of Identical New Mutations Can Not Account for the "Overdispersed" Molecular Clock

Corresponding author: Joshua L. Cherry, University of Utah, Department of Human Genetics, 15 N 2030 E RM 2100, Salt Lake City, UT 84112-5330, cherry{at}genetics.utah.edu (E-mail).

HUAI and WOODRUFF 1997 have recently claimed that "clusters of identical new mutations can account for the `overdispersed' molecular clock." Their conclusion is based on erroneous reasoning in which they wrongly equate the variance-to-mean ratio of one quantity with that of another. They correctly calculate the variance-to-mean ratio of the number of newly arising (in their sense) mutations in each generation according to their model, and show that it is greater than one. However, they are incorrect in their conclusion that this leads to a higher index of dispersion for the number of mutations accumulated in a single line of descent. It is this second value whose inflation is referred to as overdispersion of the molecular clock.

Perhaps the easiest way to see that their conclusion is incorrect is to consider that an early premeiotic mutation in an individual is essentially equivalent to a mutation arising in one of the gametes that formed that individual. The only difference is that we will consider the resulting allele to have arisen one generation later. This difference in reckoning makes no difference to the long-term index of dispersion of the molecular clock. This consideration has prevented me from simulating a model with only "clusters" to show their conclusion wrong; I do not see how such a simulation would differ from one for a model with no "clusters," except perhaps for some inconsequential details of how the first and last generations would be handled. Indeed the variance in the number of copies of "new mutations" in their model (with only "clusters") is equal to the variance in the number of copies of "one-generation-old" mutations in a standard model. This variance is inflated because a small amount (one generation's worth) of genetic drift has occured.

The quantities relevant to the index of dispersion of the molecular clock are the mean and variance of the number of mutations that arise in a given line of descent (not in the entire population). This total number of mutations is the sum of the numbers that arise in each generation in that line of descent. On HUAI and WOODRUFF's model, the number of newly arising mutations carried by an individual gamete is still a Poisson random variable. The number that arise in a lineage is the sum of these independent Poisson random variables, so it is itself a Poisson random variable. Therefore it has index of dispersion equal to one. The fact that there is a higher variance-to-mean ratio for the number of "new" mutations arising in a generation is irrelevant to the molecular clock, so long as the number of newly arising mutations carried by an individual gamete is Poisson distributed. HUAI and WOODRUFF's reference to the first quantity as the variance-to-mean ratio of the mutation rate is misleading; a given line of descent experiences a constant mutation rate in the situation that they describe. The phenomenom that they describe does not lead to a temporal clustering of mutations along a given line of descent. Their equation 8b certainly does not follow from what precedes it, given the usual meaning of R(t) in this context. What they have calculated is the variance-to-mean ratio for the number of mutations that have ever arisen in a population. This quantity is unrelated to the index of dispersion of the molecular clock. It cannot even be estimated from the kind of data generally used to estimate R(t). In fact the historical value of this quantity is unobservable.

LITERATURE CITED

HUAI, H. and R. C. WOODRUFF, 1997  Clusters of identical new mutations can account for the `overdispersed' molecular clock. Genetics 147:339-348[Abstract].