Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution

Deena Schmidt
Mathematical Biosciences Institute (MBI), The Ohio State University

(February 19, 2009 2:30 PM - 3:30 PM)

Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution

Abstract

Results of Nowak and collaborators concerning the onset of cancer due to the inactivation of tumor suppresor genes give the distribution of the time until some individual in a population has experienced two prespecified mutations, and the time until this mutant phenotype becomes fixed in the population. Here we apply these results to obtain insights into regulatory sequence evolution in Drosophila and humans. In particular, we examine the waiting time for a pair of mutations, the first of which inactivates an existing transcription factor binding site and the second which creates a new one. Consistent with recent experimental observations for Drosophila, we find that a few million years is sufficient, but for humans with a much smaller effective population size, this type of change would take more than 100 million years. In addition, we use these results to expose flaws in some of Michael Behe's arguments concerning mathematical limits to Darwinian evolution.