Dynamics of microsatellite divergence under stepwise mutation and proportional slippage/point mutation models

Recently Kruglyak, Durrett, Schug, and Aquadro showed that microsatellite equilibrium distributions can result from a balance between polymerase slippage and point mutations. Here, we introduce an elaboration of their model that keeps track of all parts of a perfect repeat and a simplification that ignores point mutations. We develop a detailed mathematical theory for these models that exhibits properties of microsatellite distributions, such as positive skewness of allele lengths, that are consistent with data but are inconsistent with the predictions of the stepwise mutation model. We use our theoretical results to analyze the successes and failures of the genetic distances (delta(mu))(2) and D(SW) when used to date four divergences: African vs. non-African human populations, humans vs. chimpanzees, Drosophila melanogaster vs. D. simulans, and sheep vs. cattle. The influence of point mutations explains some of the problems with the last two examples, as does the fact that these genetic distances have large stochastic variance. However, we find that these two features are not enough to explain the problems of dating the human-chimpanzee split. One possible explanation of this phenomenon is that long microsatellites have a mutational bias that favors contractions over expansions.