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

Recently Kruglyak, Durrett, Schug, and Aquadro showed that microsatellite e quilibrium distributions can result from a balance between polymerase slipp age and point Mutations. Here, we introduce an elaboration of their model t hat keeps track of all parts of a perfect repeat and a simplification that ignores point mutations. We develop a detailed mathematical theory for thes e 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 ou r theoretical results to analyze the successes and failures of the genetic distances (delta mu)(2) and D-SW when used to date four divergences: Africa n vs. non-African human populations, humans vs. chimpanzees, Drosophila mel anogaster vs. D. simulans, and sheep vs. cattle. The influence of point mut ations explains some of the problems with the last two examples, as does th e 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 phenom enon is that long microsatellites have a mutational bias that favors contra ctions over expansions.