A maximum-likelihood approach to fitting equilibrium models of microsatellite evolution

Here, we develop a new approach to Markov chain modeling of microsatellite evolution through polymerase slippage and introduce new models: a constant-slippage-rate'' model, in which there is no dependence of slippage rate on microsatellite length, as envisaged by Moran; and a linear-with-constant model, in which slippage rate increases linearly with microsatellite length, but the line of best fit is not constrained to go through the origin. We show how these and a linear no-constant model can be fitted to data hierarchically using maximum likelihood. This has advantages over previous methods in allowing statistical comparisons between models. When applied to a previously analyzed data set, the method allowed us to statistically establish that slippage rate increases with microsatellite length for dinucleotide microsatellites in humans, mice, and fruit flies, and suggested that no slippage occurs in very short microsatellites of one to four repeats. The suggestion that slippage rates are zero or close to zero for very short microsatellites of one to four repeats has important implications for understanding the mechanism of polymerase slippage.