Persistence of microsatellite arrays in finite populations

Given that most microsatellite arrays are of no obvious functional significance, it is natural to ask how long these sequences persist during evolution. The expected persistence time was calculated for microsatellite arrays undergoing replication slippage and random genetic drift using diffusion theory and Monte Carlo simulation. In each of the three models of replication slippage compared, copy number changes involve only single steps. In one model, the rates of addition or loss of repeat units are constant; in the other two models, they are dependent on array length in a linear or quadratic way. For all three models, it was found that persistence time of microsatellite loci increases with population size in a sublinear fashion. A heuristic argument is presented as to why this result holds true for a more general class of mutation mechanisms, including models that incorporate base substitutions in addition to replication slippage. This suggests that the approximately 30% deficiency of microsatellite loci on chromosome X (relative to autosomes) that has been well documented for several mammalian species cannot be explained by the fact that the X chromosome has a smaller effective population size than do autosomes, as has been hypothesized.