Size-dependent mutability and microsatellite constraints

We investigate a model of microsatellite evolution in which both the mutation rate and the average change in array size caused by each mutation increase with the size of the array. Consequently, 'mutability', the rate at which mutation creates variance in size, increases rapidly. Mutation is upwardly biased for arrays of all sizes. We find a pattern of microsatellite array size evolution that is not directional but cyclical. Throughout the greater part of each cycle, array size increases steadily. Longer array sizes entail a progressive increase in mutability, which inevitably leads to the array returning to a small size. Both the duration and the amplitude of each cycle are stochastic, but array size never remains large for a long period. Because of this property, size dependence in mutability can limit both the mean and variance in array size. This mechanism provides a novel explanation for the observed constraints on microsatellite array sizes.