On the genealogy of a duplicated microsatellite

When a microsatellite locus is duplicated in a diploid organism, a single pair of PCR primers may amplify as many as four distinct alleles. To study the evolution of a duplicated microsatellite, we consider a coalescent model with symmetric stepwise mutation. Conditional on the time of duplication and a mutation rate, both in a model of completely unlinked loci and in a model of completely linked loci, we compute the probabilities for a sampled diploid individual to amplify one, two, three, or four distinct alleles with one pair of microsatellite PCR primers. These probabilities are then studied to examine the nature of their dependence on the duplication time and the mutation rate. The mutation rate is observed to have a stronger effect than the duplication time on the four probabilities, and the unlinked and linked cases are seen to behave similarly. Our results can be useful for helping to interpret genetic variation at microsatellite loci in species with a very recent history of gene and genome duplication.