Journal
THEORETICAL POPULATION BIOLOGY
Volume 71, Issue 2, Pages 147-159Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.tpb.2006.10.001
Keywords
microsatellites; Markov process; generating functions
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This paper takes from the collection of models considered by Whittaker et al. [2003. Likelihood-based estimation of microsatellite mutation rates. Genetics 164, 781-787] derived from direct observation of microsatellite mutation in parent-child pairs and provides analytical expressions for the probability distributions for the change in number of repeats over any given number of generations. The mathematical framework for this analysis is the theory of Markov processes. We find these expressions using two approaches, approximating by circulant matrices and solving a partial differential equation satisfied by the generating function. The impact of the differing choice of models is examined using likelihood estimates for time to most recent common ancestor. The analysis presented here may play a role in elucidating the connections between these two approaches and shows promise in reconciling differences between estimates for mutation rates based on Whittaker's approach and methods based on phylogenetic analyses. (c) 2006 Elsevier Inc. All rights reserved.
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