Microsatellite evolution: Markov transition functions for a suite of models. (English) Zbl 1118.92050
Summary: This paper takes from the collection of models considered by J. C. Whittaker et al. [Likelihood-based estimation of microsatellite mutation rates. Genetics 164, 781–787 (2003)] derived from direct observations of microsatellite mutations 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 the time to the 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.
The impact of the differing choice of models is examined using likelihood estimates for the time to the 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.
MSC:
| 92D15 | Problems related to evolution |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
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