A Markov chain description of the stepwise mutation model: local and global behaviour of the allele process.
The stepwise mutation model (SMM) is a simple, widely used model to describe the evolutionary behaviour of microsatellites. We apply a Markov chain description of the SMM and derive the marginal and joint properties of this process. In addition to the standard SMM, we also consider the normalised allele process. In contrast to the standard process, the normalised process converges to a stationary distribution. We show that the marginal stationary distribution is unimodal. The standard and normalised processes capture the global and the local behaviour of the SMM, respectively.
Caliebe
Amke
A
Institut für Medizinische Informatik und Statistik, Haus 31, Christian-Albrechts-Universität Kiel, Arnold-Heller-Str 3, 24105 Kiel, Germany. caliebe@medinfo.uni-kiel.de
Jochens
Arne
A
Krawczak
Michael
M
Rösler
Uwe
U
D000483:Alleles; D003198:Computer Simulation; D019143:Evolution, Molecular; D005828:Genetics, Population; D008390:Markov Chains; D018895:Microsatellite Repeats / Q000235:genetics*; D008957:Models, Genetic; D009154:Mutation / Q000235:genetics*