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Quasi-stationary distributions of a pair of Markov chains related to time evolution of a DNA locus

  • A. Bobrowski (a1)

Abstract

We consider a pair of Markov chains representing statistics of the Fisher-Wright-Moran model with mutations and drift. The chains have absorbing state at 0 and are related by the fact that some random time τ ago they were identical, evolving as a single Markov chain with values in {0,1,…}; from that time on they began to evolve independently, conditional on a state at the time of split, according to the same transition probabilities. The distribution of τ is a function of deterministic effective population size 2N(·). We study the impact of demographic history on the shape of the quasi-stationary distribution, conditional on nonabsorption at the margin (where one of the chains is at 0), and on the speed with which the probability mass escapes to the margin.

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Postal address: Department of Mathematics, Faculty of Electrical Engineering, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland. Email address: adambob@antenor.pol.lublin.pl

References

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Quasi-stationary distributions of a pair of Markov chains related to time evolution of a DNA locus

  • A. Bobrowski (a1)

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