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

  • A. Bobrowski (a1)


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.


Corresponding author

Postal address: Department of Mathematics, Faculty of Electrical Engineering, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland. Email address:


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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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