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Markov Model of Haploid Random Mating with Given Distribution of Population Size

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Abstract

An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.

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Authors and Affiliations

  1. Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003, 1432, Ås, Norway

    Peder A. Tyvand

  2. AFL-Informatics, Tromsø University College, 9293, Tromsø, Norway

    Steinar Thorvaldsen

Authors
  1. Peder A. Tyvand
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  2. Steinar Thorvaldsen
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Correspondence to Steinar Thorvaldsen.

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Tyvand, P.A., Thorvaldsen, S. Markov Model of Haploid Random Mating with Given Distribution of Population Size. Bull. Math. Biol. 68, 807–819 (2006). https://doi.org/10.1007/s11538-005-9026-z

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  • DOI: https://doi.org/10.1007/s11538-005-9026-z

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