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Markov models in population genetics.
Peder A. Tyvand, Department of Mathematical
Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003
1432 Ås - Norway.
Steinar Thorvaldsen, ILP Informatics, University of Tromsø,
9037 Tromsø - Norway.
steinar.thorvaldsen@uit.no
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Abstract. Several exact Markov chain models are
formulated for haploid, diploid, haplodiploid and bisexual random mating,
including Wright-Fisher models and Moran models. The founder population is
given, and the Wright-Fisher model allows the population size to change with
the generations. Bottlenecks, endangered species and social insect
populations (bees) may be studied. Expected genotype frequencies, their
standard deviations and fixation probabilities are calculated.
Papers: P.A. Tyvand and S. Thorvaldsen:
“Wright–Fisher model of social insects with haploid males and diploid
females.” J. theor. Biol. 266 (2010), 470-478.
P.A. Tyvand and S. Thorvaldsen: “Exact Markov chains versus diffusion theory
for haploid random mating.” Mathematical
Biosciences. 225 (2010), 18-23.
P.A. Tyvand and S. Thorvaldsen: “A sexually neutral discrete Markov model for
given sum males + females.” Theoretical
Population Biology, 72 (2007), 148-152.
P.A. Tyvand and S. Thorvaldsen: “Markov model of haploid random mating with given
distribution of population size.” Bulletin
of Mathematical Biology, 68 (2006), 807-819.
P.A. Tyvand: “An exact algebraic theory of genetic drift in finite diploid
populations with random mating.” J. theor. Biol. 163 (1993), 315-331.
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