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.

Download Matlab code of the models here!

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.

Edited by: Steinar Thorvaldsen
Latest update: September 1, 2010.