Inhomogeneous Markov Chain Model of Genetic Drift in Finite Autotetraploid Populations

An inhomogeneous discrete Markov model of genetic drift in finite autotetraploid populations with random mating is developed. The populations are monoecious, with two alleles at one locus. There is a given probability of self-fertilization. The generations are assumed to be non-overlapping. The transition probability matrices are defined on the genotype level. The population size may be varied from generation to generation, allowing an exact statistical description of bottlenecks. Average genotypic frequencies, standard deviations and probabilities of fixation in homozygosis are calculated. Agreement is found with the classical theory by Wright (1938, Proc. natn. Acad. Sci. U.S.A.24, 372-377). The Markov model is also verified by some numerical Monte Carlo simulations.