Looking forwards and backwards in the multi-allelic neutral Cannings population model. (English) Zbl 1210.60078

Möhle, M.

J. Appl. Probab. 47, No. 3, 713-731 (2010).

The author considers the multi-allelic neutral exchangeable Cannings model with fixed population size and nonoverlapping generations. The Markov chain is studied, which describes the allelic composition of the population forward in time. Explicit expressions are derived for the so-called backward matrix of the multi-allelic Cannings model, the probabilities of the matrix being expressed in terms of the offspring distribution. The results are applied to fundamental multi-allelic Cannings models such as Moran model, Wright-Fisher model, Kimura model, Karlin and McGregor model, and uniform model.

Reviewer: Ivan Křivý (Ostrava)

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
92D10	Genetics and epigenetics
60K35	Interacting random processes; statistical mechanics type models; percolation theory
92D25	Population dynamics (general)

Keywords:

Cannings model; Markov chain; duality; neutrality; exchangeability; inversion formula; multi-allele model; principle of inclusion and exclusion

References:

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