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The method developed for the treatment of the classical drift models of Wright and Moran, and their generalizations, in Cannings (1974) are extended to more complex haploid models. The possibility of subdivision of the population, as for migration models and age-structured models, is incorporated. Models with variable size or reproductive structure determined by another Markov chain are analysed.

Haploid models of genetic drift in populations of constant size are considered. Generalizations of the models of Moran and Wright have been developed by Karlin and McGregor (for multiple alleles and non-overlapping generations), by Chia and Watterson (for two alleles and overlapping or non-overlapping generations) and by Chia (for multiple alleles and overlapping or non-overlapping generations), using conditioned branching processes. A new approach is developed which contains the models mentioned above and provides simpler expressions for the latent roots. A greater dependence between the birth events and death events can be permitted, and non-independent mutations treated.

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The latent roots of certain Markov chains arising in genetics: A new approach, II. Further haploid models

The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models

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2 results

The latent roots of certain Markov chains arising in genetics: A new approach, II. Further haploid models

The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models