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

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.