The infinitely-many-neutral-alleles diffusion model
- 1 March 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 13 (03) , 429-452
- https://doi.org/10.1017/s0001867800036211
Abstract
A diffusion process X(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown that X(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown that X(·) has a unique stationary distribution and is reversible and ergodic. Kingman's limit theorem for the descending order statistics of the symmetric Dirichlet distribution is obtained as a corollary.Keywords
This publication has 14 references indexed in Scilit:
- A transition density expansion for a multi-allele diffusion modelAdvances in Applied Probability, 1979
- Exact sampling distributions from the infinite neutral alleles modelAdvances in Applied Probability, 1979
- On the distribution of allele frequencies in a diffusion modelTheoretical Population Biology, 1979
- Random partitions in population geneticsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Ergodicity of diffusion and temporal uniformity of diffusion approximationJournal of Applied Probability, 1977
- The population structure associated with the Ewens sampling formulaTheoretical Population Biology, 1977
- Reversibility and the age of an allele. I. Moran's infinitely many neutral alleles modelTheoretical Population Biology, 1976
- Semigroups of Conditioned Shifts and Approximation of Markov ProcessesThe Annals of Probability, 1975
- The eigenvalues of the neutral alleles processTheoretical Population Biology, 1975
- The sampling theory of selectively neutral allelesAdvances in Applied Probability, 1974