Limit diffusions of some stepping-stone models
- 1 September 1983
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (3) , 460-471
- https://doi.org/10.2307/3213884
Abstract
A Markov chain model of a population consisting of a finite or countably infinite number of colonies withNparticles at each colony is considered. There aredtypes of particle and transition from thenth generation to the (n+ 1)th is made up of three stages: reproduction, migration, and sampling. Natural selection works in the reproduction stage. The limiting diffusion operator (asN→∞) for the proportion of types at colonies is found. Convergence to the diffusion is proved under certain conditions.Keywords
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