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Limit Diffusions of Some Stepping-Stone Models

Ken-Iti Sato
Journal of Applied Probability
Vol. 20, No. 3 (Sep., 1983), pp. 460-471
DOI: 10.2307/3213884
Stable URL: http://www.jstor.org/stable/3213884
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Limit Diffusions of Some Stepping-Stone Models
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Abstract

A Markov chain model of a population consisting of a finite or countably infinite number of colonies with N particles at each colony is considered. There are d types of particle and transition from the n th 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 (as N → ∞) for the proportion of types at colonies is found. Convergence to the diffusion is proved under certain conditions.

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