A NOTE ON THE BALANCE BETWEEN RANDOM SAMPLING AND POPULATION SIZE (ON THE 30TH ANNIVERSARY OF G. MALÉCOT'S PAPER)
Open Access
- 1 July 1974
- journal article
- research article
- Published by Oxford University Press (OUP) in Genetics
- Vol. 77 (3) , 607-610
- https://doi.org/10.1093/genetics/77.3.607
Abstract
Wright's model for the effects of random fluctuations in gene frequency in a population of fixed size is generalized to randomly fluctuating population size, and treated from the viewpoint of G. Malécot, using a martingale convergence theorem. The gene frequency approaches a limit, whose value depends on the actual realization, or history, of the process; that is, convergence is with probability one (or: almost surely) in statistical language. The limit does not necessarily represent a state of fixation of either allele; in particular, the limiting probability distribution is not necessarily trivial. For the special case of deterministically varying population size, a necessary and sufficient condition for such non-triviality is given.Keywords
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