A note on the balance between random sampling and population size. (On the 30th anniversary of G. Malécot's paper).
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.
D000483:Alleles; D000818:Animals; D005602:France; D005787:Gene Frequency; D005823:Genetics / Q000266:history*; D005828:Genetics, Population; D006666:History of Medicine; D006801:Humans; D008954:Models, Biological; D011336:Probability