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On the two-locus sampling distribution. (English) Zbl 0729.92012
This paper is concerned with the distribution of gametic types in a random sample of size n of a two-locus stationary diffusion model with infinitely many neutral alleles. Two methods are used to study the Ewens sampling formula [W. J. Ewens, Theor. Population Biology 3, 87-112 (1972; Zbl 0245.92009)]. The first is due to G. B. Golding [Genetics 108, 257-274 (1984)] and includes additional probabilities in systems of linear equations satisfied by the probabilities required. This method allows some members of the sample to be specified at one locus only; it is used for numerical computations.
The second method considers the joint distribution of the sample configuration and the number of recombination events, since the time of the most recent ancestor. This new method due to the authors is used to derive a two-locus version of an urn model of F. M. Hoppe [J. Math. Biol. 20, 91-94 (1984; Zbl 0547.92009)]. Simulation of the two-locus sampling distribution is possible, when the recombination parameter is not too large. The authors point out that a number of their results may also be derived using genealogical processes analogous to the coalescent. Detailed proofs are collected in a 10 page appendix.

MSC:
92D10 Genetics and epigenetics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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