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The infinitely-many-sites model (with no recombination) is reformulated, with sites labelled by elements of 0, 1 and "type" space E = 0, 1^Z_+. A gene is of type x = (x₀, x₁, ) E if x₀, x₁, is the sequence of sites at which mutations have occurred in the line of descent of that gene. The model is approximated by a diffusion process taking values in P⁰ₐ (E), the set of purely atomic Borel probability measures on E with the property that the locations of every n 1 atoms of form a family tree, and the diffusion is shown to have a unique stationary distribution. The principal object of investigation is the (d) -expectation of the probability that a random sample from a population with types distributed according to has a given tree structure. Ewens' (1972) sampling formula and Watterson's (1975) segregating-sites distribution are obtained as corollaries.
Ethier et al. (Wed,) studied this question.