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Various expressions related to the length of a conserved haplotype around a polymorphism of known frequency are derived. We obtain exact expressions for the probability that no recombination has occurred in a sample or subsample. We obtain an approximation for the probability that no recombination that could give rise to a detectable recombination event (through the four-gamete test) has occurred. The probabilities can be used to obtain approximate distributions for the length of variously defined haplotypes around a polymorphic site. The implications of our results for data analysis, and in particular for detecting selection, are discussed.
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Innan et al. (2003) studied this question.
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