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Using the variance of pairwise differences to estimate the recombination rate



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Genet Res Camb 1997 69 pp 45 48 With 1 text figure Copyright 1997 Cambridge University Press 45 Using the variance of pairwise differences to estimate the recombination rate JOHN WAKELEY Department of Biological Sciences Rutgers Uni ersity New Jersey USA Recei ed 12 August 1996 and in re ised form 14 October 1996 Summary A new estimator is proposed for the parameter C 4Nc where N is the population size and c is the recombination rate in a finite population model without selection The estimator is an improved version of Hudson s 1987 estimator which takes advantage of some recent theoretical developments The improvement is slight but the smaller bias and standard error of the new estimator support its use The variance of the average number of pairwise differences is also derived and is important in the formulation of the new estimator 1 Introduction 2 The estimators Under the neutral theory of molecular evolution the average number of pairwise nucleotide differences among sequences in a random sample is independent of the recombination rate If only non identical pairs are considered the expectation of this average is equal to 4Nu where N is the effective population size and u is the neutral mutation rate in an infinite sites model The variance of pairwise differences however does depend on the recombination parameter C 4Nc where c is the recombination rate Nearly a decade ago Hudson 1987 made use of this fact and introduced an estimator of C based on the sample distribution of pairwise differences Since that time Hudson s estimator has become the most frequently used of the available estimators Some recent related theoretical results now suggest improvements to Hudson s original work Here a new estimator of C is proposed which differs from Hudson s in that only non identical pairs of sequences are considered and because an unbiased estimator of is employed in its calculation The statistical properties of the new estimator are investigated using computer simulations



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