The use of map functions in multipoint mapping.

The analysis of multipoint data in humans involves detection of linkage, inferences about order, and estimation of map lengths. In order to calculate likelihoods, it is necessary to have predictive formulas for multiple recombination frequencies. In the present study the Markovian assumption of Morton and MacLean is generalized to give predictive formulas for multiple-region recombination using realistic map functions. The best-fitting map functions have been determined by fitting the nine-locus data of Morgan et al. and the seven-locus data of Weinstein on the Drosophila X chromosome. Two map functions fit the data better than other published functions: that of Rao et al. with a map parameter of P = .33 and a new function suggested in the present paper. The close agreement of the estimate of the mapping parameter with a previous estimate inferred from human male meiosis suggests that the map function is robust. A further improvement in the fit to the data can be obtained by the addition of a second parameter to reduce the expected number of multiple recombinants. By comparison with the map functions recommended in the present paper, the assumption of no interference gives a poor fit to the data.