Construction of genetic maps using distance geometry.

The techniques of distance geometry, which generate coordinates from observed interpoint distances, have been applied to the problem of determining the relative positions of linked genetic loci from observed interlocus distances. Only the most precise data needed to join the loci are used, with missing distances substituted by sums of precise intermediate distances. Good initial positions (and therefore the order) of loci on a linear map are obtained in an operation of complexity O(N3). The method can therefore be used to generate good initial framework maps for the large numbers of markers encountered in current mapping projects. The locus positions can be subsequently refined to maximize the agreement with the originally observed distances, taking account of the weights of individual interlocus distances. By choosing only small distances from which to construct the map, the method reduces any error due to an incorrect choice of mapping function. It also prevents undue expansion of the map due to error-prone markers, since such markers are accommodated in higher dimensions. The method estimates the error in the positions of individual markers on the final map and identifies well- and ill-defined regions of the map.