Preliminary ranking procedures for multilocus ordering.

N linked loci can be arranged in N!/2 possible orders. We describe two criteria for providing a preliminary ranking of the possible orders based on the N(N-1)/2 pairwise lod score curves for the loci. For a given order the first criterion is the sum of the N-1 maximal lod scores corresponding to the adjacent pairs of loci in the order. The second criterion is the minimum of a least-squares problem due to J.M. Lalouel (1977, Heredity 38(1): 61-77). This least-squares problem requires the maximum likelihood recombination fraction estimates and their standard errors. For N small it is feasible to evaluate these measures for every possible order. For N large we use a simulated annealing algorithm. This gives a fairly complete listing of the best-candidate orders without sampling every possible order. These ranking methods are applied to data from linkage groups on chromosomes 1, 6, 11, and 13.