Crossover counts and likelihood in multipoint linkage analysis.

For large numbers of genetic loci, jointly tested to determine their order along a chromosome, likelihood methods become unfeasible owing to the very large numbers of discrete alternative hypotheses (locus orderings) whose likelihoods must be separately evaluated. A method to order loci according to the criterion of minimizing the obligatory crossover count is therefore proposed. A branch-and-bound algorithm implementing this proposal has been programmed; the properties of this algorithm are investigated. The statistical properties of the proposed method are also considered. It is shown to be consistent under wide conditions, including arbitrary locus spacings, variable amounts of information per locus, and some patterns of interference. The relationship between the minimum crossover order and the maximum likelihood order is discussed. For fully informative gametes, and tight linkage, there is a virtual equivalence of the two criteria. For looser linkage, there remains a close relationship.