A major simplification in the preliminary ordering of linked loci

For ordering n loci there are n!/2 distinct orders to be evaluated. Each order has a different set of event probabilities where the events are the occurrence and nonoccurrence of recombination in each interval determined by that order. To choose between the distinct orders, further assumptions are necessary. The biologically natural one is that the recombination rate over a subinterval is always less than or equal to the recombination rate over the larger interval. A second assumption is necessary, and the one commonly made is that there is no interference. Using a simple matrix approach it is shown that a consequence of these assumptions is that the optimal order is the order with the minimum value of the product of the adjoining pairwise recombination rates. This result gives a very simple procedure for obtaining preliminary genetic maps that may be used as starting points for more computer-intensive, maximum-likelihood, multipoint techniques.