THE RELIABILITY OF LOCUS ORDERINGS

Locus orders are frequently presented in graphical form, supported by likelihood statements relating to less likely orders. Many imply genetic distances which are inconsistent with the meiotic evidence, usually by a factor of about 2. While such orders may be the best possible on the data available, measures of their reliability are difficult: the common assumption that an order is correct because changes lead to less likely orders only relates to the subset of orders tested. It is only possible to deduce the order of any set of loci if a recombinant separates every pair. This usually requires a number of recombinants substantially exceeding the number of loci. Orders may be inferred from distance in the absence of consistent separation. However, if reasonable reliability is to be achieved, the number of meioses necessary to define distances with sufficient precision will be many times the number of loci. Some estimates of the minimum number of recombinants necessary for a correct ordering to achieve a probability of a half, the 'half-right' solution, would be helpful. As a first approximation to this, we use the probability of no 'null gap', i.e. no pair of adjacent loci with no recombination between them. Where the number of recombinant events is not available from counting, rough guidance can be given by estimating the number of equivalent meioses from lod scores. Where data are not available from homologies from other mammals or from pulsed-field studies, deductive methods of family analysis should be used, followed by pairwise optimizing methods for positioning. This will allow orders to be deduced independently for loci conveyed by the male and female gametes and provides a simple test of the procedure: if the orders are not identical at least one must be wrong.