Constructing meiotic maps with known error probability

We propose methods to construct meiotic gene maps while controlling the probability of a decision-error. First, a single step gene ordering procedure is presented whose decision-error probability is bounded above by a prespecified threshold. The bound for the error probability is valid under quite general circumstances. The ordering procedure is optimal in the sense of having maximal predictive probability of correct ordering among all procedures subject to the same bound on the error probability. Second, to reduce the number of hypotheses to be tested, a stepwise ordering procedure is presented. A Monte Carlo simulation study demonstrated the integrity of the proposed error bound for the stepwise procedure under a wide variety of situations, including data coming from different laboratories and marker typing errors. The stepwise procedure was applied to version 2 of the public database maintained by the Cooperative Human Linkage Center and maps of the 23 chromosomes were generated such that the probability that the order of the markers in a given chromosome is incorrect is less than 1%.