A note on the combination of estimates of a recombination fraction.

A number of ways of combining two or more independent estimates of the same recombination fraction can be found in the literature. We revisit this topic in the context of human gene mapping, and explore the value of transforming the recombination fraction to a new parameter whose log-likelihood function is more nearly quadratic. It is shown that the arcsine of the cube-root is one such function. These observations lead naturally to a way of summarizing and combining the summarized set of log-likelihood functions of a common recombination fraction. This idea is illustrated using pedigree data concerning six loci on chromosome 10 from the CEPH consortium. A comparison is also made with the method of summarizing and combining using 'equivalent numbers' of recombinants and informative meioses.