The appropriate threshold for declaring linkage when allowing sex-specific recombination rates

In human genetics, two loci are declared to be linked when the lod score at the maximum likelihood recombination fraction theta exceeds the threshold of 3.0. Since recombination rates differ between the sexes, one can alternatively detect linkage by estimating separate recombination rates, theta m and theta f, for male and female meiosis and examining the corresponding sex-specific lod scores. The question arises: In order to maintain the same chance of falsely declaring linkage, what is the correct threshold for declaring linkage when sex-specific lod scores are used? We show here that the appropriate threshold is about 3.5. If the restriction that theta f greater than theta m is added, the appropriate threshold falls to about 3.25. We also discuss the relative efficiency of detecting linkage by using sex-specific and sex-averaged lod scores.