Alternative test for linkage between two loci

When using the maximum likelihood method to test for linkage it is traditionally assumed that the female (theta f) and male (theta m) recombination fractions are equal. However, this assumption is not always realistic. In this paper we present a testing for linkage that does not require this assumption. Specifically, we propose testing for linkage by testing the null hypothesis H0: theta f + theta m = 1 vs. the alternative HA: theta f + theta m < 1, treating theta f - theta m as a nuisance parameter. This leads to a likelihood ratio test statistic that is asymptotically distributed as a chi-square with one degree of freedom. By examining the expected values of the maximum lod scores, we show that for data from phase-known meioses this test can provide a more powerful test for linkage-especially so when theta f not equal to theta m-unless the recombination fraction is zero. For data from phase-unknown meioses, the proposed test is a more powerful test for linkage only for large values of theta f - theta m; otherwise, the traditional test has higher power. Thus, the proposed test can lead to gain in power for detecting linkage when either phase is known for most meioses or when there is a large absolute difference between the male and female recombination fractions.