Permutation tests for the correlation among genetic distances and measures of heterosis

It is often found that heterosis tends to increase with genetic distance of the parents, though the correlation is not usually very close. It is therefore important to test the null hypothesis that the correlation is zero. The present work shows that standard procedures tend to yield too liberal tests, owing to the lack of independence among genetic distances and among heterosis estimates. A valid alternative is to use a permutation test, which was first suggested by Mantel [(1967) Cancer Res 27: 209--220). This test is well-known among plant breeders and geneticists, who often use it to test the correlation among two distance matrices. Its use is not restricted to the comparison of distance matrices. This is demonstrated in the present work, using two published datasets on marker-based genetic distances of maize inbreds or populations and heterosis of their crosses. It is shown that the test is also applicable in the presence of missing data.