Orr's Quantitative Trait Loci Sign Test Under Conditions of Trait Ascertainment

ORR (1998) presents two statistical tests for testing whether a quantitative trait has evolved neutrally. His quantitative trait loci (QTL) sign test (QTLST) rejects the null hypothesis of neutrality if the number of QTL acting in a positive direction is improbably high given the magnitude of the trait difference between the two lines studied. His second test, the QTL sign test with equal effects (QTLST-EE), rejects neutrality when the number of QTL acting in a positive direction is improbably high given only that the trait difference is positive between the two lines. Orr points out that, although the QTLST-EE is not as biologically realistic as the QTLST, it is still preferable to a simple sign test. However, the statistical properties of the QTLST-EE are not clear from Orr (1998). The recent publication of a report (Rieseberg et al. 2002) applying the QTLST-EE to numerous traits and rejecting the neutral evolution hypothesis for many of them prompted us to investigate the statistical behavior of the QTLST and QTLST-EE. Of particular concern is whether the type 1 error rate of either test is greater than the reported P value when the test is applied to traits that are particularly divergent between the “high” and the “low” lines. This is important because, in practice, the traits to which the test is applied tend to be more divergent than average. Such traits are said to have been “ascertained” for study. The actual ascertainment process is typically unknown; nonetheless, it is possible to simulate traits under simple ascertainment schemes. Applying the QTLST and the QTLST-EE to these simulated traits provides insight into how robust the tests are to ascertainment bias.