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 (QTLSTEE), 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 QTLSTEE is not as biologically realistic as the QTLST, it is still preferable to a simple sign test. However, the statistical properties of the QTLSTEE are not clear from Orr (1998). The recent publication of a report (Rieseberget al. 2002) applying the QTLSTEE to numerous traits and rejecting the neutral evolution hypothesis for many of them prompted us to investigate the statistical behavior of the QTLST and QTLSTEE. 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 QTLSTEE to these simulated traits provides insight into how robust the tests are to ascertainment bias.
We simulated traits under a simple ascertainment scheme in which the traits selected for study were the maximally different of T identically and independently distributed traits. Larger values of T correspond to more extreme ascertainment of traits. Applying the two tests to these simulated traits, we find that the QTLST is conservative—the risk of falsely rejecting the null hypothesis using the QTLST is lower than the reported P value. Further, the QTLST remains conservative even when T is as high as 50. However, our results indicate that the QTLSTEE does not enjoy this insensitivity to the ascertainment scheme and may lead one to regularly reject the hypothesis of neutral evolution of an ascertained trait, even when that hypothesis is true.
We first simulated traits under the neutral evolution model assumed for the QTLST with n = 10 loci and assuming that there was no threshold for detection of the effect of a locus. Under this model, the tth simulated trait (t = 1,..., T) has trait difference
This testing procedure was completed 1000 times for each of four different values of T = 1, 10, 25, 50, and the resulting P values of the test were recorded. The results are shown in the plots of R vs. P value in Figure 1. In the figure, a dotted line appears at the P value of 0.05. For a test of size 0.05 one would expect 50 of 1000 data sets simulated under the null hypothesis to fall beneath this line. For all levels of ascertainment, far fewer of the data sets are rejected: 2 for T = 2, 8 for T = 10, 10 for T = 25, and 12 for T = 50. Thus, while increasing the ascertainment intensity does increase the type 1 error rate, the error rate still remains much smaller than the nominal P value. The QTLST, at least when the shape and scale parameter of the effect size distribution are known, appears to be conservative and is little affected by trait ascertainment.
We performed similar simulations and applied the QTLSTEE to them. With 10 loci, if
The process by which traits come to be studied by quantitative genetics techniques is complex, involving psychological and historical factors that we may never hope to model explicitly. However, it seems evident that traits selected for study are not a random sample of all possible traits that one could investigate. Rather, in the search for QTL, investigators will focus on traits that show marked differences between lines. In this way, our simple ascertainment simulations mimic reality—when one considers the many traits available for study, ascertainment of the greatest trait difference of 50 traits does not seem extreme.
From our simulations, it appears that the QTLST, by conditioning upon a trait difference of R or greater, appropriately controls for trait ascertainment. It is clear, however, that the QTLSTEE is not robust to trait ascertainment. Accordingly, any conclusions from the QTLSTEE regarding the neutral evolution hypothesis must be regarded with caution.
Acknowledgments
We gratefully acknowledge helpful correspondence with Allen Orr and Loren Rieseberg and discussions with Jeff Townsend, Alison Galvani, and John Novembre. This work was supported by National Institutes of Health grant GM40282 to M.S.
Footnotes

Communicating editor: M. K. Uyenoyama
 Received December 30, 2002.
 Accepted May 21, 2003.
 Copyright © 2003 by the Genetics Society of America