Sirs

It is common practice to name a particular phenomenon after the person who first discovered it. This can sometimes provide useful and easily remembered shorthand for discussion of the phenomenon. But sometimes it is difficult to know whose name to use. An interesting example is provided by the phenomenon that, when undertaking whole- or partial-genome scans, estimates of significant quantitative trait loci (QTL) effects are biased upwards. This has come to be known as `the Beavis effect' (for example, see Refs 1,2) on the basis of a paper in the proceedings of a conference3, in which William D. Beavis showed the degree of bias that is expected for several situations.

This estimation bias was, however, widely recognized and a topic of discussion in the QTL-mapping community for at least a decade previously. The problem of such a bias and how to solve it was discussed explicitly by Lande and Thompson in 1990 (Ref. 4). Before that, Smith and Simpson5 had shown that the variance of estimated QTL effects was greater than the variance of true QTL effects. In more general terms, the problem of bias of estimates, when selecting a posteriori among many estimates, is a long-recognized problem in statistics (for example, see Ref. 6). An estimate is equal to the true underlying value of the parameter being estimated plus an error term. If many estimates are made and then the largest estimates are selected, the selected estimates will tend to be those that have both large underlying parameter values and large positive error terms. These positive error terms create a positive bias in the selected estimates.

In quantitative genetics, the problem of biased estimates has been considered, for example, when selecting individuals on the basis of estimated additive genetic merit (breeding value). Methods for obtaining unbiased estimates of breeding values have been found in the form of classical selection indexes7, which are the standard equations for the prediction of a response when selecting on the basis of an individual's phenotype (for example, see Ref. 8), and the generation of best linear unbiased predictions of breeding values9. So who, if anyone, should this phenomenon of biased estimators be named after? Arguments could be made for virtually any of the authors listed above. Restricting eligibility to the QTL literature, Smith and Simpson5 and Lande and Thompson4 both have very clear precedence over Beavis, but an exhaustive review of the literature might well turn up other claimants.