Box-Cox transformation for QTL mapping.

The maximum likelihood method of QTL mapping assumes that the phenotypic values of a quantitative trait follow a normal distribution. If the assumption is violated, some forms of transformation should be taken to make the assumption approximately true. The Box-Cox transformation is a general transformation method which can be applied to many different types of data. The flexibility of the Box-Cox transformation is due to a variable, called transformation factor, appearing in the Box-Cox formula. We developed a maximum likelihood method that treats the transformation factor as an unknown parameter, which is estimated from the data simultaneously along with the QTL parameters. The method makes an objective choice of data transformation and thus can be applied to QTL analysis for many different types of data. Simulation studies show that (1) Box-Cox transformation can substantially increase the power of QTL detection; (2) Box-Cox transformation can replace some specialized transformation methods that are commonly used in QTL mapping; and (3) applying the Box-Cox transformation to data already normally distributed does not harm the result.