Mapping QTLs for traits measured as percentages

Many quantitative traits are measured as percentages. As a result, the assumption of a normal distribution for the residual errors of such percentage data is often violated. However, most quantitative trait locus (QTL) mapping procedures assume normality of the residuals. Therefore, proper data transformation is often recommended before statistical analysis is conducted. We propose the probit transformation to convert percentage data into variables with a normal distribution. The advantage of the probit transformation is that it can handle measurement errors with heterogeneous variance and correlation structure in a statistically sound manner. We compared the results of this data transformation with other transformations and found that this method can substantially increase the statistical power of QTL detection. We develop the QTL mapping procedure based on the maximum likelihood methodology implemented via the expectation-maximization algorithm. The efficacy of the new method is demonstrated using Monte Carlo simulation.