Pleiotropic QTL analysis

Statistical methods for the detection of genes influencing quantitative trait (QTLs) with the aid of genetic markers are well developed for the analysis of a single trait. In practice, many experimental data contain observations on multiple correlated traits and methods that permit joint analysis of all traits are now required. Generalisation of the maximum likelihood method to a multitrait analysis is a good approach, but the increase in complexity due to the number of parameters to be estimated simultaneously, could restrain its practical use when the number of traits is large. We propose an alternative method based on two separate steps. The first step is to estimate the (co)variance matrix of the traits and use this estimate to obtain the canonical variables associated to the traits. The second step is to apply a single-trait maximum likelihood method to each of the canonical variables and to combine the results. Working in a local asymptotic framework for the effects of the putative pleiotropic QTL, i.e., for a pleiotropic QTL whose effect is too small to be detected with certainty, we prove that the combined analysis with canonical variables is asymptotically equivalent to a multitrait maximum likehood analysis. A threshold for the mapping of the pleiotropic QTL is also given. The probability of detecting a QTL is not always increased by the addition of more correlated traits. As an example, a theoretical comparison between the power of a multitrait analysis with two variables and the power of a single-trait analysis is presented. Experimental data collected to study the polygenic resistance of tomato plants to bacterial wilt are used to illustrate the combined analysis with canonical variables.