PLEIOTROPIC QTL ANALYSIS

Statistical methods for the detection of genes influencing quantitativ e trait (QTLs) with the aid of genetic markers are well developed for the analysis of a single trait. In practice, many experimental data co ntain observations on multiple correlated traits and methods that perm it joint analysis of all traits are now required. Generalisation of th e maximum likelihood method to a multitrait analysis is a good approac h, but the increase in complexity due to the number of parameters to b e estimated simultaneously, could restrain its practical use when the number of traits is large. We propose an alternative method based on t wo separate steps. The first step is to estimate the (co)variance matr ix of the traits and use this estimate to obtain the canonical variabl es associated to the traits. The second step is to apply a single-trai t maximum likelihood method to each of the canonical variables and to combine the results. Working in a local asymptotic framework for the e ffects of the putative pleiotropic QTL, i.e., for a pleiotropic QTL wh ose effect is too small to be detected with certainty, we prove that t he combined analysis with canonical variables is asymptotically equiva lent to a multitrait maximum likehood analysis. A threshold for the ma pping of the pleiotropic QTL is also given. The probability of detecti ng a QTL is not always increased by the addition of more correlated tr aits. As an example, a theoretical comparison between the power of a m ultitrait analysis with two variables and the power of a single-trait analysis is presented. Experimental data collected to study the polyge nic resistance of tomato plants to bacterial wilt are used to illustra te the combined analysis with canonical variables.