On stochastic processes for Quantitative Trait Locus mapping under selective genotyping

International audienceWe consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0,T] representing a chromosome. The originality is in the fact that we are under selective genotyping : only the individuals with extreme phenotypes are genotyped. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0,T] and under local alternatives with a QTL at t* on [0,T]. We show that the LRT is asymptotically the square of a '' non-linear interpolated and normalized Gaussian process ''. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that we have to genotype symetrically and that the threshold is exactly the same as in the situation where all the individuals are genotyped