Interval Mapping for Quantitative trait Loci Detection

Abstract

The advent of complete genetic linkage maps of DNA markers has made the systematic study of mapping the quantitative trait loci (QTL) in experimental organisms feasible. In recent years, methodological research on QTL mapping has been extensively carried out. However, some related statistical problems remain unsolved. In this talk, we consider these problems for the method of interval mapping under the finite mixture models proposed by Lander and Botstein (1989, Genetics). They include the identifiability of the involved irregular statistical models and the consistency of the maximum likelihood estimates of the putative QTL effect and position. The asymptotic distribution of the likelihood ratio test (LRT) statistic for the QTL detection is studied via a non-standard approach. The asymptotic results obtained provide a structure for the asymptotic distribution which enjoys the invariance property of regular models and can be used to simulate the approximate the critical values or p- values of the LRT. On the basis of the results, a new approach based on our results can be developed for the determination of threshold values to control the false positive error across the whole genome in interval mapping. The results are presented for the backcross model. They, however, are applicable for the intercross model as well. The talk is based on joint work with Dr. Zehua Chen at National University of Singapore.