Mean-Variance QTL Mapping on a Background of Variance Heterogeneity

Abstract

Most QTL mapping approaches seek to identify \"mean QTL\", genetic loci that influence the phenotype mean, after assuming that all individuals in the mapping population have equal residual variance. Recent work has broadened the scope of QTL mapping to identify genetic loci that influence phenotype variance, termed \"variance QTL\", or some combination of mean and variance, which we term \"mean-variance QTL\". Even these approaches, however, fail to address situations where some other factor, be it an environmental factor or a distant genetic locus, influences phenotype variance. We term this situation \"background variance heterogeneity\" (BVH) and used simulation to explore its effects on the power and false positive rate of tests for mean QTL, variance QTL, and mean-variance QTL. Specifically, we compared traditional tests, linear regression for mean QTL and Levenes test for variance QTL, with tests more recently developed, namely Caos tests for all three types of QTL, and tests based on the double generalized linear model (DGLM), which, unlike the other approaches, explicitly models BVH. Simulations showed that, when used in conjunction with a permutation procedure, the DGLM-based tests accurately control false positive rate and are more powerful than the other tests. We also discovered that the rank-based inverse normal transform, often used to corral unruly phenotypes, can be used to mitigate the adverse effects of BVH in some circumstances. We applied the DGLM approach, which we term \"mean-variance QTL mapping\", to publicly available data on a mouse backcross of CAST/Ei into M16i and, after accommodating BVH driven by father, identified a new mean QTL for bodyweight at three weeks of age.