A Gaussian process model and Bayesian variable selection for mapping function-valued quantitative traits with incomplete phenotypic data

Motivation: Recent advances in high dimensional phenotyping bring time as an extra dimension into the phenotypes. This promotes the quantitative trait locus (QTL) studies of function-valued traits such as those related to growth and development. Existing approaches for analyzing functional traits utilize either parametric methods or semi-parametric approaches based on splines and wavelets. However, very limited choices of software tools are currently available for practical implementation of functional QTL mapping and variable selection. Results: We propose a Bayesian Gaussian process (GP) approach for functional QTL mapping. We use GPs to model the continuously varying coefficients which describe how the effects of molecular markers on the quantitative trait are changing over time. We use an efficient gradient based algorithm to estimate the tuning parameters of GPs. Notably, the GP approach is directly applicable to the incomplete datasets having even larger than 50% missing data rate (among phenotypes). We further develop a stepwise algorithm to search through the model space in terms of genetic variants, and use a minimal increase of Bayesian posterior probability as a stopping rule to focus on only a small set of putative QTL. We also discuss the connection between GP and penalized B-splines and wavelets. On two simulated and three real datasets, our GP approach demonstrates great flexibility for modeling different types of phenotypic trajectories with low computational cost. The proposed model selection approach finds the most likely QTL reliably in tested datasets.