University of Oulu

Vanhatalo, J., Li, Z., & Sillanpää, M. J. (2019). A Gaussian process model and Bayesian variable selection for mapping function-valued quantitative traits with incomplete phenotypic data. Bioinformatics, 35(19), 3684–3692.

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

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Author: Vanhatalo, Jarno1; Li, Zitong2; Sillanpää, Mikko J.3
Organizations: 1Department of Mathematics and Statistics and Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki FI-00014, Finland
2CSIRO Agriculture & Food, GPO Box 1600, Canberra, ACT 2601, Australia
3Department of Mathematical Sciences, Biocenter Oulu and Infotech Oulu University of Oulu, Oulu FI-90014, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.9 MB)
Persistent link:
Language: English
Published: Oxford University Press, 2019
Publish Date: 2019-10-17


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.

Availability and implementation: Software and simulated data are available as a MATLAB package ‘GPQTLmapping’, and they can be downloaded from GitHub ( Real datasets used in case studies are publicly available at QTL Archive.

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Series: Bioinformatics
ISSN: 1367-4803
ISSN-E: 1460-2059
ISSN-L: 1367-4803
Volume: 35
Issue: 19
Pages: 3684 - 3692
DOI: 10.1093/bioinformatics/btz164
Type of Publication: A1 Journal article – refereed
Field of Science: 112 Statistics and probability
1184 Genetics, developmental biology, physiology
Funding: The work was funded by Academy of Finland [grant 317255].
Copyright information: © The Author(s) 2019. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact