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Open Access Methodology article

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

John S Yap1, Yao Li2, Kiranmoy Das3, Jiahan Li3 and Rongling Wu34*

Author Affiliations

1 Department of Statistics, University of Florida, Gainesville, FL 32611 USA

2 Department of Statistics, West Virginia University, Morgantown, WV 26506, USA

3 Center for Statistical Genetics, Pennsylvania State University, Hershey, PA 17033, USA

4 Center for Computational Biology, Beijing Forestry University, Beijing 100083, PR China

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BMC Plant Biology 2011, 11:23  doi:10.1186/1471-2229-11-23

Published: 26 January 2011



The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors.


We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects.


The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings.