Statistics and Its Interface

Volume 10 (2017)

Number 3

A nonparametric approach for functional mapping of complex traits

Pages: 387 – 397



Han Hao (Department of Mathematics, University of North Texas, Denton, Tx., U.S.A.)

Lidan Sun (Beijing Key Laboratory of Ornamental Plants Germplasm Innovation & Molecular Breeding, National Engineering Research Center for Floriculture, Beijing Forestry University, Beijing, China)

Xuli Zhu (Center for Computational Biology, Beijing Forestry University, Beijing, China)

Rongling Wu (Center for Statistical Genetics, Pennsylvania State University, Hershey, Penn., U.S.A.)


Functional mapping is a statistical tool for mapping quantitative trait loci (QTLs) involved with a function-valued phenotypic trait. The utility of functional mapping is often displayed when the phenotypic trait represent a developmental process and can be modeled by a parametric approach. However, there are many practical situations in which no explicit parametric forms are feasible to capture the dynamic change of phenotypic traits across a time or space scale. We address this issue to expand the applying scope of functional mapping by utilizing a nonparametric adaptive high-dimensional ANOVA (HANOVA) method. A discrete Fourier transformation was implemented to eliminate the dependence structure of errors that are assumed to be stationary along the measurement process, followed by the choice of the first several Fourier coefficients that can explain a majority of phenotypic variation for QTL mapping. From simulation tests, HANOVA-based functional mapping was observed to display high statistical power for detecting subtle variation. By analyzing the real dataset of a mapping population for mei, a woody ornamental plant naturally distributed in China, the new model has successfully identified many significant QTLs that control leaf shape. The model should find its immediate implications for mapping any high-dimensional phenotypic measurements with no explicit form.


functional mapping, functional ANOVA, QTL, discrete Fourier transformation, woody plant

2010 Mathematics Subject Classification

Primary 62G05, 62H15. Secondary 62P10.

Published 31 January 2017