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. 2014 Aug;197(4):1409-16.
doi: 10.1534/genetics.114.166306. Epub 2014 Jun 14.

A Simple Regression-Based Method to Map Quantitative Trait Loci Underlying Function-Valued Phenotypes

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Free PMC article

A Simple Regression-Based Method to Map Quantitative Trait Loci Underlying Function-Valued Phenotypes

Il-Youp Kwak et al. Genetics. .
Free PMC article

Abstract

Most statistical methods for quantitative trait loci (QTL) mapping focus on a single phenotype. However, multiple phenotypes are commonly measured, and recent technological advances have greatly simplified the automated acquisition of numerous phenotypes, including function-valued phenotypes, such as growth measured over time. While methods exist for QTL mapping with function-valued phenotypes, they are generally computationally intensive and focus on single-QTL models. We propose two simple, fast methods that maintain high power and precision and are amenable to extensions with multiple-QTL models using a penalized likelihood approach. After identifying multiple QTL by these approaches, we can view the function-valued QTL effects to provide a deeper understanding of the underlying processes. Our methods have been implemented as a package for R, funqtl.

Keywords: QTL; function-valued trait; growth curves; model selection.

Figures

Figure 1
Figure 1
Signed LOD scores from single-QTL genome scans, with each time point considered individually.
Figure 2
Figure 2
(A–D) The SLOD (A), MLOD (B), EE(Wald) (C), and EE(Residual) (D) curves for the root tip angle data. A red horizontal line indicates the calculated 5% permutation-based threshold.
Figure 3
Figure 3
(A and B) SLOD (A) and MLOD (B) profiles for a multiple-QTL model for the root tip angle data set.
Figure 4
Figure 4
(A–D) The regression coefficients estimated for the root tip angle data set: the estimated baseline function (A) and the estimated QTL effects (B-D). The red curves are for the two-QTL model (from the penalized-SLOD criterion) and the blue dashed curves are for the three-QTL model (from the penalized-MLOD criterion). Positive values for the QTL effects indicate that the Cvi allele increases the tip angle phenotype.
Figure 5
Figure 5
Power as a function of the percentage of phenotypic variance explained by a single QTL. The left column is for n = 100, the center column is for n = 200, and the right column is for n = 400. The three rows correspond to the covariance structure (autocorrelated, equicorrelated, and unstructured). In each panel, SLOD is in red, MLOD is in blue, EE(Wald) is in brown, EE(Residual) is in green, and parametric is in black.
Figure 6
Figure 6
Power as a function of the percentage of phenotypic variance explained by a single QTL, with additional noise added to the phenotypes. The left column has no additional noise; the center and right columns have independent normally distributed noise added at each time point, with standard deviations 1 and 2, respectively. The three rows correspond to the covariance structure (autocorrelated, equicorrelated, and unstructured). In each panel, SLOD is in red, MLOD is in blue, EE(Wald) is in brown, EE(Residual) is in green, and parametric is in black. The percentage of variance explained by the QTL on the x-axis refers, in each case, to the variance explained in the case of no added noise.

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