Open Access
June 2013 Visualizing genetic constraints
Travis L. Gaydos, Nancy E. Heckman, Mark Kirkpatrick, J. R. Stinchcombe, Johanna Schmitt, Joel Kingsolver, J. S. Marron
Ann. Appl. Stat. 7(2): 860-882 (June 2013). DOI: 10.1214/12-AOAS603


Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of the data for subsequent analysis. The remaining principal components are ignored since they explain little of the variation in the data. However, evolutionary biologists gain important insights from these low variation directions. Specifically, they are interested in directions of low genetic variability that are biologically interpretable. These directions are called genetic constraints and indicate directions in which a trait cannot evolve through selection. Here, we propose studying the subspace spanned by low variance principal components by determining vectors in this subspace that are simplest. Our method and accompanying graphical displays enhance the biologist’s ability to visualize the subspace and identify interpretable directions of low genetic variability that align with simple directions.


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Travis L. Gaydos. Nancy E. Heckman. Mark Kirkpatrick. J. R. Stinchcombe. Johanna Schmitt. Joel Kingsolver. J. S. Marron. "Visualizing genetic constraints." Ann. Appl. Stat. 7 (2) 860 - 882, June 2013.


Published: June 2013
First available in Project Euclid: 27 June 2013

zbMATH: 1288.62101
MathSciNet: MR3113493
Digital Object Identifier: 10.1214/12-AOAS603

Keywords: evolutionary biology , genetic constraints , principal components

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 2 • June 2013
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