The Annals of Applied Statistics

Visualizing genetic constraints

Travis L. Gaydos, Nancy E. Heckman, Mark Kirkpatrick, J. R. Stinchcombe, Johanna Schmitt, Joel Kingsolver, and J. S. Marron

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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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Ann. Appl. Stat., Volume 7, Number 2 (2013), 860-882.

First available in Project Euclid: 27 June 2013

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Principal components evolutionary biology genetic constraints


Gaydos, Travis L.; Heckman, Nancy E.; Kirkpatrick, Mark; Stinchcombe, J. R.; Schmitt, Johanna; Kingsolver, Joel; Marron, J. S. Visualizing genetic constraints. Ann. Appl. Stat. 7 (2013), no. 2, 860--882. doi:10.1214/12-AOAS603.

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Supplemental materials

  • Supplementary material A: Supplementary plots. As previously noted, supplementary material [Gaydos et al. (2013a)] contains a complete set of plots from our data analyses, as in Figures 3 through 6.
  • Supplementary material B: Nearly null space example. An additional supplementary file [Gaydos et al. (2013b)] contains a simple example that shows the benefits of the proposed methodology.