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.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS603 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
