@article { ISI:000354942900002,
	title = {Genetic Variation, Simplicity, and Evolutionary Constraints for Function-Valued Traits},
	journal = {AMERICAN NATURALIST},
	volume = {185},
	number = {6},
	year = {2015},
	month = {JUN},
	pages = {E166-E181},
	publisher = {UNIV CHICAGO PRESS},
	type = {Article},
	address = {1427 E 60TH ST, CHICAGO, IL 60637-2954 USA},
	abstract = {Understanding the patterns of genetic variation and constraint for continuous reaction norms, growth trajectories, and other function-valued traits is challenging. We describe and illustrate a recent analytical method, simple basis analysis (SBA), that uses the genetic variance-covariance (G) matrix to identify {\textquoteleft}{\textquoteleft}simple{\textquoteright}{\textquoteright} directions of genetic variation and genetic constraints that have straightforward biological interpretations. We discuss the parallels between the eigenvectors (principal components) identified by principal components analysis (PCA) and the simple basis (SB) vectors identified by SBA. We apply these methods to estimated G matrices obtained from 10 studies of thermal performance curves and growth curves. Our results suggest that variation in overall size across all ages represented most of the genetic variance in growth curves. In contrast, variation in overall performance across all temperatures represented less than one-third of the genetic variance in thermal performance curves in all cases, and genetic trade-offs between performance at higher versus lower temperatures were often important. The analyses also identify potential genetic constraints on patterns of early and later growth in growth curves. We suggest that SBA can be a useful complement or alternative to PCA for identifying biologically interpretable directions of genetic variation and constraint in function-valued traits.},
	keywords = {continuous reaction norms, function-valued traits, genetic constraints, genetic variation, growth trajectories, simplicity, thermal performance curves, trade-offs},
	issn = {0003-0147},
	doi = {10.1086/681083},
	author = {Kingsolver, Joel G. and Heckman, Nancy and Zhang, Jonathan and Carter, Patrick A. and Knies, Jennifer L. and Stinchcombe, John R. and Meyer, Karin}
}
@article { ISI:000322829800011,
	title = {VISUALIZING GENETIC CONSTRAINTS},
	journal = {ANNALS OF APPLIED STATISTICS},
	volume = {7},
	number = {2},
	year = {2013},
	month = {JUN},
	pages = {860-882},
	publisher = {INST MATHEMATICAL STATISTICS},
	type = {Article},
	address = {3163 SOMERSET DR, CLEVELAND, OH 44122 USA},
	abstract = {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{\textquoteright}s ability to visualize the subspace and identify interpretable directions of low genetic variability that align with simple directions.},
	keywords = {evolutionary biology, genetic constraints, Principal components},
	issn = {1932-6157},
	doi = {10.1214/12-AOAS603},
	author = {Gaydos, Travis L. and Heckman, Nancy E. and Kirkpatrick, Mark and Stinchcombe, J. R. and Schmitt, Johanna and Kingsolver, Joel and Marron, J. S.}
}
