Ontogeny and Individual Variation: Analysis of Patterned Covariance Matrices with Common Principal Components

1996 ◽  
Vol 45 (2) ◽  
pp. 135-150 ◽  
Author(s):  
Christian Peter Klingenberg ◽  
Beat E. Neuenschwander ◽  
Bernard D. Flury
Keyword(s):  
Principal Components ◽  
Individual Variation ◽  
Covariance Matrices ◽  
Variation Analysis ◽  
Common Principal Components ◽  
Patterned Covariance ◽  
Patterned Covariance Matrices

scholarly journals Comparing G Matrices: Are Common Principal Components Informative?

Genetics ◽  
2003 ◽  
Vol 165 (1) ◽  
pp. 411-425
Author(s):  
Jason G Mezey ◽  
David Houle
Keyword(s):  
Principal Components ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Covariance Matrices ◽  
Allele Frequencies ◽  
Modular Organization ◽  
Common Principal Components ◽  
Different Populations ◽  
G Matrices ◽  
Allele Model

Abstract Common principal components (CPC) analysis is a technique for assessing whether variance-covariance matrices from different populations have similar structure. One potential application is to compare additive genetic variance-covariance matrices, G. In this article, the conditions under which G matrices are expected to have common PCs are derived for a two-locus, two-allele model and the model of constrained pleiotropy. The theory demonstrates that whether G matrices are expected to have common PCs is largely determined by whether pleiotropic effects have a modular organization. If two (or more) populations have modules and these modules have the same direction, the G matrices have a common PC, regardless of allele frequencies. In the absence of modules, common PCs exist only for very restricted combinations of allele frequencies. Together, these two results imply that, when populations are evolving, common PCs are expected only when the populations have modules in common. These results have two implications: (1) In general, G matrices will not have common PCs, and (2) when they do, these PCs indicate common modular organization. The interpretation of common PCs identified for estimates of G matrices is discussed in light of these results.

Model-based principal components of covariance matrices

2010 ◽  
Vol 63 (1) ◽  
pp. 113-137 ◽  
Author(s):  
Robert J. Boik ◽  
Kamolchanok Panishkan ◽  
Scott K. Hyde
Keyword(s):  
Principal Components ◽  
Covariance Matrices ◽  
Model Based
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