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Genetics. Sep 2003; 165(1): 411–425.
PMCID: PMC1462744

Comparing G matrices: are common principal components informative?


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.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Badyaev AV, Hill GE. The evolution of sexual dimorphism in the house finch. I. Population divergence in morphological covariance structure. Evolution. 2000 Oct;54(5):1784–1794. [PubMed]
  • Houle David, Mezey Jason, Galpern Paul. Interpretation of the results of common principal components analyses. Evolution. 2002 Mar;56(3):433–440. [PubMed]
  • Lande R. The Genetic Covariance between Characters Maintained by Pleiotropic Mutations. Genetics. 1980 Jan;94(1):203–215. [PMC free article] [PubMed]
  • Magwene PM. New tools for studying integration and modularity. Evolution. 2001 Sep;55(9):1734–1745. [PubMed]
  • Mezey JG, Cheverud JM, Wagner GP. Is the genotype-phenotype map modular? A statistical approach using mouse quantitative trait loci data. Genetics. 2000 Sep;156(1):305–311. [PMC free article] [PubMed]
  • Service PM. The genetic structure of female life history in D. melanogaster: comparisons among populations. Genet Res. 2000 Apr;75(2):153–166. [PubMed]
  • Pfrender ME, Lynch M. Quantitative genetic variation in Daphnia: temporal changes in genetic architecture. Evolution. 2000 Oct;54(5):1502–1509. [PubMed]
  • Wagner GP. Multivariate mutation-selection balance with constrained pleiotropic effects. Genetics. 1989 May;122(1):223–234. [PMC free article] [PubMed]
  • Phillips PC, Whitlock MC, Fowler K. Inbreeding changes the shape of the genetic covariance matrix in Drosophila melanogaster. Genetics. 2001 Jul;158(3):1137–1145. [PMC free article] [PubMed]
  • Roff D. The evolution of the G matrix: selection or drift? Heredity (Edinb) 2000 Feb;84(Pt 2):135–142. [PubMed]
  • Roff Derek. Comparing G matrices: a MANOVA approach. Evolution. 2002 Jun;56(6):1286–1291. [PubMed]

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