Size correction in biology: how reliable are approaches based on (common) principal component analysis?

Oecologia. 2011 Aug;166(4):961-71. doi: 10.1007/s00442-011-1934-z. Epub 2011 Feb 22.

Abstract

Morphological traits typically scale with the overall body size of an organism. A meaningful comparison of trait values among individuals or populations that differ in size therefore requires size correction. A frequently applied size correction method involves subjecting the set of n morphological traits of interest to (common) principal component analysis [(C)PCA], and treating the first principal component [(C)PC1] as a latent size variable. The remaining variation (PC2-PCn) is considered size-independent and interpreted biologically. I here analyze simulated data and natural datasets to demonstrate that this (C)PCA-based size correction generates systematic statistical artifacts. Artifacts arise even when all traits are tightly correlated with overall size, and they are particularly strong when the magnitude of variance is heterogeneous among the traits, and when the traits under study are few. (C)PCA-based approaches are therefore inappropriate for size correction and should be abandoned in favor of methods using univariate general linear models with an adequate independent body size metric as covariate. As I demonstrate, (C)PC1 extracted from a subset of traits, not themselves subjected to size correction, can provide such a size metric.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Body Size*
  • Computer Simulation
  • Models, Statistical
  • Principal Component Analysis*
  • Smegmamorpha