, Volume 148, Issue 4, pp 547–554

Size correction: comparing morphological traits among populations and environments

  • Michael W. McCoy
  • Benjamin M. Bolker
  • Craig W. Osenberg
  • Benjamin G. Miner
  • James R. Vonesh


Morphological relationships change with overall body size and body size often varies among populations. Therefore, quantitative analyses of individual traits from organisms in different populations or environments (e.g., in studies of phenotypic plasticity) often adjust for differences in body size to isolate changes in allometry. Most studies of among population variation in morphology either (1) use analysis of covariance (ANCOVA) with a univariate measure of body size as the covariate, or (2) compare residuals from ordinary least squares regression of each trait against body size or the first principal component of the pooled data (shearing). However, both approaches are problematic. ANCOVA depends on assumptions (small variance in the covariate) that are frequently violated in this context. Residuals analysis assumes that scaling relationships within groups are equal, but this assumption is rarely tested. Furthermore, scaling relationships obtained from pooled data typically mischaracterize within-group scaling relationships. We discuss potential biases imposed by the application of ANCOVA and residuals analysis for quantifying morphological differences, and elaborate and demonstrate a more effective alternative: common principal components analysis combined with Burnaby’s back-projection method.


Analysis of covariance Common principal components Residuals Size correction Shearing 

Supplementary material

442_2006_403_MOESM1_ESM.pdf (275 kb)
Supplementary material


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Michael W. McCoy
    • 1
  • Benjamin M. Bolker
    • 1
  • Craig W. Osenberg
    • 1
  • Benjamin G. Miner
    • 1
    • 2
  • James R. Vonesh
    • 1
    • 3
  1. 1.Department of ZoologyUniversity of FloridaGainesvilleUSA
  2. 2.Biology DepartmentWestern Washington UniversityBellinghamUSA
  3. 3.Department of BiologyWashington UniversitySt. LuisUSA

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