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Size correction: comparing morphological traits among populations and environments


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.

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We thank members of the St. Mary-Osenberg-Bolker lab group and two anonymous reviewers for helpful discussions and comments on previous drafts of this manuscript. We also thank Brian Langerhans and Jonathan Losos for their comments on an earlier draft. We thank Rich Kiltie for pointing us to the literature on CPCA. This work was partially funded by NSF (OCE 0325028 to S. Morgan and B.G.M. and OCE 0242312 to C.W.O., B.M.B. and C. St. Mary) and EPA (STAR Fellowship to J.R.V.). Contribution number 2307 Bodega Marine Laboratory, University of California, Davis, USA.

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Correspondence to Michael W. McCoy.

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Communicated by Diethart Matthies

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McCoy, M.W., Bolker, B.M., Osenberg, C.W. et al. Size correction: comparing morphological traits among populations and environments. Oecologia 148, 547–554 (2006). https://doi.org/10.1007/s00442-006-0403-6

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  • Analysis of covariance
  • Common principal components
  • Residuals
  • Size correction
  • Shearing