Oecologia

, 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
Methods

Abstract

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.

Keywords

Analysis of covariance Common principal components Residuals Size correction Shearing 

Supplementary material

442_2006_403_MOESM1_ESM.pdf (275 kb)
Supplementary material

References

  1. Arnold SJ, Phillips PC (1999) Hierarchical comparison of genetic variance covariance matrices. II. Coastal inland divergence in the garter snake, Thamnophis elegans. Evolution 53:1516–1527CrossRefGoogle Scholar
  2. Blows MW, Chenoweth SF, Hine E (2004) Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits. Am Nat 163:329–340CrossRefPubMedGoogle Scholar
  3. Boidron-Mètairon IF (1988) Morphological plasticity in laboratory-reared chinoplutei of Dendraster excentricus (Eschscholtz) and Lytechinus variegatus (Lamarck) in response to food conditions. J Exp Mar Biol Ecol 119:31–41CrossRefGoogle Scholar
  4. Bolker BM, Holyoak M, Křivan V, Rowe L, Schmitz O (2003) Connecting theoretical and empirical studies of trait-mediated interactions. Ecology 84:1101–1114CrossRefGoogle Scholar
  5. Bookstein FL (1991) Morphometric tools for landmark data: geometry and biology. Cambridge University Press, New York, 435 ppGoogle Scholar
  6. Burnaby TP (1966) Growth-invariant discriminant functions and generalized distances. Biometrics 22:96–107CrossRefGoogle Scholar
  7. Dahl J, Peckarsky BL (2002) Induced morphological defenses in the wild: predator effects on a mayfly, Drunella coloradensis. Ecology 83:1620–1634CrossRefGoogle Scholar
  8. Darlington RB, Smulders TV (2001) Problems with residuals analysis. Anim Behav 62:599–602CrossRefGoogle Scholar
  9. Flury B (1988) Common principal components and related multivariate models. Wiley, New YorkGoogle Scholar
  10. Garcia-Berthou E (2001) On the misuse of residuals in ecology: testing regression residuals vs. the analysis of covariance. J Anim Ecol 70:708–711CrossRefGoogle Scholar
  11. Houle, D, Mezey, J, Galpern, P (2002) Interpretation of the results of common principal components analyses. Evolution 56:433–440PubMedGoogle Scholar
  12. Huitema BE (1980) The analysis of covariance and alternatives. Wiley, New YorkGoogle Scholar
  13. Humphries JM, Bookstein FL, Chernoff B, Smith GR, Elder RL, Elder SG (1981) Multivariate discrimination by shape in relation to size. Syst Zool 30:291–308CrossRefGoogle Scholar
  14. Jolicoeur P (1963) The multivariate generalization of the allometry equation. Biometrics 19:497–499CrossRefGoogle Scholar
  15. Klingenberg CP (1996) Multivariate allometry. In: Marcus LF, Corti M, Loy A, Naylor GJP, Slice DE (eds) Advances in morphometrics. Plenum Press, New York, pp 23–49Google Scholar
  16. Klingenberg CP, Spence JR (1993) Heterochrony and allometry—lessons from the water strider genus Limnoporus. Evolution 47:1834–1853CrossRefGoogle Scholar
  17. Klingenberg CP, Zimmerman M (1992) Static, ontogenetic and evolutionary allometry: a multivariate comparison in 9 species of water striders. Am Nat 140:601–620CrossRefGoogle Scholar
  18. Krzanowski WJ (1979) Between-group comparisons of principal components. J Am Stat Assoc 74:703–707CrossRefGoogle Scholar
  19. Krzanowski WJ (1988) Principles of multivariate analysis: a user’s perspective. Clarendon, OxfordGoogle Scholar
  20. Miner BG (2005) Evolution of feeding structure plasticity in marine invertebrate larvae: a possible trade-off between arm length and stomach size. J Exp Mar Biol Ecol 315:117–125CrossRefGoogle Scholar
  21. Osenberg CW, Sarnelle O, Cooper SD (1997) Effect size in ecological experiments: the application of biological models in meta-analysis. Am Nat 150:798–812CrossRefPubMedGoogle Scholar
  22. Osenberg CW, Sarnelle O, Cooper SD, Holt RD (1999) Resolving ecological questions through meta-analysis: goals, metrics and models. Ecology 80:1105–1117CrossRefGoogle Scholar
  23. Phillips PC, Arnold SJ (1999) Hierarchical comparison of genetic variance covariance matrices. I. Using the Flury hierarchy. Evolution 53:1506–1515CrossRefGoogle Scholar
  24. Relyea RA (2001) Morphological and behavioral plasticity of larval anurans in response to different predators. Ecology 82:523–540CrossRefGoogle Scholar
  25. Relyea R (2004) Fine-tuned phenotypes: tadpole plasticity under 16 combinations of predators and competitors. Ecology 85:172–179CrossRefGoogle Scholar
  26. Relyea RA, Hoverman JT (2003) The impact of larval predators and competitors on the morphology and fitness of juvenile treefrogs. Oecologia 134:596–604PubMedGoogle Scholar
  27. Smith RJ (1999) Statistics of sexual size dimorphism. J Hum Evol 36:423–459CrossRefPubMedGoogle Scholar
  28. Sokal RR, Rohlf FJ (1995) Biometry: the principles and practice of statistics in biological research, 3rd edn. Freeman, New YorkGoogle Scholar
  29. Somers KM (1986) Multivariate allometry and removal of size with principal components analysis. Syst Zool 35:359–368CrossRefGoogle Scholar
  30. Steppan SJ (1997a) Phylogenetic analysis of phenotypic covariance structure. 1. Contrasting results from matrix correlation and common principal component analyses. Evolution 51:571–586CrossRefGoogle Scholar
  31. Steppan SJ (1997b) Phylogenetic analysis of phenotypic covariance structure. 2. Reconstructing matrix evolution. Evolution 51:587–594CrossRefGoogle Scholar
  32. Tollrian RR, Harvell CD (1999) The ecology and evolution of inducible defenses. Princeton University Press, New JerseyGoogle Scholar
  33. Van Buskirk J (2002) A comparative test of the adaptive plasticity hypothesis: relationships between habitat and phenotype in anuran larvae. Am Nat 160:87–102CrossRefPubMedGoogle Scholar
  34. Van Buskirk J, McCollum SA (2000) Functional mechanisms of an inducible defense in tadpoles: morphology and behavior influence mortality risk from predation. J Evol Biol 13:336–347CrossRefGoogle Scholar
  35. Van Buskirk J, Relyea RA (1998) Natural selection for phenotypic plasticity: predator-induced morphological responses in tadpoles. Biol J Linn Soc 65:301–328CrossRefGoogle Scholar
  36. Werner EE, Peacor SD (2003) A review of trait-mediated indirect interactions in ecological communities. Ecology 84:1083–1100CrossRefGoogle Scholar
  37. Winer BJ, Brown DR, Michels KM (1991) Statistical principles in experimental design. McGraw Hill, New YorkGoogle Scholar

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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