Most published selection gradients are underestimated: Why this is and how to fix it

Niels Jeroen Dingemanse, Yimen G. Araya-Ajoy, David F. Westneat

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Ecologists and evolutionary biologists routinely estimate selection gradients. Most researchers seek to quantify selection on individual phenotypes, regardless of whether fixed or repeatedly expressed traits are studied. Selection gradients estimated to address such questions are attenuated unless analyses account for measurement error and biological sources of within-individual variation. Estimates of standardized selection gradients published in Evolution between 2010 and 2019 were primarily based on traits measured once (59% of 325 estimates). We show that those are attenuated: bias increases with decreasing repeatability but differently for linear versus nonlinear gradients. Others derived individual-mean trait values prior to analyses (41%), typically using few repeats per individual, which does not remove bias. We evaluated three solutions, all requiring repeated measures: (i) correcting gradients derived from classic models using estimates of trait correlations and repeatabilities, (ii) multivariate mixed-effects models, previously used for estimating linear gradients (seven estimates, 2%), which we expand to nonlinear analyses, and (iii) errors-in-variables models that account for within-individual variance, and are rarely used in selection studies. All approaches produced accurate estimates regardless of repeatability and type of gradient, however, errors-in-variables models produced more precise estimates and may thus be preferable.

Original languageEnglish
Pages (from-to)806-818
Number of pages13
Issue number4
StatePublished - Apr 2021

Bibliographical note

Funding Information:
We thank Dirk Metzler, Shinichi Nakagawa, Raphael Royauté, Anne Rutten, and Alastair Wilson. NJD was supported by the German Science Foundation (grant no. DI 1694/1‐1), YA‐A by the Research Council of Norway (Centres of Excellence funding scheme; grant no. 223257), and DFW by the U.S. National Science Foundation (grant no. IOS‐1656212) and the University of Kentucky.

Publisher Copyright:
© 2021 The Authors. Evolution published by Wiley Periodicals LLC on behalf of The Society for the Study of Evolution.


  • Bias
  • measurement error
  • multivariate mixed-modeling
  • phenotypic selection
  • plasticity
  • repeatability

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Genetics
  • Agricultural and Biological Sciences (all)


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