The indirect genetic effect interaction coefficient ψ: theoretically essential and empirically neglected

Nathan W Bailey*, Camille Desjonquères*

*Corresponding author for this work

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The interaction effect coefficient ψ has been a much-discussed, fundamental parameter of indirect genetic effect (IGE) models since its formal mathematical description in 1997. The coefficient simultaneously describes the form of changes in trait expression caused by genes in the social environment and predicts the evolutionary consequences of those IGEs. Here, we report a striking mismatch between theoretical emphasis on ψ and its usage in empirical studies. Surveying all IGE research, we find that the coefficient ψ has not been equivalently conceptualized across studies. Several issues related to its proper empirical measurement have recently been raised, and these may severely distort interpretations about the evolutionary consequences of IGEs. We provide practical advice on avoiding such pitfalls. The majority of empirical IGE studies use an alternative variance-partitioning approach rooted in well-established statistical quantitative genetics, but several hundred estimates of ψ (from 15 studies) have been published. A significant majority are positive. In addition, IGEs with feedback, that is, involving the same trait in both interacting partners, are far more likely to be positive and of greater magnitude. Although potentially challenging to measure without bias, ψ has critically-developed theoretical underpinnings that provide unique advantages for empirical work. We advocate for a shift in perspective for empirical work, from ψ as a description of IGEs, to ψ as a robust predictor of evolutionary change. Approaches that "run evolution forward" can take advantage of ψ to provide falsifiable predictions about specific trait interactions, providing much-needed insight into the evolutionary consequences of IGEs.

Original languageEnglish
Article numberesab056
Pages (from-to)79–90
Number of pages12
JournalJournal of Heredity
Issue number1
Early online date1 Nov 2021
Publication statusPublished - Jan 2022


  • Indirect genetic effect
  • Interacting phenotype
  • Interaction coefficient
  • Social evolution
  • Trait-based analysis
  • Variance partitioning


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