Polychotomous traits and evolution under conformity

Kaleda K. Denton, Uri Liberman, Marcus W. Feldman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Conformist and anticonformist transmission of dichotomous cultural traits (i.e., traits with two variants) have been studied both experimentally, in many species, and theoretically, with mathematical models. Signatures of types of conformity to polychotomous traits (with more than two variants; e.g., baby names and syllables in bird song) have been inferred from population-level data, but there are few models that include individual-level biases among more than two discrete variants. We generalize the standard dichotomous trait conformity model by Boyd and Richerson to incorporate n ≥ 3 role models and m ≥ 2 variants. Our analysis shows that in the case of n = 3 role models, under anticonformity, the central polymorphic equilibrium p∗ = ( 1 m , . . . , 1 m ) is globally stable, whereas under conformity, if initially the frequencies of ℓ variants are all equal to the maximum variant frequency in the population, there is global convergence to an equilibrium in which the frequencies of these variants are all 1/ℓ and all other variants are absent. With a general number n of role models, the same result holds with conformity, whereas under anticonformity, global convergence is not guaranteed, and there may be stable frequency cycles or chaos. If both conformity and anticonformity occur for different configurations of variants among the n role models, a variety of novel polymorphic equilibriamay exist and be stable. Future empirical studies may use this formulation to directly quantify an individual's level of (anti)conformist bias to a polychotomous trait.

Original languageEnglish
Article numbere2205914119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number39
StatePublished - 27 Sep 2022


  • conformity
  • global convergence
  • polychotomous trait
  • polymorphism
  • stable equilibria


Dive into the research topics of 'Polychotomous traits and evolution under conformity'. Together they form a unique fingerprint.

Cite this