TY - JOUR
T1 - Polychotomous traits and evolution under conformity
AU - Denton, Kaleda K.
AU - Liberman, Uri
AU - Feldman, Marcus W.
N1 - Publisher Copyright:
© 2022 the Author(s).
PY - 2022/9/27
Y1 - 2022/9/27
N2 - 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.
AB - 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.
KW - conformity
KW - global convergence
KW - polychotomous trait
KW - polymorphism
KW - stable equilibria
UR - http://www.scopus.com/inward/record.url?scp=85138129716&partnerID=8YFLogxK
U2 - 10.1073/pnas.2205914119
DO - 10.1073/pnas.2205914119
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
C2 - 36122242
AN - SCOPUS:85138129716
SN - 0027-8424
VL - 119
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 39
M1 - e2205914119
ER -