Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases

Sylvain Billiard (1) , Maxime Derex (2) , Ludovic Maisonneuve (3) , Thomas Rey (4)

1 Evo-Eco-Paléo (EEP) - Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198
2 TSE-R - Toulouse School of Economics
3 ISYEB - Institut de Systématique, Evolution, Biodiversité
4 RAPSODI - Reliable numerical approximations of dissipative systems

Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work, we introduce a mathematically oriented model that shares properties with individual based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker, S. Smale, Bull. Amer. Math. Soc, 39 (1), 2002] and [F. Cucker, S. Smale and D. X Zhou, Found. Comput. Math., 2004]. After deriving the model, we study some of its mathematical properties, and establish theoretical and quantitative results in a simplified case. Finally, we run numerical simulations to illustrate some properties of the model.

Mots clés: language evolution; inhomogeneous Markov chains; concentration inequalities; numerical simulations; convergence to equilibrium; Individual based model; cultural evolution; cumulative culture

Domaines: Probabilités [math.PR]; Anthropologie sociale et ethnologie

Sylvain Billiard, Maxime Derex, Ludovic Maisonneuve, Thomas Rey. Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases. Mathematical Models and Methods in Applied Sciences, 2020, 30 (14), pp.2691-2723. ⟨10.1142/S0218202520500529⟩. ⟨hal-02357188v2⟩