Title :

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

Author(s) :

Billiard, Sylvain [Auteur]
Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198 [Evo-Eco-Paléo (EEP)]
Derex, Maxime [Auteur]
Maisonneuve, Ludovic [Auteur]
Institut de Systématique, Evolution, Biodiversité [ISYEB ]
Rey, Thomas [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]

Journal title :

Mathematical Models and Methods in Applied Sciences

Pages :

2691-2723

Publisher :

World Scientific Publishing

Publication date :

2020-12-07

ISSN :

0218-2025

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Sciences de l'Homme et Société/Anthropologie sociale et ethnologie

English abstract : [en]

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. ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Modèles multi-échelles et simulation numérique hybride de semi-conducteurs
Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Institut for Advanced Study in Toulouse

Collections :

• Évolution, Écologie et Paléontologie (Evo Eco Paleo) - UMR 8198

Source :

Harvested from HAL