Coherence thresholds in models of language change and evolution: the effects of noise, dynamics and network of interactions

TL;DR

This paper investigates how network structure and noise influence the critical coherence threshold in models of language evolution, combining simulations and theoretical analysis to understand the robustness of linguistic coherence.

Contribution

It provides a detailed analysis of the effects of network topology and dynamics on the coherence threshold in language evolution models, extending previous mean field results.

Findings

Coherence threshold is robust in replicator-mutator models across network types.

Network structure can significantly affect the coherence threshold in fitness-driven models.

Numerical simulations and theoretical analysis confirm the impact of interaction networks on language stability.

Abstract

A simple model of language evolution, proposed in \cite{K_N}, is characterized by a pay-off in communicative function, and by an error in learning, that measures the accuracy in language acquisition. In the mean field approximation, this model exhibits a critical coherence threshold, i.e. a minimal accuracy in the learning process is required to maintain linguistic coherence. In this work, we analyse in detail the effects of different fitness based dynamics driving linguistic coherence and of the network of interactions on the nature of the coherence threshold, by performing numerical simulations and theoretical analyses of generalized replicator-mutator dynamics in populations with two types of structure: fully connected networks and regular random graphs. We find that although the threshold of the replicator-mutator evolutionary model is robust with respect to the structure of the network of contacts, the coherence threshold of related fitness driven models may be strongly affected by this feature.