Replicator-mutator dynamics of linguistic convergence and divergence

Area of Science:

• Sociolinguistics
• Evolutionary Game Theory
• Mathematical Modeling

Background:

• Individuals often adjust their language to match their ingroup and differentiate from outgroups.
• This sociolinguistic identity maintenance is a widespread human behavior.

Purpose of the Study:

• To model sociolinguistic identity maintenance as an evolutionary game.
• To analyze the dynamics of language use in multi-population settings.
• To test the model against empirical data from adolescent language behavior.

Main Methods:

• Utilized a multi-population extension of the replicator-mutator equation.
• Employed linearization to determine the stability of dynamic equilibria in a two-population model.
• Applied numerical solution methods to an asymmetric three-population extension.

Main Results:

• Identified stable equilibria for the symmetric two-population game.
• Found that empirical adolescent language data aligns with a stable equilibrium under plausible mutation rates.
• The three-population model predicts specific equilibrium convergence.

Conclusions:

• The evolutionary game model successfully captures sociolinguistic identity maintenance.
• The model provides a framework for understanding language dynamics in social groups.
• Predictive power demonstrated for adolescent language behavior and convergence to stable states.