Abstract
People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity maintenance as an evolutionary game in which individuals play the field and the dynamics are supplied by a multi-population extension of the replicator–mutator equation. Using linearization, the stabilities of all dynamic equilibria of the game in its fully symmetric two-population special case are found. The model is then applied to an empirical test case from adolescent sociolinguistic behaviour. It is found that the empirically attested population state corresponds to one of a number of stable equilibria of the game under an independently plausible value of a parameter controlling the rate of linguistic mutations. An asymmetric three-population extension of the game, explored with numerical solution methods, furthermore predicts to which specific equilibrium the system converges.
Highlights
Most mathematical models of linguistic variation and change fall into one of two classes: (i) those that study homogeneous populations of speakers in frameworks that admit an analytical exploration of the model’s dynamics [1,2,3], and (ii) those that aim to elucidate complex interactions of language learning and use in social networks through agent-based simulations [4,5,6]
The results presented in this paper suggest that classical patterns of variation and change can arise from an intuitively plausible source, but one that has not received much attention in the modelling literature—the opposing forces arising from the dynamics of subpopulations which lie, in one sense or another, in an antagonistic relation to each other
A formal investigation of this model reveals that the ‘convergence–divergence game’, as I shall call it below, has a number of stable equilibria depending on a combination of global parameters, namely, parameters describing the strength of ingroup social convergence and outgroup divergence on the one hand, and parameters describing the linguistic mutation dynamics of competing variants, on the other
Summary
Most mathematical models of linguistic variation and change fall into one of two classes: (i) those that study homogeneous populations of speakers in frameworks that admit an analytical exploration of the model’s dynamics [1,2,3], and (ii) those that aim to elucidate complex interactions of language learning and use in social networks through agent-based simulations [4,5,6]. A formal investigation of this model reveals that the ‘convergence–divergence game’, as I shall call it below, has a number of stable equilibria depending on a combination of global parameters, namely, parameters describing the strength of ingroup social convergence and outgroup divergence on the one hand, and parameters describing the linguistic mutation (innovation or mistransmission) dynamics of competing variants, on the other One of these stable equilibria is found to correspond to data on sociolinguistic stratification in adolescents [25] for an independently estimated value of the relevant mutation rate parameter.
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