Utterance Selection Model of Language Change
arXiv:cond-mat/0512588 · doi:10.1103/PhysRevE.73.046118
Abstract
We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.
21 pages, 17 figures
References in corpus (1)
Cited by in corpus (39)
- Statistical physics of social dynamics
- Diffusion of Lexical Change in Social Media
- Stochastic Models of Evolution in Genetics, Ecology and Linguistics
- Fixation and consensus times on a network: a unified approach
- Exact Solution of the Multi-Allelic Diffusion Model
- Population genetics on islands connected by an arbitrary network: An analytic approach
- A generalized voter model on complex networks
- Frequency patterns of semantic change: Corpus-based evidence of a near-critical dynamics in language change
- Extracting information from S-curves of language change
- How individuals change language
- Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion
- Neutral evolution: A null model for language dynamics
- A multi-state voter model with imperfect copying
- Spatial evolution of human dialects
- Evolution of Vocabulary on Scale-free and Random Networks
- Noise-induced dynamical transition in systems with symmetric absorbing states
- Geospatial distributions reflect rates of evolution of features of language
- Challenges in detecting evolutionary forces in language change using diachronic corpora
- Hierarchy of Scales in Language Dynamics
- Voter Model with Time dependent Flip-rates
- Predicting language diversity with complex network
- Replicator-mutator dynamics of linguistic convergence and divergence
- Generic modes of consensus formation in stochastic language dynamics
- The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population
- Continuous time limits of the Utterance Selection Model
- Statistical Physics of Language Maps in the USA
- Fast fixation without fast networks
- Critical behavior in a cross-situational lexicon learning scenario
- Self-contained Beta-with-Spikes Approximation for Inference Under a Wright-Fisher Model
- Language change in a multiple group society
- Voter Model with Arbitrary Degree Dependence: Clout, Confidence and Irreversibility
- Random copying in space
- Conjugate Distribution Laws in Cultural Evolution via Statistical Learning
- Conceptual similarity and communicative need shape colexification: an experimental study
- Self-organization of the Sound Inventories: Analysis and Synthesis of the Occurrence and Co-occurrence Networks of Consonants
- Spatial evidence that language change is not neutral
- On the relation between structural diversity and geographical distance among languages: observations and computer simulations
- Diversity, competition, extinction: the ecophysics of language change
- Exploiting individual differences to bootstrap communication