Modeling the life and death of competing languages from a physical and mathematical perspective

Recent contributions address the problem of language coexistence as that of two species competing to aggregate speakers, thus focusing on the dynamics of linguistic traits across populations. They draw inspiration from physics and biology and share some underlying ideas -- e. g. the search for minimal schemes to explain complex situations or the notion that languages are extant entities in a societal context and, accordingly, that objective, mathematical laws emerge driving the aforementioned dynamics. Different proposals pay attention to distinct aspects of such systems: Some of them emphasize the distribution of the population in geographical space, others research exhaustively the role of bilinguals in idealized situations (e. g. isolated populations), and yet others rely extremely on equations taken unchanged from physics or biology and whose parameters bear actual geometrical meaning. Despite the sources of these models -- so unrelated to linguistics -- sound results begin to surface that establish conditions and make testable predictions regarding language survival within populations of speakers, with a decisive role reserved to bilingualism. Here we review the most recent works and their interesting outcomes stressing their physical theoretical basis, and discuss the relevance and meaning of the abstract mathematical findings for real-life situations.Comment: 22 pages, 4 figures. Fifth chapter of the book Bilingualism and Minority Languages in Europe: Current trends and developments by F. Lauchlan, M. C. Parafita Couto, ed

Diversity, competition, extinction: the ecophysics of language change

As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of information exchanges and communicative constraints in groups of agents under selective scenarios. These models have been very helpful in providing a rationale on how complex forms of communication emerge under evolutionary pressures. However, other patterns of large-scale organization can be described using mathematical methods ignoring communicative traits. These approaches consider shorter time scales and have been developed by exploiting both theoretical ecology and statistical physics methods. The models are reviewed here and include extinction, invasion, origination, spatial organization, coexistence and diversity as key concepts and are very simple in their defining rules. Such simplicity is used in order to catch the most fundamental laws of organization and those universal ingredients responsible for qualitative traits. The similarities between observed and predicted patterns indicate that an ecological theory of language is emerging, supporting (on a quantitative basis) its ecological nature, although key differences are also present. Here we critically review some recent advances lying and outline their implications and limitations as well as open problems for future research.Comment: 17 Pages. A review on current models from statistical Physics and Theoretical Ecology applied to study language dynamic

Language competition with bilinguals in social networks

Several models have been proposed to study the dynamics of competition between languages. Among them, and starting from the dynamics of endangered languages, recent approaches have addressed the issue of bilingualism. Along these lines we consider the dynamics of language use, allowing for bilingualism, within a social network in the case where the two languages are equivalent. Understanding this case is a first step to describe the case of an endangered language competing against a language with higher status. Local effects are analyzed, studying interface dynamics and growth laws of the system. Power laws for the decay of interface density and bilingual population density are obtained. A final state is reached, where one of the languages disappears. We also study the stability of bilingual communities, which suggests possible explanations for the difficulty of coexistence of languages in the long term.Complex systems, Language competition, social networks

Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions

We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language $X$ or language $Y$, while the second model incorporates a third state XY, representing individuals that use both languages (bilinguals). We analyze the models on complex networks and two-dimensional square lattices by analytical and numerical methods, and show that they exhibit a transition from one-language dominance to language coexistence. We find that the coexistence of languages is more difficult to maintain in the Bilinguals model, where the presence of bilinguals in use facilitates the ultimate dominance of one of the two languages. A stability analysis reveals that the coexistence is more unlikely to happen in poorly-connected than in fully connected networks, and that the dominance of only one language is enhanced as the connectivity decreases. This dominance effect is even stronger in a two-dimensional space, where domain coarsening tends to drive the system towards language consensus.Comment: 30 pages, 11 figure

Simulation for competition of languages with an ageing sexual population

Recently, individual-based models originally used for biological purposes revealed interesting insights into processes of the competition of languages. Within this new field of population dynamics a model considering sexual populations with ageing is presented. The agents are situated on a lattice and each one speaks one of two languages or both. The stability and quantitative structure of an interface between two regions, initially speaking different languages, is studied. We find that individuals speaking both languages do not prefer any of these regions and have a different age structure than individuals speaking only one language.Comment: submitted to International Journal of Modern Physics

Coupled dynamics of node and link states in complex networks: A model for language competition

Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it, which we model, respectively, as a property of the interactions between speakers (a link state) and as a property of the speakers themselves (a node state). Furthermore, we restrict our attention to the case of two socially equivalent languages and to socially inspired network topologies based on a mechanism of triadic closure. As opposed to most of the previous literature, where language extinction is an inevitable outcome of the dynamics, we find a broad range of possible asymptotic configurations, which we classify as: frozen extinction states, frozen coexistence states, and dynamically trapped coexistence states. Moreover, metastable coexistence states with very long survival times and displaying a non-trivial dynamics are found to be abundant. Interestingly, a system size scaling analysis shows, on the one hand, that the probability of language extinction vanishes exponentially for increasing system sizes and, on the other hand, that the time scale of survival of the non-trivial dynamical metastable states increases linearly with the size of the system. Thus, non-trivial dynamical coexistence is the only possible outcome for large enough systems. Finally, we show how this coexistence is characterized by one of the languages becoming clearly predominant while the other one becomes increasingly confined to "ghetto-like" structures: small groups of bilingual speakers arranged in triangles, with a strong preference for the minority language, and using it for their intra-group interactions while they switch to the predominant language for communications with the rest of the population.Comment: 21 pages, 15 figure

Phase transition in a sexual age-structured model of learning foreign languages

The understanding of language competition helps us to predict extinction and survival of languages spoken by minorities. A simple agent-based model of a sexual population, based on the Penna model, is built in order to find out under which circumstances one language dominates other ones. This model considers that only young people learn foreign languages. The simulations show a first order phase transition where the ratio between the number of speakers of different languages is the order parameter and the mutation rate is the control one.Comment: preliminary version, to be submitted to Int. J. Mod. Phys.

Memory effects in language acquisition and attrition processes

https://www.ester.ee/record=b5151746*es

The fate of bilingualism in a model of language competition

The original publication is available at Springer website: http://www.springer.com/computer/mathematics/book/978-4-431-73150-4.In the general context of dynamics of social consensus, we study an agent based model for the competition between two socially equivalent languages, addressing the role of bilingualism and social structure. In a regular network, we study the formation of linguistic domains and their interaction across the boundaries. We analyse also a small world social structure, in order to capture the effect of long range social interactions. In both cases, a final scenario of dominance of one language and extinction of the other is obtained, but with smaller times for extinction in the latter case. In addition, we compare our results to our previous work on the agent based version of Abrams-Strogatz model.We acknowledge financial support from the MEC (Spain) through project CONOCE2 (FIS2004-00953). X. C. also acknowledges financial support from a Ph.D. fellowship of the Govern de les Illes Balears (Spain). L. L-P. also acknowledges financial support from the Autonomous Government of Galicia (PGIDIT05PXIC20401PN), and the MEC (Spain) and the ERDF (HUM2004-00940).http://dx.doi.org/10.1007/978-4-431-73167-