Date Published: January 26, 2010
Publisher: Public Library of Science
Author(s): Laetitia Chapel, Xavier Castelló, Claire Bernard, Guillaume Deffuant, Víctor M. Eguíluz, Sophie Martin, Maxi San Miguel, Thomas Mailund. http://doi.org/10.1371/journal.pone.0008681
Abstract: We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (finite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.
Partial Text: The study of language dynamics using computer simulations has become a research field of increasing interest in the scientific community. Models studying language dynamics range from social impact theory applied to language competition  to genetic approaches for the evolution of universal grammar . We are here interested in the problem of language competition, i.e., the dynamics of language use among a population of interacting agents speaking different languages. Around 50% of the 6000 languages spoken today are in danger and will disappear during the current century according to the recent studies in language contact . Beyond Weinreich’s Languages in contact, several studies in sociolinguistics have addressed questions regarding the level of endangerment of specific languages  and the challenge to find a common pattern that might relate language choice to ethnicity, community identity or the like . Lately, the need to provide a quantitative analysis in the field of sociolinguistics is getting an increasing attention . This fact has triggered an effort in order to model and understand the mechanisms within scenarios of language competition: some models study the competition between many languages in order to reproduce the distribution of language sizes in the world in terms of the number of speakers , ; while others focus on the case of language contact between few languages (for a review see Refs , ). In particular, Abrams and Strogatz  proposed a simple mathematical model of competition between two languages. The model describes the system by aggregated variables that represent the fraction of speakers of each language, where a higher local density of speakers and a higher prestige, the relative status of a language, tend to increase the density of speakers of a language. The analytical study of the model and the fitting to real data from the competition between Quechua-Spanish, Scottish Gaelic-English and Welsh-English, predict that the coexistence of two languages is unstable, irrespective of the prestige of the languages and their initial density of speakers in the model, in contrast to the evidence that bilingual societies exist today. The paper finished with the following remarks: