Conclusions
Processes of cultural shift, and in particular of language shift, are present throughout history and have had a great importance into shaping the current day society and diversity.
Language is an inherent part of what people use to define their identity, and therefore, the study of the processes that yield a population to abandoning their own language in favour of an alien language is important to understand human evolution. Linguistic studies have described several mechanisms leading to language shift, such as language displacement due to a demographic substitution, due to being militarily conquered by speakers of another language, or as a result of language acquisition from a neighbouring region.We are particularly interested in the last process, since it produces an advancing linguistic frontier whose speed can be predicted by a mathematical model. We have presented a model that has been developed to describe the dynamics of language shift in a region where the speakers of a native language are under the influence of a neighbour language regarded as being socially and economically more advantageous (Isern and Fort 2014). We have also applied our language shift model as an interaction term in a reaction-diffusion model in order to estimate the speed at which the more advantageous languages spreads geographically, increasing its range of prevalence and, in consequence, diminishing the area of influence of the minority language. Testing this model over modern data corresponding to the retreat of the Welsh-English border has yielded very accurate results, thus indicating that the model provides a good description of the process. In addition, on a wider context, the model presented here could be applied as well to the study of other cases of cultural shift for traits also related to national or ethnic identity, such as religious affiliations.
Acknowledgments This work was funded in part by FBBVA grant Neodigit-PIN2015, ICREA (JF) and the MINECO grants SimulPast-CSD2010-00034 and FIS-2012-31307 (all authors).