This paper presents an advance in the study of the behaviour of speakers of language varieties in contact and its impact on the vitality of these varieties.   

From a mathematical point of view, the researchers attempt to model the behaviour of speakers of language varieties in contact, including factors such as linguistic prestige, preference for one or another variety, or the degree of contact between speakers, in order to see how this affects the evolution and survival of languages. 

This research effort is worthwhile since these models can be particularly useful in predicting how languages will evolve in contact situations in different societies. In this work, the effects of speakers' linguistic ideology are specifically tested. This concept, widely discussed in the sociology of language and sociolinguistics, refers to the beliefs, assumptions and feelings towards a given language variety and its speakers. 

The modelling results indicate that language attitudes may lead to the less prestigious variety being maintained in situations of contact between languages with different degrees of prestige. This corroborates the results of some of the studies in the field, which, based on data from real speakers, show that language attitudes can act as a subjective variable that can act as a strong counterbalance to prestige relations. In addition, the study also includes data on the degree of contact between individuals with different ideologies, which is also consistent with the results of studies in real populations. 

This is an approach to a subjective variable such as linguistic ideology, which opens the way to include other variables in this type of model, such as the context in which the interaction takes place, which we also know also conditions the preference for one or another linguistic variety.

We should always welcome [research] efforts to understand, by means of formal models, the process of why groups of individuals of a society change the use of a language (i.e. language shift). In the present case, a group of researchers from the IFISC tackle, once again, this issue. As usual for this research group, the authors publish serious work exploring the implication of introducing ideologies into the language choices made by fractions of people of a given society. This is a novel research venue. In particular, the researchers assume that ideologies shape linguistic preferences and that every individual is endowed with a fixed preference defined on a set of two varieties of one language: the standard language variety, denoted X, and the vernacular one, a kind of dialect, denoted Y. Preferences are strict: either you prefer always one variety or the other. Also, your preference for a variety does not necessarily coincide with the variety you speak. Since the individual agents may interact continuously between them, the conflict between preferences is sensitive to imitation effects (following precise rules) from neighbouring agents, so that the distribution of agents in favour of each variety changes in time. For example, an agent who prefers X may start speaking Y, but in the medium run could be influenced by the neighbours and speak X, and finally return to Y later. The model has no empirical relation with a specific sociolinguistic situation. But the authors claim that their theoretical setting is sufficiently general to encompass a broad range of sociolinguistic situations. 

We first note that in their preference model, indifference between the varieties is not allowed. Further, there are no barriers or costs of any nature (such as costs of learning the variety you prefer but do not speak). People may move smoothly from one speech community to the other. 

Now, let us suppose that instead of one language, the model faces a sociolinguistic situation of two different languages competing for speakers, the dominant A and the minority language B. If I understood well their model, in this new sociolinguistic situation, as an implication of their assumptions, all individuals must be bilingual (i.e. the existence of a bilingual education system allows for this assumption). Hence the dynamic analysis of the preference conflict would be inside the community of bilingual speakers. But then they are not alone in this analytical territory. Without going far, Uriarte and Sperlich (2021), a paper quoted by the authors, studied the dynamics of language shift inside the communities of bilinguals of the Basque Country, Ireland and Wales (these three societies have languages in contact).   

There are indeed formal differences between the two models. In our model, language choices are made under uncertainty and preference intensity allow for language indifference. But there is no need to discuss those formalities here. We could do that elsewhere. The relevant issue would be how well the two models perform empirically with respect to their specific sociolinguistic context. I dare to advise the IFISC group to confront their model with empirical data to see how well it performs.  

There is also another empirical message that I would like to share (which the authors probably already know). In certain sociolinguistic contexts (like the Basque Country, Catalonia and Wales, to mention a few), any dynamic model of language shift intending to have some degree of empirical validity should produce stable fixed points (that is, linguistic conventions or consensus) in the interior of the relevant space, never converging into a linguistic convention where the minoritarian language B becomes extinct. Why? Because of the ideology of those bilingual speakers, their political stand and their loyalty to a language and its related culture. In short, due to their strong preferences in favour of language B. This is one of the reasons that makes the IFISC research truly relevant.