On the coexistence of competing languages

Abstract

We investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others. Since coexistence of languages is observed in reality, we here revisit the question of language competition, with an emphasis on uncovering the ways in which coexistence might emerge. We find that this emergence is related to symmetry breaking, and explore two particular scenarios -the first relating to an imbalance in the population dynamics of language speakers in a single geographical area, and the second to do with spatial heterogeneity, where language preferences are specific to different geographical regions. For each of these, the investigation of paradigmatic situations leads us to a quantitative understanding of the conditions leading to language coexistence. We also obtain predictions of the number of surviving languages as a function of various model parameters.

Evolution of grammatical forms: some quantitative approaches

“…The dynamical system (28) shares a remarkable property with that encountered in earlier work [27]. For generic values of the attractiveness parameters η a and the conversion rates C ab , the coupled evolution equations ( 28) have a single attractor, which consists of an attractive fixed point x ⋆ = {x ⋆ a }.…”

“…The second term has been rescaled by 1/N 2 , in order to ensure that the strengths of both competing mechanisms remain comparable in the regime of large N , i.e., for very mature languages. The description of this conversion mechanism is similar to that used in earlier work on the coexistence of two or more languages in competition [27].…”

Hearings and mishearings: decrypting the spoken word

“…the relative difficulty of decryption depending on whether mishearings occur at the beginning or the end of a word [23], which is clearly important for real-world decryption. We aim to include the effect of such and other correlations in future work [26].…”

“…We would therefore expect that this high degree of correspondence between phonology and orthography would persist in modern languages; and have, in order to confirm this expectation, performed a preliminary analysis of this question in the case of three languages (German, Dutch and English), based on the CELEX database [3]. Our main conclusion is that there is a fixed ratio r ≈ 0.85 between the numbers of sounds and letters in typical words [26]: we obtain nearly identical values of r for unique words (when every word of the lexicon is counted once) and token words (when words are counted according to their frequencies of occurrence). Furthermore, this value of the ratio r appears to have a high degree of universality and in particular, does not show any appreciable difference among the three languages we have tested.…”

Geographical modelling of language decline

“…This model was comparatively simple, and a range of subsequent approaches have expanded upon this model theoretically, such as the inclusion of multilingualism, different interaction networks, population shift and reproduction and spatial dependence via reaction–diffusion equations [ 17 – 21 ]. Alternative approaches to a similar problem are also taken, such as using the Lokta–Volterra ‘predator–prey’ equations [ 22 ], the incorporation of more mechanistic details such as schooling and language in the home [ 23 ], and processed-based study of language diversity based on models commonly used in ecology [ 24 ].…”