Front Speed of Language Replacement

Abstract

We use two coupled equations to analyze the space-time dynamics of two interacting languages.Firstly, we introduce a cohabitation model, which is more appropriate for human populations than classical (non-cohabitation) models. Secondly, using numerical simulations we …nd the front speed of a new language spreading into a region where another language was previously used. Thirdly, for a special case we derive an analytical formula that makes it possible to check the validity of our numerical simulations. Finally, as an example, we …nd that the observed front speed for the spread of the English language into Wales in the period 1961-1981 is consistent with the model predictions. We also …nd that the e¤ects of linguistic parameters are much more important than those of parameters related to population dispersal and reproduction. If the initial population densities of both languages are similar, they have no e¤ect on the front speed. We outline the potential of the new model to analyze relationships between language replacement and genetic replacement.

Language extinction and linguistic fronts

“…All of the speeds have been computed using dimensionless units (left axis), and the right axis corresponds to the dimensional speed () for an example with γ = 0.1 yr −1 (figure 2 a ) and D = 5.08 km 2 yr −1 . This value of the diffusion coefficient has been estimated from [43] and observed values from modern populations for the generation time ( T = 25 yr [25]) and the mean-squared displacement ( [44,45]). The latter was obtained from modern human populations in the Parma Valley, Italy, during the twentieth century, and is therefore coetaneous with the data in the studied period (figure 2).…”

Quantifying the driving factors for language shift in a bilingual region

“…Their differential equation system considered only temporal and no spatial development, but the paper has drawn a tail of publications in its wake, many of them including spatial development. Spatial and temporal development of languages are usually combined in reaction-diffusion equations (13)(14)(15)(16)(17)(18)(19) of the form ∂u/∂t = D·∂ 2 u/∂x 2 + f(u). These types of equation are also used in other fields, for example, biology or chemistry, to describe all kinds of spread phenomena (20).…”

Population Spread and Cultural Transmission in Neolithic Transitions

“…[13] is useful for modern populations but not for the Neolithic transition, because it assumes the same carrying capacity for both populations. But a model that allows for different carrying capacities [14] also leads, in the linear case, to an equation with the form of Eq. (7).…”

“…In conclusion, some models originally devised to describe language competition also lead to the conclusion we have stressed above, namely that the wave-of-advance speed is independent of max P P . For completeness, in the non-linear case the following two limitations of the language-competition models discussed in the previous paragraph [12][13][14] should be noted in the context of the Neolithic transition.…”

“…(3) was derived from cultural transmission theory, the non-linear models introduced to describe language competition [12][13][14] (Eqs. (8)- (9)) were not.…”