Principles of parametric estimation in modeling language competition

Abstract

It is generally difficult to define reasonable parameters and interpret their values in mathematical models of social phenomena. Rather than directly fitting abstract parameters against empirical data, we should define some concrete parameters to denote the sociocultural factors relevant for particular phenomena, and compute the values of these parameters based upon the corresponding empirical data. Taking the example of modeling studies of language competition, we propose a language diffusion principle and two language inheritance principles to compute two critical parameters, namely the impacts and inheritance rates of competing languages, in our language competition model derived from the Lotka-Volterra competition model in evolutionary biology. These principles assign explicit sociolinguistic meanings to those parameters and calculate their values from the relevant data of population censuses and language surveys. Using four examples of language competition, we illustrate that our language competition model with thus-estimated parameter values can reliably replicate and predict the dynamics of language competition, and it is especially useful in cases lacking direct competition data.prestige | Fourier's law of heat conduction | Hardy-Weinberg genetic inheritance principle | logistic curve | lexical diffusion dynamics H ow to define informative parameters in mathematical models of real-world phenomena remains a tough problem; in particular, how to assign explicit meanings to parameters and interpret their values in models of social phenomena critically affects the explanatory power of these models. This issue becomes more serious in recent modeling studies of language dynamics (1-5), especially competition (the process whereby local tongues are being replaced by hegemonic languages due to population migration and sociocultural exchange) (6).Among the numerous modeling approximations of two-language competition (7-15), the most influential one was the Abrams and Strogatz (AS) model (8). It defined prestige (the socioeconomic status of the speakers of a language) of competing languages to determine the dynamics of language competition, and reported well-fitting curves to some historical data under a fixed range of prestige value. However, this abstract parameter lacked explicit sociocultural meanings; it remained unclear what were the characteristics of a language having a prestige value, say 1.2, and what was the sociocultural condition corresponding to the difference between two languages having prestige values, say 1.2 and 1.3, respectively. Lacking such empirical foundations, the prestige value had to be obtained via curve fitting, thus making this model useless in cases lacking sufficient empirical data. Although many recent models (9-15) extended the AS model in certain aspects [e.g., the Mira and Paredes (MP) model (9) incorporated bilinguals into competition, the Stauffer and Schulze (SS) model (10) adopted network structures to confine language contact, and the Minett and Wang (MW) model (11) revealed ...

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