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Principles of parametric estimation in modeling language competition.

Menghan Zhang¹, Tao Gong

¹Institute of Linguistics, Shanghai Normal University, Shanghai 200234, China.

Proceedings of the National Academy of Sciences of the United States of America

|May 30, 2013

Summary

This study introduces a new method for modeling social phenomena like language competition by defining concrete parameters from empirical data. This approach enhances the reliability and predictive power of mathematical models in sociolinguistics.

Keywords:

Fourier's law of heat conduction Hardy-Weinberg genetic inheritance principle lexical diffusion dynamics logistic curve prestige

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Area of Science:

Mathematical modeling of social phenomena
Sociolinguistics
Evolutionary biology applications

Background:

Mathematical models of social phenomena often struggle with defining and interpreting abstract parameters.
Directly fitting abstract parameters to empirical data can be challenging and lead to misinterpretations.

Purpose of the Study:

To propose a novel approach for defining concrete, socioculturally relevant parameters in mathematical models.
To apply this approach to language competition modeling using principles of language diffusion and inheritance.
To enhance the interpretability and predictive accuracy of social dynamics models.

Main Methods:

Developed a language competition model based on the Lotka-Volterra competition model.
Introduced a language diffusion principle and two language inheritance principles to compute critical parameters.
Calculated parameter values (impacts and inheritance rates) from population census and language survey data.

Main Results:

The proposed model reliably replicates and predicts language competition dynamics using estimated parameter values.
Demonstrated the model's effectiveness with four case studies of language competition.
Showcased the model's utility in scenarios with limited direct competition data.

Conclusions:

The new method provides explicit sociolinguistic meaning to model parameters.
This approach improves the reliability and predictive capability of mathematical models for social phenomena.
The model is particularly valuable for understanding language competition dynamics, even with incomplete data.