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Geospatial distributions reflect rates of evolution of features of language

Henri Kauhanen, Deepthi Gopal, Tobias Galla, Ricardo Bermúdez-Otero

Abstract

Quantifying the speed of linguistic change is challenging due to the fact that the historical evolution of languages is sparsely documented. Consequently, traditional methods rely on phylogenetic reconstruction. In this paper, we propose a model-based approach to the problem through the analysis of language change as a stochastic process combining vertical descent, spatial interactions, and mutations in both dimensions. A notion of linguistic temperature emerges naturally from this analysis as a dimensionless measure of the propensity of a linguistic feature to undergo change. We demonstrate how temperatures of linguistic features can be inferred from their present-day geospatial distributions, without recourse to information about their phylogenies. Thus the evolutionary dynamics of language, operating across thousands of years, leaves a measurable geospatial signature. This signature licenses inferences about the historical evolution of languages even in the absence of longitudinal data.

Geospatial distributions reflect rates of evolution of features of language

Abstract

Quantifying the speed of linguistic change is challenging due to the fact that the historical evolution of languages is sparsely documented. Consequently, traditional methods rely on phylogenetic reconstruction. In this paper, we propose a model-based approach to the problem through the analysis of language change as a stochastic process combining vertical descent, spatial interactions, and mutations in both dimensions. A notion of linguistic temperature emerges naturally from this analysis as a dimensionless measure of the propensity of a linguistic feature to undergo change. We demonstrate how temperatures of linguistic features can be inferred from their present-day geospatial distributions, without recourse to information about their phylogenies. Thus the evolutionary dynamics of language, operating across thousands of years, leaves a measurable geospatial signature. This signature licenses inferences about the historical evolution of languages even in the absence of longitudinal data.

Paper Structure

This paper contains 18 sections, 88 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model: faithful horizontal transmission
  3. Spin flip probability
  4. Stationary-state feature frequency $\rho$
  5. Pair correlation function
  6. Stationary-state isogloss density $\sigma$
  7. Sanity check: the limits $\tau \to 0$ and $\tau \to \infty$
  8. Model: undirected horizontal error
  9. Spin flip probability
  10. Stationary-state feature frequency $\rho$
  11. Correlation function and isogloss density
  12. Model: no restrictions on error rates
  13. Robustness of method
  14. The two hemispheres test
  15. Varying the spatial scale
  16. ...and 3 more sections

Figures (3)

  • Figure S1: Correlations between quantities predicted by theory [Eqs. (\ref{['eq:steady-rho-full']}), (\ref{['eq:tau-full']}) and (\ref{['eq:sigma-full']})] and measured from numerical simulations ($\rho$: feature frequency, $\sigma$: isogloss density, $\tau$: temperature). One hundred independent features on a $50\times 50$ lattice at 25,000,000 iterations.
  • Figure S2: Left: Temperature estimates computed with varying neighbourhood sizes correlated against the temperature estimates of the main analysis (neighbourhood size $k = 10$). Right: Distribution (Gaussian kernel estimate) of distance to $k$th neighbour ($k=1, 10, 50$).
  • Figure S3: Correlations between quantities predicted by theory [Eqs. (\ref{['eq:steady-rho-full']}), (\ref{['eq:tau-full']}) and (\ref{['eq:sigma-full']})] and measured from numerical simulations on an adjacency graph inferred from the WALS atlas ($\rho$: feature frequency, $\sigma$: isogloss density, $\tau$: temperature). One hundred independent features at 25,000,000 iterations.