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A Likelihood Ratio Test of Genetic Relationship among Languages

V. S. D. S. Mahesh Akavarapu, Arnab Bhattacharya

TL;DR

The paper tackles the problem of statistically validating genetic relatedness among languages using lexical data, addressing shortcomings of prior permutation tests that can produce false positives or require proto-forms. It introduces a likelihood-ratio test (LRT) that leverages the proportion of invariant sites within a fixed phylogenetic tree, avoiding proto-language reconstruction and enabling a principled statistical framework. The method relies on parametric bootstrapping to calibrate the null distribution and demonstrates reduced false positives while supporting macro-family groupings such as Nostratic and Macro-Mayan. Compared with multilateral and distance-based approaches, the probabilistic ML-tree framework shows competitive phylogenetic performance, offering a robust alternative for historical-comparative linguistics.

Abstract

Lexical resemblances among a group of languages indicate that the languages could be genetically related, i.e., they could have descended from a common ancestral language. However, such resemblances can arise by chance and, hence, need not always imply an underlying genetic relationship. Many tests of significance based on permutation of wordlists and word similarity measures appeared in the past to determine the statistical significance of such relationships. We demonstrate that although existing tests may work well for bilateral comparisons, i.e., on pairs of languages, they are either infeasible by design or are prone to yield false positives when applied to groups of languages or language families. To this end, inspired by molecular phylogenetics, we propose a likelihood ratio test to determine if given languages are related based on the proportion of invariant character sites in the aligned wordlists applied during tree inference. Further, we evaluate some language families and show that the proposed test solves the problem of false positives. Finally, we demonstrate that the test supports the existence of macro language families such as Nostratic and Macro-Mayan.

A Likelihood Ratio Test of Genetic Relationship among Languages

TL;DR

The paper tackles the problem of statistically validating genetic relatedness among languages using lexical data, addressing shortcomings of prior permutation tests that can produce false positives or require proto-forms. It introduces a likelihood-ratio test (LRT) that leverages the proportion of invariant sites within a fixed phylogenetic tree, avoiding proto-language reconstruction and enabling a principled statistical framework. The method relies on parametric bootstrapping to calibrate the null distribution and demonstrates reduced false positives while supporting macro-family groupings such as Nostratic and Macro-Mayan. Compared with multilateral and distance-based approaches, the probabilistic ML-tree framework shows competitive phylogenetic performance, offering a robust alternative for historical-comparative linguistics.

Abstract

Lexical resemblances among a group of languages indicate that the languages could be genetically related, i.e., they could have descended from a common ancestral language. However, such resemblances can arise by chance and, hence, need not always imply an underlying genetic relationship. Many tests of significance based on permutation of wordlists and word similarity measures appeared in the past to determine the statistical significance of such relationships. We demonstrate that although existing tests may work well for bilateral comparisons, i.e., on pairs of languages, they are either infeasible by design or are prone to yield false positives when applied to groups of languages or language families. To this end, inspired by molecular phylogenetics, we propose a likelihood ratio test to determine if given languages are related based on the proportion of invariant character sites in the aligned wordlists applied during tree inference. Further, we evaluate some language families and show that the proposed test solves the problem of false positives. Finally, we demonstrate that the test supports the existence of macro language families such as Nostratic and Macro-Mayan.
Paper Structure (19 sections, 7 equations, 5 figures, 6 tables)

This paper contains 19 sections, 7 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Character Matrix
  5. Substitution Model
  6. Maximum Likelihood Tree (ML-tree)
  7. Invariant Sites
  8. Likelihood Ratio Test (LRT)
  9. Experimental Setup
  10. Datasets
  11. Multilateral Permutation Test
  12. Implementation
  13. Results
  14. Tree Construction
  15. Evaluation of Macro Families
  16. ...and 4 more sections

Figures (5)

  • Figure 1: A section of character matrix for Uto-Aztecan family consisting of concatenated Multiple Sequence Alignments (MSAs) of consonant classes, one from each concept
  • Figure 2: Bilateral (pairwise) significance among the languages of Nostratic grouping. The yellow shade implies that the relationship is statistically significant ($p < 0.05$), while the purple shade implies otherwise.
  • Figure 3: Comparison of unrooted ML-trees on various groupings of Nostratic language families
  • Figure 4: Bilateral (pairwise) significance among the languages of Macro-Mayan/Amerind grouping. The yellow shade implies that the relationship is statistically significant ($p < 0.05$), while the purple shade implies otherwise. While moving across the diagonal, the first cluster of significantly related languages is that of Mayan, the second is that of Mixe-Zoque and the thrid, Uto-Aztecan
  • Figure 5: Comparison of unrooted ML-trees on various groupings of Macro-Mayan/Amerind language families