Likelihood Ratio Test for Determining Genetic Relationships among Languages

Core Concepts

The core message of this paper is to propose a likelihood ratio test (LRT) to determine the genetic relatedness of a group of languages based on the proportion of invariant character sites in the aligned wordlists, which overcomes the limitations of previous permutation-based tests.

Abstract

The paper presents a likelihood ratio test (LRT) to determine the genetic relatedness of a group of languages. The key idea is that related languages are expected to have a higher proportion of invariant character sites in the aligned wordlists compared to unrelated languages.
The methodology involves:

Encoding the wordlists as a character matrix, where each row represents a language and each column represents a sound class.
Assuming a simple Jukes-Cantor substitution model, the authors compute the maximum likelihood tree for the given data under two hypotheses:

Null hypothesis (H0): The proportion of invariant sites is low (1%)
Alternate hypothesis (Ha): The proportion of invariant sites is higher (6%)

The likelihood ratio test statistic δ is computed as the difference in log-likelihoods of the best trees under H0 and Ha.
The distribution of δ under the null hypothesis is obtained through parametric bootstrapping, and the p-value is computed to determine if the alternate hypothesis is preferred.

The authors evaluate the proposed LRT on various language families and show that it does not exhibit the problem of false positives, unlike previous permutation-based tests. They also find supporting evidence for the existence of macro-families such as Nostratic and Macro-Mayan using the LRT.
Additionally, the authors compare the performance of the proposed method with other distance-based and character-based phylogenetic inference methods on a tree construction task, and find that the probabilistic methods based on character matrices perform better than distance-based approaches.

Stats

The proportion of invariant sites is estimated to be around 1% under the null hypothesis and 6% under the alternate hypothesis.

Quotes

"Related languages should have more positions where a character or a sound class is invariant than unrelated languages."
"The null hypothesis assumes negligible proportion of invariant sites while the alternate hypothesis assumes significant proportion of invariant sites."

Key Insights Distilled From

A Likelihood Ratio Test of Genetic Relationship among Languages

by V.S.D.S.Mahe... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00284.pdf

Deeper Inquiries

How can the optimal values of the proportion of invariant sites under the null and alternate hypotheses be determined in a more principled way, beyond the rough estimates used in this work?

In order to determine the optimal values of the proportion of invariant sites more accurately, a more principled approach would involve conducting a systematic analysis based on a larger and more diverse set of language families. This would require collecting a comprehensive dataset that includes a wide range of languages with known genetic relationships as well as unrelated languages. By analyzing the data from these language families, statistical methods such as Bayesian inference or maximum likelihood estimation could be employed to estimate the optimal values of the proportion of invariant sites under the null and alternate hypotheses. These methods would allow for a more rigorous and data-driven determination of the optimal values, taking into account the variability and complexity of language evolution.

How would the inclusion of Uralic, another important language family, affect the analysis and conclusions regarding the Nostratic macro-family?

The inclusion of the Uralic language family in the analysis of the Nostratic macro-family would have significant implications for the analysis and conclusions drawn. Uralic languages, which include Finnish, Hungarian, and Estonian, are considered to be part of the proposed Nostratic macro-family. By including Uralic languages in the analysis, the genetic relationships between Uralic and other language families within the Nostratic grouping could be more accurately assessed. This inclusion would provide a more comprehensive understanding of the linguistic connections and shared ancestry between Uralic and other language families, potentially strengthening the evidence for the existence of the Nostratic macro-family. Additionally, the inclusion of Uralic languages would allow for a more robust evaluation of the proposed macro-family, providing insights into the deep historical relationships between these language groups.

Can the proposed LRT framework be extended to incorporate additional evolutionary factors, such as semantic shifts, to further improve the accuracy of genetic relationship testing?

Yes, the proposed Likelihood Ratio Test (LRT) framework can be extended to incorporate additional evolutionary factors, such as semantic shifts, to enhance the accuracy of genetic relationship testing. By integrating information about semantic changes in words over time, the LRT framework could account for the impact of language evolution on lexical similarities and dissimilarities. This extension would involve developing models that capture the rates and patterns of semantic shifts in word meanings across different language families. By incorporating semantic information into the analysis, the LRT framework could provide a more nuanced understanding of genetic relationships among languages, taking into consideration not only phonetic and lexical similarities but also semantic changes over time. This holistic approach would contribute to a more comprehensive and accurate assessment of language relatedness, offering valuable insights into the evolutionary history of languages.