A Likelihood Ratio Test of Genetic Relationship among Languages (2024)

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.

## introduction languages that descend from a common ancestral language are termed to be genetically related. the existence of lexical resemblances between the two languages is a preliminary indication that they could be related. such resembling lexicons that truly have a common origin are called cognates. for instance, sanskrit nāma and english name are cognates that can be traced to proto-indo-european *h 3 nómn. however, such resemblances can also occur out of sheer chance. for instance, persian bad and behtar accidentally resemble english bad and better respectively, but are not true cognates 1 . 1 persian bad is of uncertain origin while behtar ultimately derives from pie *h1wésus. on the other hand, english better hence, it is necessary to show statistical significance on any appropriate measure that captures the lexical relatedness before arguing for a genetic relationship among any group of languages or language families @xcite . several significance tests appeared in the past to address this problem, with the majority of them based on permutation tests, starting from oswalt @xcite . given wordlists of a group of languages to be evaluated for a genetic relationship, these tests obtain the null distribution of a certain measure capturing similarity between word pairs by random permutations of the wordlists. such tests either act bilaterally, i.e., on a pair of languages or proto-languages, or multilaterally on a group of languages. among these, the multilateral comparison, which was made famous by @xcite @xcite in traditional historical linguistics, has been a subject of much criticism @xcite . hence, the preferred way of comparing two language families has been to compare their reconstructed proto-forms bilaterally. however, @xcite argues that genetic classification should precede proto-language reconstruction. moreover, there is often a lack of agreement on reconstructed proto-forms both in terms of phonology and semantics which gives room for sufficient manipulation of wordlists that can in turn alter the results of significance tests @xcite . further, we demonstrate that multilateral permutation tests @xcite yield false negatives even after incorporating complex word similarity metrics such as sca and lexstat @xcite . to overcome these issues, we turn to phylogenetic analysis @xcite that is known to approximately capture the ancestral states and has been applied to phonological reconstruction tasks such as proto-language and cognate derives from pie *b h edrós and is cognate with sanskrit bhadrá reflex prediction tasks @xcite with reasonably good results. specifically, we propose a likelihood ratio test (lrt) where we expect the difference in likelihoods of the best trees under null and alternate hypotheses to capture genetic relatedness. the null hypothesis assumes negligible proportion of invariant sites while the alternate hypothesis assumes significant proportion of invariant sites. intuitively, related languages should have more positions where a character or a sound class is invariant than unrelated languages. hence, we essentially capture the notion of relatedness as possessing a relatively high proportion of invariant sites. further in this test, reconstructed proto-forms are not required and at the same time, the evolutionary tree structure is strictly imposed by design, unlike the multilateral model, thereby effectively circumventing the aforementioned methodological problems. although inspired by similar tests from molecular phylogenetics, the test we propose is novel in the sense that the problem of testing common descent never arises in biology since monogenesis is accepted as a fact therein @xcite . we further evaluate the test on various language families and demonstrate that the test does not misclassify unrelated languages as related. we finally show that the test supports the existence of the macro-families nostratic @xcite and macro-mayan @xcite . while such an attempt to justify the existence of macro-families using bootstrap analysis of distance-based phylogeny is found in @xcite , expressing statistical significance in terms of likelihood ratio is preferred over bootstrap support values whose interpretation is debated in molecular phylogenetics @xcite . our contributions are summarized as follows. the rest of the paper is summarized as follows. related work is discussed in §2. the methodology of the test is presented in §3. evaluation details such as datasets and details of previous methods and variants are discussed in §4. the results are discussed in §5. the application of the method on long-range comparisons is discussed in §6. the paper is concluded in §7. ## related work permutation test for bilateral language relationship comparisons was introduced by @xcite . the significance of sound correspondences by brute force probability calculation was proposed by @xcite . this approach was however criticized for not being able to show significance for known related pairs of languages like latin-english and also for accounting phonologically implausible sound correspondences @xcite . multilateral permutation tests were proposed by @xcite . several applications of permutation tests exist such as @xcite . some notable likelihood ratio tests in molecular phylogenetics, mostly on topologies, include @xcite @xcite where bootstrap analysis is argued to be not so optimal to establish statistical significance on phylogenies. otherwise, support for macrofamilies through bootstrap analysis for distancebased trees is shown in @xcite . comparisons of various methods of phylogenetic reconstruction such as distance-based and binary-character-based are given by @xcite . sound-class characterbased phylogenetic analysis is found in @xcite . usually, bayesian phylogenetic inference on binary cognate encodings gives good results @xcite . although the likelihood ratio metric is common for both past and present-day language models, the utility of this test using invariant sites outside computational historical linguistics is unknown. ## methodology the key concept revolves around the idea that any hypothesis, in this case, a hypothesis on a phylogeny, is preferred over a competing null hypothesis if it is significantly more likely, i.e., has a higher likelihood than the latter. given the wordlist data encoded as an aligned character matrix, related languages are expected to have a higher number of invariant columns. thus, our null hypothesis con-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 sists of a phylogeny with a small proportion (fixed at 1%) of invariant sites, whereas the alternative hypothesis consists of a phylogeny with a larger but reasonable proportion (fixed at 6%) of invariant sites. the observed difference in their likelihood of real data is compared with that of data simulated from the null hypothesis through parametric bootstrapping and, accordingly, one of the hypotheses is rejected. the steps are elaborated next. ## experimental setup the section discusses the details of the experiments including datasets, baseline models, and implementation details. ## results the primary results of the paper are tabulated in one can observe that false positives, indicated in red, are absent for lrt, in contrast with multilateral permutation tests which exhibit false positives in all cases (except p1-dolgo for mkh-uaz). however, we note that the similarity scores of the turchin measure are consistently small (< 0.005) for negatives irrespective of the significance implied by the p-value. hence, it may be noted that turchin could be a good measure for permutation tests when similarity scores are taken into consideration. further, one can observe from for these families consists of a lower number of taxa (see ## evaluation of macro families we apply the tests on groupings of a few families from proposed macro families, namely nostratic, macro-mayan, and amerind. under nostratic, we test for groupings dravidian-indo-european (drav-ie) and dravidian-indo-european-kartvelian (drav-ie-kart) while we test mayan-mixe-zoque (may-mz) under macro-mayan and mayan-uto-aztecan (may-uaz), mayan-mixe-zoque-uto-aztecan (may-mz-uaz) under amerind. the results are tabulated in ## conclusions in this paper, we have presented a likelihood ratio test based on the proportions of invariant sites to determine the genetic relatedness of a group of languages. our proposed test does not yield false positives, which is in contrast with previous permutation-based tests that proved to be good only for pairwise language comparisons and not for validating a language group. by applying this test, we have found strong supporting evidence for macro-families such as dravidian-indo-european, macro-mayan (for mayan-mixe-zoque, and weak evidence for nostratic (dravidian-indo-european-kartvelian) and amerind (for mayan-uto-aztecan). through secondary analyses, we have also shown that probabilistic-based methods are superior to distance-based ones based on tree construction and the correlation of topologies with geography. in this work we did not touch upon semantic shifts, i.e., words changing meaning over time; for example, the word quick initially meant 'lively'. while considering semantic shifts may provide room for data manipulation favoring any particular hypothesis, few semantic slots such as 'bark'-'skin' are often found to have common words. in such cases, the slots may be merged into one as suggested by @xcite . in summary, before constructing phylogenies of a group of languages, the relatedness of the group should be established through a significance test such as the one we have presented. otherwise, the phylogenic grouping would not only be questionable but may also alter the topology of a related sub-group. peter turchin, ilia peiros, and murray gell-mann. 2010. analyzing genetic connections between languages by matching consonant classes. journal of language relationship, (5 (48)):117-126. edward orlando wiley and bruce s lieberman. 2011. phylogenetics: theory and practice of phylogenetic systematics. john wiley & sons. s. s. wilks. 1938. the large-sample distribution of the likelihood ratio for testing composite hypotheses. the annals of mathematical statistics, 9(1):60-62. (a) mayan (b) mayan-mixe-zoque (c) mayan-uto-aztecan (d) mayan-mixe-zoque-uto-aztecan figure 5: comparison of unrooted ml-trees on various groupings of macro-mayan/amerind language families