Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures

Abstract

Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures. The two main sources of syntactic data are the SSWL database and Longobardi's recent data of syntactic parameters. We compute phylogenetic invariants and estimates of the Euclidean distance functions for two sets of Germanic languages, a set of Romance languages, a set of Slavic languages and a set of early Indo-European languages, and we compare the results with what is known through historical linguistics.

Topological Analysis of Syntactic Structures

“…Using these invariants and estimates of the Euclidean distance in the ambient affine space between the point P and the phylogenetic variety V T , a best candidate tree is chosen. As shown in [37], trees that were reconstructed via this method from SSWL and LanGeLin data were correctly corresponding to the actual phylogenetic trees known to historical linguists. The authors also argued that this method is better at generating phylogenetic trees from syntactic parameters than other distance based methods.…”

“…This finding will be confirmed, by different methods, in the present paper. The results of [37] show that both dataset perform reasonably well in terms of phylogenetic reconstruction, provided some care is taken into dealing with the lacunae of the SSWL data, but still with a tendency for the LanGeLin dataset to have better performance. Again we will confirm here, with a different method, that the LanGeLin data behave better in terms of phylogenetic reconstruction, although the trees we construct in this paper should not be regarded as phylogenetic trees but as hierarchical clustering structures of syntactic features.…”

“…It was argued in [37] and [41] that for the purpose of considering dynamical models of language change, either in the Markov models on trees used in the phylogenetic algebraic geometry method in [37] or in the spin glass models considered in [41] one should not consider it satisfactory to assume that the syntactic parameters are independent identically distributed random variables, because of the existence of unspecified relations between them. Thus, it would be more natural to weight the syntactic parameters by an indicator of dependence/independence.…”

“…There is some controversy over the use of computational methods for the reconstruction of language phylogenetic trees, especially for the Indo-European family, see [34]. In [39] the authors discuss the advantages of the algebro-geometric approach used in [37] over other distance based methods. It is shown that the Algebro-Geometric approach yields better results, especially when additional information, such is the subdivision into subfamilies and the position of the old languages is taken into account.…”

“…With respect to the second question, the use of syntactic parameters as a method for computational reconstruction of phylogenetic trees of language families was developed in [19], [20], [22], [23] and recently also considered from the perspective of phylogenetic algebraic geometry in [37] and from the topological perspective we consider here in [35]. The first question has been approached with mathematical methods in [18], [27], [31], [33], [38], [41].…”