Syntactic Phylogenetic Trees

Abstract

In light of recent controversies surrounding the use of computational methods for the reconstruction of phylogenetic trees of language families (especially the Indo-European family), a possible approach based on syntactic information, complementing other linguistic methods, appeared as a promising possibility, largely developed in recent years in Longobardi’s Parametric Comparison Method. In this paper we identify several serious problems that arise in the use of syntactic data from the SSWL database for the purpose of computational phylogenetic reconstruction. We show that the most naive approach fails to produce reliable linguistic phylogenetic trees. We identify some of the sources of the observed problems and we discuss how they may be, at least partly, corrected by using additional information, such as prior subdivision into language families and subfamilies, and a better use of the information about ancient languages. We also describe how the use of phylogenetic algebraic geometry can help in estimating to what extent the probability distribution at the leaves of the phylogenetic tree obtained from the SSWL data can be considered reliable, by testing it on phylogenetic trees established by other forms of linguistic analysis. In simple examples, we find that, after restricting to smaller language subfamilies and considering only those SSWL parameters that are fully mapped for the whole subfamily, the SSWL data match extremely well reliable phylogenetic trees, according to the evaluation of phylogenetic invariants. This is a promising sign for the use of SSWL data for linguistic phylogenetics. We also argue how dependencies and nontrivial geometry/topology in the space of syntactic parameters would have to be taken into consideration in phylogenetic reconstructions based on syntactic data. A more detailed analysis of syntactic phylogenetic trees and their algebro-geometric invariants will appear elsewhere [33].

Appendix: The SSWL Parameters of the Latin languages

The phylogenetic invariants for the tree of Latin languages of Fig. 11 are evaluated at the probability distribution $p_{i_1,i_2.i_3,i_4,i_5}$ at the leaves, based on the SSWL parameters for this group of languages. There are 106 parameters in the SSWL database that are completely mapped for all of these five languages. We have excluded from the list all those SSWL parameters that are only mapped for some but not all of the languages in this group. With the notation $\ell _1=$ French, $\ell _2=$ Italian, $\ell _3 =$ Latin, $\ell _4=$ Spanish, and $\ell _5=$ Portuguese, the syntactic parameters are given by the following list. The column on the left lists the SSWL parameters P as labeled in the database, [37].

One can see by inspecting the different groups of parameters in this list that several parameters within the “same group” tend to behave in the same way (e.g. all the Neg parameters) or in more highly correlated way than across groups of parameters. This observation is consistent with the more general observation of dependencies observed through the Kanerva networks method in [26]. Thus, in order to better fit this set of binary variables with the hypothesis of independent equally distributed variables in Markov processes, it may be better to select a subset of the SSWL parameters that cuts across the various groups of more closely correlated variables. We will discuss this aspect more in details elsewhere.

The probability $p_{i_1,i_2.i_3,i_4,i_5}$ is then computed by counting the frequencies of occurrence of binary vectors $[i_1,i_2,i_3,i_4,i_5] \epsilon \{0,1\}^5$ among the 106 vectors of SSWL parameters above. The only nonzero frequencies are

$$ p_{0,0,0,0,0}=\frac{31}{106}, \ \ \ p_{0,0,0,0,1}=\frac{1}{106}, \ \ \ p_{0,0,0,1,0}=\frac{1}{106}, \ \ \ p_{0,0,1,0,0}=\frac{23}{106}, $$

$$ p_{0,0,1,0,1}= \frac{3}{106}, \ \ \ p_{0,0,1,1,1}=\frac{2}{106}, \ \ \ p_{0,1,0,0,0}=\frac{1}{106}, \ \ \ p_{0,1,0,1,1}=\frac{1}{106}, $$

$$ p_{0,1,1,0,1}= \frac{1}{106}, \ \ \ p_{0,1,1,1,1}=\frac{3}{106}, \ \ \ p_{1,0,0,0,0} = \frac{5}{106}, \ \ \ p_{1,0,0,1,0}=\frac{2}{106}, $$

$$ p_{1,1,0,1,0}=\frac{1}{106}, \ \ \ p_{1,1,0,0,0}=\frac{2}{106}, \ \ \ p_{1,1,0,1,1}=\frac{8}{106}, \ \ \ p_{1,1,1,1,1}=\frac{21}{106}. $$

Note how these frequencies confirm some well known facts about the Latin languages. Syntactic parameters (as recorded in SSWL) are very likely to have remained the same across all five languages in the family, with a higher probability of a feature not allowed in Latin remaining not allowed in the other languages (31/106) than of a feature allowed in Latin remaining allowed in the other languages (21 / 106). It is also very likely that a feature is the same in all the modern ones but different from Latin, with a much higher incidence of cases of a feature allowed in Latin becoming disallowed in all the other languages (23/106) than the other way around (8/106). Among the remaining possibilities, we see incidences where French has an allowed feature that is missing in the other languages (5/106) of disallowed (3/106) and cases where Latin and Portuguese have the same feature allowed, which is disallowed in the other languages (3/106): all other nonzero entries have only two or less occurrences. The resulting matrices for the edge flattenings of the tree of Fig. 11 are then as computed in Sect. 5.