Quantifying uncertainty in the phylogenetics of Australian numeral systems

Abstract

Researchers have long been interested in the evolution of culture and the ways in which change in cultural systems can be reconstructed and tracked. Within the realm of language, these questions are increasingly investigated with Bayesian phylogenetic methods. However, such work in cultural phylogenetics could be improved by more explicit quantification of reconstruction and transition probabilities. We apply such methods to numerals in the languages of Australia. As a large phylogeny with almost universal 'lowlimit' systems, Australian languages are ideal for investigating numeral change over time. We reconstruct the most likely extent of the system at the root and use that information to explore the ways numerals evolve. We show that these systems do not increment serially, but most commonly vary their upper limits between 3 and 5. While there is evidence for rapid system elaboration beyond the lower limits, languages lose numerals as well as gain them. We investigate the ways larger numerals build on smaller bases, and show that there is a general tendency to both gain and replace 4 by combining 2 þ 2 (rather than inventing a new unanalysable word 'four'). We develop a series of methods for quantifying and visualizing the results.

Phylogenetic approach to the evolution of color term systems

“…To evaluate the basic evolutionary claims of the WCS theory, we use a Bayesian phylogenetic method for the study of trait evolution, implemented with the BayesTraits software package (19). These methods have previously been used in numerous studies of linguistic and cultural evolution (20)(21)(22)(23). Modeling the evolution of cultural traits using phylogenetic comparative methods developed for biological processes is not entirely uncontroversial (24); however, arguments that these approaches are invalidated by differences in the transmission of cultural and biological material have been discussed thoroughly and largely refuted (25,26).…”

The deep history of the number words

“…More work on each of these hypotheses would be a welcome addition to understanding the beguiling stability of the number words. In contrast to the unusual conservation of the low-limit number words (and especially two to five), higher-level number words such as the 'teens' (in English [13][14][15][16][17][18][19] and the names of the numbers that are powers of 10 can be more variable [30]. The form these higher-level number words take-for example, sometimes adding a base number to 10, sometimes adding 10 to a base number-correlates with features of a language's grammar [30].…”

“…The Pama-Nyungan language family is widely geographically distributed throughout Australia [19,20]. Its languages typically have simple low-limit number systems often not exceeding five [19]. A dated phylogenetic tree for this language family is not available, making it impossible to calculate lexical replacement rates.…”

How numerals support new cognitive capacities

“…numerical comparisons for small numbers are supported by the parallel individuation system (Cheung and Le Corre, forthcoming). One could thus draw the border at the limit of that system, so around four, which Zhou and Bowern (2015) also suggests as a natural 'low-limit' case, based on a study of Australian languages.…”