1. Institute for Advanced Study, Princeton, New Jersey 08540, USA
2. School of Biological Sciences, Royal Holloway, University of London, Egham Surrey, TW20 0EX UK

Correspondence to: Martin A. Nowak¹ Correspondence and requests for materials should be addressed to M.A.N. (e-mail: Email: nowak@ias.edu).

Abstract

Animal communication is typically non-syntactic, which means that signals refer to whole situations^{1, 2, 3, 4, 5, 6, 7}. Human language is syntactic, and signals consist of discrete components that have their own meaning⁸. Syntax is a prerequisite for taking advantage of combinatorics, that is, "making infinite use of finite means"^{9, 10, 11}. The vast expressive power of human language would be impossible without syntax, and the transition from non-syntactic to syntactic communication was an essential step in the evolution of human language^{12, 13, 14, 15, 16}. We aim to understand the evolutionary dynamics of this transition and to analyse how natural selection can guide it. Here we present a model for the population dynamics of language evolution, define the basic reproductive ratio of words and calculate the maximum size of a lexicon. Syntax allows larger repertoires and the possibility to formulate messages that have not been learned beforehand. Nevertheless, according to our model natural selection can only favour the emergence of syntax if the number of required signals exceeds a threshold value. This result might explain why only humans evolved syntactic communication and hence complex language.

1. Institute for Advanced Study, Princeton, New Jersey 08540, USA
2. School of Biological Sciences, Royal Holloway, University of London, Egham Surrey, TW20 0EX UK

Correspondence to: Martin A. Nowak¹ Correspondence and requests for materials should be addressed to M.A.N. (e-mail: Email: nowak@ias.edu).