title: The basic reproductive ratio of a word, the maximum size of a lexicon.
abstract: Language is about words and rules. While there is some discussion to what extent rules are learned or innate, it is clear that words have to be learned. Here I construct a mathematical framework for the population dynamics of language evolution with particular emphasis on how words are propagated over generations. I define the basic reproductive ratio of word, R, and show that R > 1 is required for words to be maintained in the lexicon of a language. Assuming that the frequency distribution of words follow Zipf's law, an upper limit is obtained for the number of words in a language that relies exclusively on oral transmission.
authors.affiliation: Institute for Advanced Study, Princeton, NJ 08540, USA.
authors.forename: M A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D006801:Humans; D007804:Language Development; D007858:Learning; D008037:Linguistics; D008954:Models, Biological