The Basic Reproductive Ratio of a Word, the Maximum Size of a Lexicon

✍ Scribed by MARTIN A. NOWAK

• Book ID: 102611324
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 205 KB
• Volume: 204
• Category: Article
• ISSN: 0022-5193
• DOI: 10.1006/jtbi.2000.1085

✦ Synopsis

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.