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Journal of Theoretical Biology
Volume 204, Issue 2, 21 May 2000, Pages 179-189
 
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doi:10.1006/jtbi.2000.1085    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2000 Academic Press. All rights reserved.

Regular Article

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

MARTIN A. NOWAK

Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

Received 7 September 1999; 
accepted 20 December 1999. ;
Available online 19 March 2002.

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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.


 
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