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URL: http://www.ptb.ias.edu/nowak/pdf/JTB00c.pdf

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Authoritative: http://dx.doi.org/10.1006/jtbi.2000.1085   (Publisher's PDF... likely be available here.)

Source: http://www.ptb.ias.edu/nowak/publications.html

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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.

@article{nowak00theBasic,
  author={M. A. Nowak},
  title={The basic reproductive ratio of a word, the maximum size of a lexicon},
  journal={Journal of Theoretical Biology},
  year={2000},
  month={May},
  volume={204},
  number={2},
  pages={179-189},
  doi={10.1006/jtbi.2000.1085},
  url={http://groups.lis.illinois.edu/amag/langev/paper/nowak00theBasic.html}
}