The basic reproductive ratio of a word, the maximum size of a lexicon |
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Authors: | Nowak M A |
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Institution: | Institute for Advanced Study, Princeton, NJ 08540, USA. |
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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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