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On the relation between the type–token and species-area problems

Published online by Cambridge University Press:  14 July 2016

Barron Brainerd
Barron Brainerd*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1.
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Abstract

The species-area problem in biology and the type-token problem in literary studies are analogues of one another but have nearly disjoint literatures. Here their relationship is treated, a critique of models used in each is made and Markovian models are provided for two well-known empirical models from the species-area literature. Finally, some of the assumptions underlying each of these models are considered in the light of literary data.

Keywords

TYPESTOKENSHAPAX LOGOMENAMARKOV CHAINS WITH A COUNTABLE NUMBER OF STATESKIERKEGAARD
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 785 - 793
Copyright
Copyright © Applied Probability Trust 1982 

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References

Arrhenius, O. (1921) Species and area. J. Ecol. 9, 95–99.CrossRefGoogle Scholar
Brainerd, B. (1972) On the relation between types and tokens in literary text. J. Appl. Prob. 9, 507–518.CrossRefGoogle Scholar
Brainerd, B. (1981) Some elaborations upon Gani's model for the type-token relationship. J. Appl. Prob. 18, 452–460.CrossRefGoogle Scholar
Engen, S. (1978) Stochastic Abundance Models. Chapman and Hall, London.CrossRefGoogle Scholar
Gani, J. (1975) Stochastic models for type counts in a literary text. In Perspectives in Probability and Statistics, ed. Gani, J., Distributed by Academic Press, London, for the Applied Probability Trust, Sheffield.Google Scholar
Gleason, H. A. Sr. (1922) On the relation between species and area. Ecology 3, 156–162.CrossRefGoogle Scholar
Kucera, H. and Francis, W. N. (1967) Computational Analysis of Present-Day American English. Brown University Press, Providence, RI.Google Scholar
Mandelbrot, B. (1961) On the theory of word frequencies and on related Markovian models of discourse. Proc. Symp. Appl. Math. 12, 190–219.CrossRefGoogle Scholar
Mcneil, D. R. (1973) Estimating an author's vocabulary. J. Amer. Statist. Assoc. 69, 92–96.CrossRefGoogle Scholar
Pielou, E. C. (1977) Mathematical Ecology. Wiley, New York.Google Scholar