Open Access
October 1996 Spatial models for species area curves
Maury Bramson, J. Theodore Cox, Richard Durrett
Ann. Probab. 24(4): 1727-1751 (October 1996). DOI: 10.1214/aop/1041903204


The relationship between species number and area is an old problem in biology. We propose here an interacting particle system--the multitype voter model with mutation--as a mathematical model to study this problem. We analyze the species area curves of this model as the mutation rate $\alpha$ tends to zero. We obtain two basic types of behavior depending on the size of the spatial region under consideration. If the region is a square with area $\alpha^{-r}, r > 1$, then, for small $\alpha$, the number of species is of order $\alpha^{1-r}(\log \alpha)^2$, whereas if $r < 1$, the number of species is bounded.


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Maury Bramson. J. Theodore Cox. Richard Durrett. "Spatial models for species area curves." Ann. Probab. 24 (4) 1727 - 1751, October 1996.


Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0939.92032
MathSciNet: MR1415227
Digital Object Identifier: 10.1214/aop/1041903204

Primary: 60K35 , 92D25

Keywords: coalescing random walk , multitype contact process , multitype voter model , Species area curves

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 4 • October 1996
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