The Annals of Probability

Spatial models for species area curves

Maury Bramson, J. Theodore Cox, and Richard Durrett

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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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Ann. Probab. Volume 24, Number 4 (1996), 1727-1751.

First available in Project Euclid: 6 January 2003

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92D25: Population dynamics (general)

Species area curves multitype contact process multitype voter model coalescing random walk


Bramson, Maury; Cox, J. Theodore; Durrett, Richard. Spatial models for species area curves. Ann. Probab. 24 (1996), no. 4, 1727--1751. doi:10.1214/aop/1041903204.

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