Abstract
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.
Citation
Maury Bramson. J. Theodore Cox. Richard Durrett. "Spatial models for species area curves." Ann. Probab. 24 (4) 1727 - 1751, October 1996. https://doi.org/10.1214/aop/1041903204
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