Spatial models for species area curves
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 α 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 α-r, r > 1, then, for small α, the number of species is of order α1r(log α)2, whereas if r < 1, the number of species is bounded.
Bramson, M; Cox, JT; Durrett, R
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