Math @ Duke

Publications [#243467] of Richard T. Durrett
Papers Published
 Bramson, M; Cox, JT; Durrett, R, Spatial models for species area curves,
The Annals of Probability, vol. 24 no. 4
(January, 1996),
pp. 17271751, Institute of Mathematical Statistics [doi]
(last updated on 2019/06/24)
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 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 αr, 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.


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