Spatial models for species area curves

Maury Bramson, J. Theodore Cox, Richard Durrett

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 α1 r(log α)2, whereas if r < 1, the number of species is bounded.

Original languageEnglish (US)
Pages (from-to)1727-1751
Number of pages25
JournalAnnals of Probability
Issue number4
StatePublished - Oct 1996


  • Coalescing random walk
  • Multitype contact process
  • Multitype voter model
  • Species area curves

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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