A spatial model for the abundance of species

Maury Bramson, J. Theodore Cox, Richard Durrett

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The voter model, with mutations occurring at a positive rate a, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d ≥ 2. We show that, as α → 0, the limiting distribution is right triangular in d = 2 and uniform in d > 3. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.

Original languageEnglish (US)
Pages (from-to)658-709
Number of pages52
JournalAnnals of Probability
Issue number2
StatePublished - Apr 1998


  • Coalescing random walk
  • Multitype voter model
  • Species abundance distributions

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'A spatial model for the abundance of species'. Together they form a unique fingerprint.

Cite this