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A spatial model for the abundance of species

Publication ,  Journal Article
Bramson, M; Cox, JT; Durrett, R
Published in: Annals of Probability
January 1, 1998

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.

Duke Scholars

Published In

Annals of Probability

DOI

ISSN

0091-1798

Publication Date

January 1, 1998

Volume

26

Issue

2

Start / End Page

658 / 709

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4904 Pure mathematics
  • 0104 Statistics
  • 0101 Pure Mathematics
 

Citation

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Bramson, M., Cox, J. T., & Durrett, R. (1998). A spatial model for the abundance of species. Annals of Probability, 26(2), 658–709. https://doi.org/10.1214/aop/1022855647
Bramson, M., J. T. Cox, and R. Durrett. “A spatial model for the abundance of species.” Annals of Probability 26, no. 2 (January 1, 1998): 658–709. https://doi.org/10.1214/aop/1022855647.
Bramson M, Cox JT, Durrett R. A spatial model for the abundance of species. Annals of Probability. 1998 Jan 1;26(2):658–709.
Bramson, M., et al. “A spatial model for the abundance of species.” Annals of Probability, vol. 26, no. 2, Jan. 1998, pp. 658–709. Scopus, doi:10.1214/aop/1022855647.
Bramson M, Cox JT, Durrett R. A spatial model for the abundance of species. Annals of Probability. 1998 Jan 1;26(2):658–709.

Published In

Annals of Probability

DOI

ISSN

0091-1798

Publication Date

January 1, 1998

Volume

26

Issue

2

Start / End Page

658 / 709

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4904 Pure mathematics
  • 0104 Statistics
  • 0101 Pure Mathematics