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Spatial models for species area curves

Publication ,  Journal Article
Bramson, M; Cox, JT; Durrett, R
Published in: Annals of Probability
January 1, 1996

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.

Duke Scholars

Published In

Annals of Probability

DOI

ISSN

0091-1798

Publication Date

January 1, 1996

Volume

24

Issue

4

Start / End Page

1727 / 1751

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. (1996). Spatial models for species area curves. Annals of Probability, 24(4), 1727–1751. https://doi.org/10.1214/aop/1041903204
Bramson, M., J. T. Cox, and R. Durrett. “Spatial models for species area curves.” Annals of Probability 24, no. 4 (January 1, 1996): 1727–51. https://doi.org/10.1214/aop/1041903204.
Bramson M, Cox JT, Durrett R. Spatial models for species area curves. Annals of Probability. 1996 Jan 1;24(4):1727–51.
Bramson, M., et al. “Spatial models for species area curves.” Annals of Probability, vol. 24, no. 4, Jan. 1996, pp. 1727–51. Scopus, doi:10.1214/aop/1041903204.
Bramson M, Cox JT, Durrett R. Spatial models for species area curves. Annals of Probability. 1996 Jan 1;24(4):1727–1751.

Published In

Annals of Probability

DOI

ISSN

0091-1798

Publication Date

January 1, 1996

Volume

24

Issue

4

Start / End Page

1727 / 1751

Related Subject Headings

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