A spatial model for the abundance of species

Maury Bramson; J. Theodore Cox; Richard Durrett

doi:10.1214/aop/1022855647

A spatial model for the abundance of species

Maury Bramson, J. Theodore Cox, Richard Durrett

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	658-709
Number of pages	52
Journal	Annals of Probability
Volume	26
Issue number	2
DOIs	https://doi.org/10.1214/aop/1022855647
State	Published - Apr 1998

Keywords

Coalescing random walk
Multitype voter model
Species abundance distributions

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/aop/1022855647

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abstract = "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.",

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AU - Cox, J. Theodore

AU - Durrett, Richard

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AB - 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.

KW - Coalescing random walk

KW - Multitype voter model

KW - Species abundance distributions

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ER -

A spatial model for the abundance of species

Abstract

Keywords

ASJC Scopus subject areas

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