A spatial model for the abundance of species
Bramson, Maury ; Cox, J. Theodore ; Durrett, Richard
Ann. Probab., Tome 26 (1998) no. 1, p. 658-709 / Harvested from Project Euclid
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The voter model, with mutations occurring at a positive rate $\alpha$, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in $d \geq 2$. We show that, as $\alpha \to \infty$, the limiting distribution is right triangular in $d = 2$ and uniform in $d \geq 3$. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.
Publié le : 1998-04-14
Classification:  Species abundance distributions,  multitype voter model,  coalescing random walk,  60K35,  92D25 
@article{1022855647,
     author = {Bramson, Maury and Cox, J. Theodore and Durrett, Richard},
     title = {A spatial model for the abundance of species},
     journal = {Ann. Probab.},
     volume = {26},
     number = {1},
     year = {1998},
     pages = { 658-709},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022855647}
}

Bramson, Maury; Cox, J. Theodore; Durrett, Richard. A spatial model for the abundance of species. Ann. Probab., Tome 26 (1998) no. 1, pp.  658-709. http://gdmltest.u-ga.fr/item/1022855647/