Spatial models for species area curves
Bramson, Maury ; Cox, J. Theodore ; Durrett, Richard
Ann. Probab., Tome 24 (1996) no. 2, p. 1727-1751 / Harvested from Project Euclid
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 $\alpha$ 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 $\alpha^{-r}, r > 1$, then, for small $\alpha$, the number of species is of order $\alpha^{1-r}(\log \alpha)^2$, whereas if $r < 1$, the number of species is bounded.
Publié le : 1996-10-14
Classification:  Species area curves,  multitype contact process,  multitype voter model,  coalescing random walk,  60K35,  92D25
@article{1041903204,
     author = {Bramson, Maury and Cox, J. Theodore and Durrett, Richard},
     title = {Spatial models for species area curves},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 1727-1751},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1041903204}
}
Bramson, Maury; Cox, J. Theodore; Durrett, Richard. Spatial models for species area curves. Ann. Probab., Tome 24 (1996) no. 2, pp.  1727-1751. http://gdmltest.u-ga.fr/item/1041903204/