TY - JOUR

T1 - Spatial models for species area curves

AU - Bramson, Maury

AU - Cox, J. Theodore

AU - Durrett, Richard

N1 - Funding Information:
We would like to thank Steve Hubbell for sharing his ideas with us\ and Linda Buttel for performing the simulations and making the graphs in Figs 0 3[ We are grateful to referees Alan Hastings and Michael Rosenweig for suggestions and criticisms that inspired us to improve this paper[ Durrett was partially supported by the National Science Foundation and by the Army Research O.ce through the Mathematical Sciences Institute at Cornell University[ Levin is pleased to acknowledge the support of the Department of Energy through grant DE!FG91!83ER 50704 and the National Aeronautics and Space Adminis! tration through grants NAGW!2013 and NAGW!2630 to Princeton University[

PY - 1996/10

Y1 - 1996/10

N2 - 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 α1 r(log α)2, whereas if r < 1, the number of species is bounded.

AB - 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 α1 r(log α)2, whereas if r < 1, the number of species is bounded.

KW - Coalescing random walk

KW - Multitype contact process

KW - Multitype voter model

KW - Species area curves

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U2 - 10.1214/aop/1041903204

DO - 10.1214/aop/1041903204

M3 - Article

AN - SCOPUS:0030376913

VL - 24

SP - 1727

EP - 1751

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 4

ER -