Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1727-1751 |
| Number of pages | 25 |
| Journal | Annals of Probability |
| Volume | 24 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 1996 |
| Externally published | Yes |
Bibliographical note
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[
Keywords
- Coalescing random walk
- Multitype contact process
- Multitype voter model
- Species area curves