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Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in EcologyWe study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.
Document ID
19990019266
Acquisition Source
Goddard Space Flight Center
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Gandhi, Amar
(Princeton Univ. NJ United States)
Levin, Simon
(Princeton Univ. NJ United States)
Orszag, Steven
(Princeton Univ. NJ United States)
Date Acquired
August 19, 2013
Publication Date
January 1, 1998
Publication Information
Publication: Journal of Theoretical Biology
Publisher: Academic Press Ltd.
Volume: 192
ISSN: 0022-5193
Subject Category
Environment Pollution
Funding Number(s)
CONTRACT_GRANT: NAG5-6422
CONTRACT_GRANT: N00014-92-J-1796
CONTRACT_GRANT: ASF 97-3-5
CONTRACT_GRANT: NAGw-4688
CONTRACT_GRANT: N00014-92-J-1527
Distribution Limits
Public
Copyright
Other

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