TY - JOUR
T1 - 'Critical slowing down' in time-to-extinction
T2 - An example of critical phenomena in ecology
AU - Gandhi, Amar
AU - Levin, Simon Asher
AU - Orszag, Steven
N1 - Funding Information:
The authors acknowledge many useful and insightful discussions with Rick Durrett\ Peter Kramer\ Claudia Neuhauser and Victor Yakhot[ They also thank one of the reviewers for asking the question] does the limit exist for the time!to!extinction as L : a< A[S[G[ and S[A[O[ acknowl! edge the support of ONR:DARPA URI grant N99903!81! J!0685[ SAL acknowledges support from NASA\ grants NAGW!3577 and NAG4!5311^ Andrew W[ Mellon Foundation^ O.ce of Naval Research\ grant ONR!URIP N99903!81!J!0416^ Alfred P[ Sloan Foundation\ grant 86!2!4[
PY - 1998/6/7
Y1 - 1998/6/7
N2 - We 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.
AB - We 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.
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U2 - 10.1006/jtbi.1998.0660
DO - 10.1006/jtbi.1998.0660
M3 - Article
C2 - 9650292
AN - SCOPUS:0032493182
SN - 0022-5193
VL - 192
SP - 363
EP - 376
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
IS - 3
ER -