TY - JOUR
T1 - Moment expansions in spatial ecological models and moment closure through Gaussian approximation
AU - Gandhi, Amar
AU - Levin, Simon Asher
AU - Orszag, Steven
N1 - Funding Information:
ASG acknowledges many useful and insightful discussions with Peter Kramer. ASG and SAO acknowledge the support of ONR/DARPA URI grant N00014-92-J-1796. ASG and SAL acknowledge support from NASA, grants NAGW-4688 and NAG5-6422; Andrew W. Mellon Foundation; Office of Naval Research, grant ONR-URIP N00014-92-J-1527; Alfred P. Sloan Foundation, grant 97-3-5.
PY - 2000
Y1 - 2000
N2 - We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation. (C) 2000 Society for Mathematical Biology.
AB - We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation. (C) 2000 Society for Mathematical Biology.
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U2 - 10.1006/bulm.1999.0119
DO - 10.1006/bulm.1999.0119
M3 - Article
C2 - 10938625
AN - SCOPUS:0033863602
SN - 0092-8240
VL - 62
SP - 595
EP - 632
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
IS - 4
ER -