TY - JOUR
T1 - The effect of spatial heterogeneity on the extinction transition in stochastic population dynamics
AU - Kessler, David A.
AU - Shnerb, Nadav M.
PY - 2009/4/9
Y1 - 2009/4/9
N2 - Stochastic logistic-type growth on a static heterogeneous substrate is studied both above and below the drift-induced delocalization transition. Using agent-based simulations, the delocalization of the highest eigenfunction of the deterministic operator is connected with the large N limit of the stochastic theory. It is seen that the localization length of the deterministic theory controls the divergence of the spatial correlation length with N at the transition. It is argued that, in the presence of a strong wind, the extinction transition belongs to the directed percolation universality class, as any finite colony made of discrete agents is washed away from a heterogeneity with compact support. Some of the difficulties in the analysis of the extinction transition in the presence of a weak wind, where there is a localized active state, are discussed.
AB - Stochastic logistic-type growth on a static heterogeneous substrate is studied both above and below the drift-induced delocalization transition. Using agent-based simulations, the delocalization of the highest eigenfunction of the deterministic operator is connected with the large N limit of the stochastic theory. It is seen that the localization length of the deterministic theory controls the divergence of the spatial correlation length with N at the transition. It is argued that, in the presence of a strong wind, the extinction transition belongs to the directed percolation universality class, as any finite colony made of discrete agents is washed away from a heterogeneity with compact support. Some of the difficulties in the analysis of the extinction transition in the presence of a weak wind, where there is a localized active state, are discussed.
UR - http://www.scopus.com/inward/record.url?scp=66449110824&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/11/4/043017
DO - 10.1088/1367-2630/11/4/043017
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AN - SCOPUS:66449110824
SN - 1367-2630
VL - 11
JO - New Journal of Physics
JF - New Journal of Physics
M1 - 043017
ER -