David A Kessler and Nadav M Shnerb 2009 New J. Phys. 11 043017 doi:10.1088/1367-2630/11/4/043017
The effect of spatial heterogeneity on the extinction transition in stochastic population dynamics
David A Kessler1 and Nadav M Shnerb
Show affiliationsStochastic 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.
- PACS
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87.23.Cc Population dynamics and ecological pattern formation
- Subjects
- Dates
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Issue 4 (April 2009)
Received 25 December 2008
Published 9 April 2009
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The effect of spatial heterogeneity on the extinction transition in stochastic population dynamics
David A Kessler and Nadav M Shnerb 2009 New J. Phys. 11 043017
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