TY - JOUR
T1 - Patchiness and Demographic Noise in Three Ecological Examples
AU - Bonachela, Juan A.
AU - Muñoz, Miguel A.
AU - Levin, Simon A.
N1 - Funding Information:
Acknowledgements We gratefully acknowledge support from the Cooperative Institute for Climate Science (CICS) of Princeton University and the National Oceanographic and Atmospheric Administration’s (NOAA) Geophysical Fluid Dynamics Laboratory (GFDL), the National Science Foundation (NSF) under grant OCE-1046001, the Spanish MICINN-FEDER under project FIS2009-08451, and from Junta de Andalucía (Proyecto de Excelencia P09FQM-4682). MAM thanks I. Dornic, H. Chaté and, C. López, and F. Ramos, for a long term collaboration on some of the issues presented here.
PY - 2012/9
Y1 - 2012/9
N2 - Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only-at most-local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.
AB - Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only-at most-local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.
KW - Demographic noise
KW - Langevin equations
KW - Non-equilibrium phase transition
KW - Patterns
KW - Self-organization
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U2 - 10.1007/s10955-012-0506-x
DO - 10.1007/s10955-012-0506-x
M3 - Article
AN - SCOPUS:84866306355
SN - 0022-4715
VL - 148
SP - 723
EP - 739
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 4
ER -