Criticality and disturbance in spatial ecological systems.

Classical criticality describes sudden changes in the state of a system when underlying processes change slightly. At this transition, patchiness develops which lacks a characteristic or dominant spatial scale. Thus, criticality lies at the interface of two important subjects in ecology, threshold behavior and patchiness. Most ecological examples of criticality involve processes of disturbance and recovery; the spatial and temporal scales of these processes enable three different types of critical system to be distinguished: classical phase transitions, self organized criticality (SOC) and 'robust' criticality. Here, we review the properties defining these three types and their implications for threshold behavior and large intermittent temporal fluctuations, with examples taken from spatial stochastic models for predator-prey, infected-susceptible, and disturbance-recovery interactions. In critical systems, spatial properties of patchiness alone are insufficient indicators of impending sudden changes, unless complemented by the spatial and temporal scales of disturbance and recovery themselves.

[1]  Frédéric Guichard,et al.  Mussel Disturbance Dynamics: Signatures of Oceanographic Forcing from Local Interactions , 2003, The American Naturalist.

[2]  J. Connell Diversity in tropical rain forests and coral reefs. , 1978, Science.

[3]  Nico Stollenwerk,et al.  Meningitis, pathogenicity near criticality: the epidemiology of meningococcal disease as a model for accidental pathogens. , 2003, Journal of theoretical biology.

[4]  A. Fisher,et al.  The Theory of Critical Phenomena: An Introduction to the Renormalization Group , 1992 .

[5]  Watson Mr.,et al.  Signs of Life , 1997 .

[6]  Ricard V. Solé,et al.  Are rainforests self-organized in a critical state? , 1995 .

[7]  R. Durrett,et al.  From individuals to epidemics. , 1996, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[8]  R. Anderson,et al.  Power laws governing epidemics in isolated populations , 1996, Nature.

[9]  S. Levin,et al.  Competitive coexistence in a dynamic landscape. , 2004, Theoretical population biology.

[10]  J. Timothy Wootton,et al.  Local interactions predict large-scale pattern in empirically derived cellular automata , 2001, Nature.

[11]  C. S. Holling,et al.  Resilience and adaptive cycles , 2002 .

[12]  D. Claessen,et al.  Evolution of virulence in a host-pathogen system with local pathogen transmission , 1995 .

[13]  D. Turcotte,et al.  Forest fires: An example of self-organized critical behavior , 1998, Science.

[14]  Drossel,et al.  Self-organized critical forest-fire model. , 1992, Physical review letters.

[15]  Christian Wissel,et al.  The Geometry of Ecological Interactions: Grid-based Models as Tools for Ecological Research , 2000 .

[16]  A. J. Belsky,et al.  Effects of grazing, competition, disturbance and fire on species composition and diversity in grassland communities , 1992 .

[17]  Benton,et al.  Criticality and scaling in evolutionary ecology. , 1997, Trends in ecology & evolution.

[18]  B. Drossel,et al.  Self-organized criticality in forest-fire models , 1999 .

[19]  Yoh Iwasa,et al.  Forest Spatial Dynamics with Gap Expansion: Total Gap Area and Gap Size Distribution , 1996 .

[20]  Simon A. Levin,et al.  Stochastic Spatial Models: A User's Guide to Ecological Applications , 1994 .

[21]  S. Carpenter,et al.  Catastrophic regime shifts in ecosystems: linking theory to observation , 2003 .

[22]  Solé,et al.  Self-similarity in rain forests: Evidence for a critical state. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  David A. Rand,et al.  Invasion, stability and evolution to criticality in spatially extended, artificial host—pathogen ecologies , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[24]  William G. Wilson,et al.  Mobility versus density-limited predator-prey dynamics on different spatial scales , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[25]  Robert A. Desharnais,et al.  HISTORY AND CURRENT DEVELOPMENT OF A PARADIGM OF PREDATION IN ROCKY INTERTIDAL COMMUNITIES , 2002 .

[26]  H. B. Wilson,et al.  Using spatio-temporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[27]  Jorge X Velasco-Hernández,et al.  Extinction Thresholds and Metapopulation Persistence in Dynamic Landscapes , 2000, The American Naturalist.

[28]  Mercedes Pascual,et al.  Broad scaling region in a spatial ecological system , 2003, Complex..

[29]  L. Sander,et al.  Percolation on heterogeneous networks as a model for epidemics. , 2002, Mathematical biosciences.

[30]  William G. Wilson,et al.  COOPERATION AND COMPETITION ALONG SMOOTH ENVIRONMENTAL GRADIENTS , 1997 .

[31]  Mercedes Pascual,et al.  Cluster size distributions: signatures of self-organization in spatial ecologies. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[32]  W. Sousa Disturbance in Marine Intertidal Boulder Fields: The Nonequilibrium Maintenance of Species Diversity , 1979 .

[33]  M. Keeling The Geometry of Ecological Interactions: Evolutionary Dynamics in Spatial Host–Parasite Systems , 2000 .

[34]  M. Katori,et al.  Forest Dynamics with Canopy Gap Expansion and Stochastic Ising Model , 1998 .

[35]  J. Socolar,et al.  Evolution in a spatially structured population subject to rare epidemics. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Christensen,et al.  Self-organized critical forest-fire model: Mean-field theory and simulation results in 1 to 6 dimenisons. , 1993, Physical review letters.

[37]  Ulf Dieckmann,et al.  The Geometry of Ecological Interactions: Simplifying Spatial Complexity , 2000 .

[38]  Per Bak,et al.  How Nature Works , 1996 .

[39]  Makoto Katori,et al.  Analysis of Canopy-Gap Structures of Forests by Ising-Gibbs States - Equilibrium and Scaling Property of Real Forests - , 1999 .

[40]  R. Paine,et al.  Intertidal Landscapes: Disturbance and the Dynamics of Pattern , 1981 .

[41]  M. Rietkerk,et al.  Self-Organized Patchiness and Catastrophic Shifts in Ecosystems , 2004, Science.

[42]  Peter Grassberger,et al.  On a self-organized critical forest-fire model , 1993 .

[43]  Franz Schwabl,et al.  PHASE TRANSITIONS IN A FOREST-FIRE MODEL , 1997 .