Spatial self-organisation in ecology: pretty patterns or robust reality?

Many seemingly plausible mathematical models of small-scale ecological interactions predict the self-organisation of dynamic, coherent and large scale spatial patterns (e.g. spirals). If true, such patterns would have important ecological and evolutionary consequences. For the most part, however, empirical studies have not corroborated their existence, suggesting erroneous dynamics in the models, shortcomings in empirical methodology, or both. Arguments for categorically dismissing self-organized patterns have been based on their assumed sensitivity to symmetry-breaking stochastic noise. However, many plausible mechanisms for generating patterns are robust to noise, and consequently broken symmetry is insufficient grounds for dismissing these self-organized patterns.

[1]  A. Winfree,et al.  Sudden cardia death: a problem in topology. , 1983, Scientific American.

[2]  Lee A. Segel,et al.  PATTERN GENERATION IN SPACE AND ASPECT. , 1985 .

[3]  M. Hassell,et al.  Persistence of multispecies host-parasitoid interactions in spatially distributed models with local dispersal. , 1996, Journal of theoretical biology.

[4]  W. Baxter,et al.  Stationary and drifting spiral waves of excitation in isolated cardiac muscle , 1992, Nature.

[5]  David Griffeath,et al.  Self-Organization of Random Cellular Automata: Four Snapshots , 1994 .

[6]  W. C. Allee The social life of animals , 1938 .

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

[8]  G. Ruxton,et al.  The consequences of stochasticity for self-organized spatial dynamics, persistence and coexistence in spatially extended host-parasitoid communities , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[9]  Michael Begon,et al.  Host–pathogen systems in a spatially patchy environment , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[10]  Jack D. Cowan,et al.  CONNECTIVITY AND THE DYNAMICS OF INTEGRATE-AND-FIRE NEURAL NETWORKS , 1994 .

[11]  J. Keener,et al.  Effects of high frequency stimulation on cardiac tissue with an inexcitable obstacle. , 1993, Journal of theoretical biology.

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

[13]  Philip K. Maini,et al.  Cellular pattern formation during Dictyostelium aggregation , 1995 .

[14]  M A Nowak,et al.  Spatial games and the maintenance of cooperation. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[15]  J. Tyson,et al.  Cyclic AMP waves during aggregation of Dictyostelium amoebae. , 1989, Development.

[16]  Robert M. May,et al.  Large-Scale Ecology and Conservation Biology. , 1995 .

[17]  I. Hanski Spatial scale, patchiness and population dynamics on land , 1994 .

[18]  A. Winfree Electrical instability in cardiac muscle: phase singularities and rotors. , 1989, Journal of theoretical biology.

[19]  Gottfried Mayer-Kress,et al.  Noise controlled spiral growth in excitable media. , 1995, Chaos.

[20]  T. Czárán,et al.  Spatiotemporal dynamic models of plant populations and communities. , 1992, Trends in ecology & evolution.

[21]  Geoffrey Grimmett,et al.  Probability and Phase Transition , 1994 .

[22]  Arun V. Holden,et al.  Spatiotemporal Irregularity in a Two-Dimensional Model of Cardiac Tissue , 1991 .

[23]  T. Pedley,et al.  Hydrodynamic Phenomena in Suspensions of Swimming Microorganisms , 1992 .

[24]  Ricard V. Solé,et al.  Spiral waves, chaos and multiple attractors in lattice models of interacting populations , 1992 .

[25]  Robert M. May,et al.  The spatial dynamics of host-parasitoid systems , 1992 .

[26]  A. Ōkubo Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. , 1986, Advances in biophysics.

[27]  W. Wilson,et al.  Spatial Instabilities within the Diffusive Lotka-Volterra System: Individual-Based Simulation Results , 1993 .

[28]  Kazuhiro Satoh,et al.  Computer Experiment on the Complex Behavior of a Two-Dimensional Cellular Automaton as a Phenomenological Model for an Ecosystem , 1989 .

[29]  S. Hastings,et al.  Spatial Patterns for Discrete Models of Diffusion in Excitable Media , 1978 .

[30]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[31]  Florian Siegert,et al.  Spiral and concentric waves organize multicellular Dictyostelium mounds , 1995, Current Biology.

[32]  Uno Wennergren,et al.  Connecting landscape patterns to ecosystem and population processes , 1995, Nature.

[33]  Jon C. Allen,et al.  Mathematical Models of Species Interactions in Time and Space , 1975, The American Naturalist.

[34]  Jung,et al.  Spatiotemporal stochastic resonance in excitable media. , 1995, Physical review letters.

[35]  Robert M. May,et al.  Species coexistence and self-organizing spatial dynamics , 1994, Nature.

[36]  James P. Keener,et al.  Dynamics of Dissipative Structures in Reaction-Diffusion Equations , 1995, SIAM J. Appl. Math..

[37]  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.

[38]  Robert E. Kenward,et al.  HAWKS AND DOVES: FACTORS AFFECTING SUCCESS AND SELECTION IN GOSHAWK ATTACKS ON WOODPIGEONS. , 1978 .

[39]  K. Satoh Single and multiarmed spiral patterns in a cellular automaton model for an ecosystem , 1990 .

[40]  Pejman Rohani,et al.  Host―parasitoid metapopulations : the consequences of parasitoid aggregation on spatial dynamics and searching efficiency , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[41]  R. A. Gray,et al.  Mechanisms of Cardiac Fibrillation , 1995, Science.

[42]  S. Wood,et al.  Space, time and persistence of virulent pathogens , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[43]  R. May,et al.  Population dynamics and plant community structure: Competition between annuals and perrenials , 1987 .

[44]  Maarten C. Boerlijst,et al.  Evolutionary consequences of spiral waves in a host—parasitoid system , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[45]  Michael P. Hassell,et al.  Spatial structure and chaos in insect population dynamics , 1991, Nature.