A New Kind of Ecology?

Abstract Mathematical models have a long history of use for understanding ecological systems. In a recent book, A New Kind of Science, Steve Wolfram calls into question traditional modeling approaches and calls for the increased application of cellular automata (CA) models in all areas of scientific inquiry. With reference to Wolfram's book, we review the past uses of CA models in ecology and discuss the relative utility of using traditional models versus CA models to understand ecological communities.

[1]  V. Volterra.  Fluctuations in the Abundance of a Species considered Mathematically , 1926 .

[2]  V. Volterra.  Fluctuations in the Abundance of a Species considered Mathematically , 1926, Nature.

[3]  J. G. Skellam.  Random dispersal in theoretical populations , 1951, Biometrika.

[4]  R. Levins.  The strategy of model building in population biology , 1966 .

[5]  R. Macarthur,et al.  The Theory of Island Biogeography , 1969 .

[6]  R. Levins.  Some Demographic and Genetic Consequences of Environmental Heterogeneity for Biological Control , 1969 .

[7]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.

[8]  J. Diamond,et al.  Ecology and Evolution of Communities , 1976, Nature.

[9]  D. Tilman.  Resource Competition between Plankton Algae: An Experimental and Theoretical Approach , 1977 .

[10]  Alfred J. Lotka,et al.  The growth of mixed populations: Two species competing for a common food supply , 1978 .

[11]  明 大久保,et al.  Diffusion and ecological problems : mathematical models , 1980 .

[12]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[13]  O. Inghe,et al.  Genet and ramet survivorship under different mortality regimes—A cellular automata model , 1989 .

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

[15]  Jonathan Silvertown,et al.  Cellular Automaton Models of Interspecific Competition for Space--The Effect of Pattern on Process , 1992 .

[16]  J. P. Grime,et al.  Resource dynamics and vegetation processes: a deterministic model using two-dimensional cellular automata , 1993 .

[17]  Jane Molofsky,et al.  POPULATION DYNAMICS AND PATTERN FORMATION IN THEORETICAL POPULATIONS , 1994 .

[18]  R. Durrett,et al.  The Importance of Being Discrete (and Spatial) , 1994 .

[19]  Christian Valentin,et al.  A model simulating the genesis of banded vegetation patterns in Niger , 1995 .

[20]  Florian Jeltsch,et al.  Tree Spacing and Coexistence in Semiarid Savannas , 1996 .

[21]  David E. Hiebeler,et al.  Stochastic Spatial Models: From Simulations to Mean Field and Local Structure Approximations , 1997 .

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

[23]  Peter Kareiva,et al.  Spatial ecology : the role of space in population dynamics and interspecific interactions , 1998 .

[24]  Hal Caswell,et al.  Habitat fragmentation and extinction thresholds on fractal landscapes , 1999 .

[25]  Simon A. Levin,et al.  The Geometry of Ecological Interactions: Moment Methods for Ecological Processes in Continuous Space , 2000 .

[26]  Ádám Kun,et al.  THE EFFECT OF CLONAL INTEGRATION ON PLANT COMPETITION FOR MOSAIC HABITAT SPACE , 2000 .

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

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

[29]  K. Moloney,et al.  CONSTRAINTS ON THE ESTABLISHMENT OF PLANTS ALONG A FLUCTUATING WATER‐DEPTH GRADIENT , 2001 .

[30]  D. O. Logofet.  Matrix Population Models: Construction, Analysis, and Interpretation , 2002 .

[31]  L. Berec.  Techniques of spatially explicit individual-based models: construction, simulation, and mean-field analysis , 2002 .

[32]  J. Molofsky,et al.  A novel theory to explain species diversity in landscapes: positive frequency dependence and habitat suitability , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[33]  S. Weinberg,et al.  The Universe as Computer , 2002, Science.

[34]  Bai-Lian Li,et al.  The Geometry of Ecological Interactions: Simplifying Spatial Complexity , 2002 .

[35]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[36]  Lawrence F. Gray,et al.  A Mathematician Looks at Wolfram''s New Kind of Science , 2003 .

[37]  Michio Kondoh,et al.  High Reproductive Rates Result in High Predation Risks: A Mechanism Promoting the Coexistence of Competing Prey in Spatially Structured Populations , 2003, The American Naturalist.

[38]  D. G. Green,et al.  Simulated effects of fire, dispersal and spatial pattern on competition within forest mosaics , 1989, Vegetatio.

[39]  D. Dunkerley,et al.  Banded vegetation: development under uniform rainfall from a simple cellular automaton model , 1997, Plant Ecology.