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Stability in paradigm biological systems

Published online by Cambridge University Press:  17 February 2009

Andrew J. Rixon ,
Craig R. Johnson  and
Alans S. Jones
Andrew J. Rixon
Affiliation:
Department of Mathematics, University of Queensland, St Lucia Qld 4072, Australia
Craig R. Johnson
Affiliation:
Department of Mathematics, University of Queensland, St Lucia Qld 4072, Australia
Alans S. Jones
Affiliation:
Department of Mathematics, University of Queensland, St Lucia Qld 4072, Australia
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Abstract

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A discrete spatial model of a multi-species environment is formulated, and the behaviour of the system is studied. The model is used to explore stability and resilience of biological systems and discuss how they are dependent on spatial scale chosen.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 1 , July 1998 , pp. 23 - 34
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Brown, W., “Cheat thy neighbour - a recipe for success”, New Scientist 9 (1993) 19–20.Google Scholar
[2]Commins, H. N., May, R. M. and Hassel, M. P., “Spatial structure and chaos in insect population dynamics”, Nature 353 (1991) 255–258.Google Scholar
[3]Connel, J. H. and Sousa, W. P., “On the evidence needed to judge ecological stability or persistence”, American Naturalist 121 (1983) 789–824.CrossRefGoogle Scholar
[4]Davis, P., “Order in evolutionary chaos”, Guardian Weekly 23 Jan (1994).Google Scholar
[5]Dublin, H. T., Sinclair, A. R. E. and McGlade, J., “Elephants and fire as causes of multiple stable states in Serengeti-Mara woodlands”, J. Animal Ecology 59 (1990) 1147–1164.CrossRefGoogle Scholar
[6]Feigenbaum, M. J., “Universal behaviour in non-linear systems”, Physica 7D (1983) 16–39.Google Scholar
[7]Goh, B. S., “Global stability in two species interactions”, J. Math. Biol. 3 (1976) 313–318.CrossRefGoogle ScholarPubMed
[8]Hastings, A., “Food web theory and stability”, Ecology 69 (1988) 1665–1668.CrossRefGoogle Scholar
[9]Hastings, A. and Higgins, K., “Persistence of transients in spatially structured ecological models”, Science 263 (1994) 1133–1136.CrossRefGoogle ScholarPubMed
[10]Helleman, R. H. G., Iooss, G. and Stora, R., “Chaotic behaviour of deterministic systems”, Les Houches 85–134.Google Scholar
[11]Hogeweg, P., “Cellular automata as paradigm for ecological modelling”, Appl. Math. Comp. 27 (1988) 81–100.CrossRefGoogle Scholar
[12]Holden, A. V., Chaos (Manchester University Press Publications, 1987).Google Scholar
[13]Holling, C. S., “Resilience and stability of ecological systems”, A. Rev. Ecol. Syst. 4 (1973) 1–23.CrossRefGoogle Scholar
[14]Knowlton, N., “Thresholds and multiple stable states in coral reef dynamics”, Amer. Zool. 32 (1990) 674–682.CrossRefGoogle Scholar
[15]Langton, C. G., “Studying artificial life with cellular automata”, Physica 22D (1986) 120–149.Google Scholar
[16]Lewontin, R. C., “The meaning of stability”, Brookhaven Symp. Biol. 22 (1969) 13–23.Google ScholarPubMed
[17]May, R. M., “Stability and complexity in model ecosystems”, Nature 238 (1972) 413–414.CrossRefGoogle Scholar
[18]May, R. M., “Will a large complex system be stable?”, Nature 238 (1972) 413–414.CrossRefGoogle Scholar
[19]May, R. M., “Simple mathematical models with very complicated dynamics”, Nature 261 (1976) 459–466.CrossRefGoogle ScholarPubMed
[20]May, R. M., “Thresholds and breakpoints in ecosystems with a multiplicity of stable states”, Nature 269 (1977) 471–477.CrossRefGoogle Scholar
[21]May, R. M. and Novak, M. A., “Evolutionary games and spatial chaos”, Nature 359 (1992) 826–829.Google Scholar
[22]May, R. M. and Novak, M. A., “Spatial dilemmas of evolution”, Int. J. Bifurcation and Chaos in applied Sciences and Engineering 3 (1993) 35–78.Google Scholar
[23]Peterson, C. H., “Does a rigorous criterion for environmental identity preclude the existence of multiple stable points?”, Am. Nat. 132 (1984) 652–661.Google Scholar
[24]Pimm, S. L., “Food web design and the effect of species deletion”, OIKOS 35 (1980) 139–149.CrossRefGoogle Scholar
[25]Stewart, I., Does God Play Dice? (Penguin Publications, 1989).Google Scholar
[26]Sutherland, J. P., “Perturbations, resistance, and alternative views of the existence of multiple stable points in nature”, Am. Nat. 136 (1990) 270–275.CrossRefGoogle Scholar
[27]Wolfram, S., “Cellular automata as models of complexity”, Nature 311 (1984) 419–424.CrossRefGoogle Scholar