Advertisement

Acta Biotheoretica

, Volume 63, Issue 2, pp 203–221 | Cite as

A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata

  • Lev V. Kalmykov
  • Vyacheslav L. Kalmykov
Regular Article

Abstract

The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. The principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations of the competitive exclusion principle. This mechanism is based on timely recovery of limiting resources and their spatio-temporal allocation between competitors. Because of limitations of the black-box modeling there was a problem to formulate the exclusion principle correctly. Our white-box multiscale model of two-species competition is based on logical deterministic individual-based cellular automata. This approach provides an automatic deductive inference on the basis of a system of axioms, and gives a direct insight into mechanisms of the studied system. It is one of the most promising methods of artificial intelligence. We reformulate and generalize the competitive exclusion principle and explain why this formulation provides a solution of the biodiversity paradox. In addition, we propose a principle of competitive coexistence.

Keywords

Cellular automata Population dynamics Resource competition Complex systems Multiscale modeling Artificial intelligence 

Notes

Acknowledgments

This research was partially supported by a reward from the Charity fund of rendering of assistance to scientists “NEW IDEA”. We would like to thank Diedel J. Kornet, Editor in Chief, the anonymous reviewers and especially, Frans J.A. Jacobs, Associate Editor for many helpful suggestions and corrections that greatly improved this paper.

References

  1. Cincotta RP, Wisnewski J, Engelman R (2000) Human population in the biodiversity hotspots. Nature 404:990–992. doi: 10.1038/35010105 CrossRefGoogle Scholar
  2. Clark JS, Dietze M, Chakraborty S, Agarwal PK, Ibanez I, LaDeau S, Wolosin M (2007) Resolving the biodiversity paradox. Ecol Lett 10:647–659. doi: 10.1111/j.1461-0248.2007.01041.x CrossRefGoogle Scholar
  3. Craze P (2012) Ecological neutral theory: useful model or statement of ignorance? Available from Cell Press Discussions: http://news.cell.com/discussions/trends-in-ecology-and-evolution/ecological-neutral-theory-useful-model-or-statement-of-ignorance
  4. Dornelas M, Connolly SR, Hughes TP (2006) Coral reef diversity refutes the neutral theory of biodiversity. Nature 440:80–82. doi: 10.1038/nature04534 CrossRefGoogle Scholar
  5. Ehrlich PR, Ehrlich AH (2008) The dominant animal: human evolution and the environment. Island Press, Washington, DCGoogle Scholar
  6. Gauze GF (1934) The struggle for existence. The Williams & Wilkins company, BaltimoreCrossRefGoogle Scholar
  7. Grubb PJ (1977) The maintenance of species-richness in plant communities: the importance of the regeneration niche. Biol Rev 52:107–145. doi: 10.1111/j.1469-185X.1977.tb01347.x CrossRefGoogle Scholar
  8. Hardin GJ (1959) Nature and man’s fate. Rinehart, New YorkGoogle Scholar
  9. Hardin G (1960) The competitive exclusion principle. Science 131:1292–1297. doi: 10.1126/science.131.3409.1292 CrossRefGoogle Scholar
  10. Hardin G (1968) The tragedy of the commons. Science 162:1243–1248. doi: 10.1126/science.162.3859.1243 CrossRefGoogle Scholar
  11. Hubbell SP (2001) The unified neutral theory of biodiversity and biogeography. Monographs in population biology, vol 32. Princeton University Press, PrincetonGoogle Scholar
  12. Huston M, DeAngelis D, Post W (1988) New computer models unify ecological theory. BioScience 38:682–691. URL: http://www.jstor.org/stable/1310870
  13. Hutchinson GE (1961) The paradox of the plankton. Am Nat 95:137–145. doi: 10.2307/2458386 CrossRefGoogle Scholar
  14. Kalmykov LV, Kalmykov VL (2013) Verification and reformulation of the competitive exclusion principle Chaos. Solitons Fractals 56:124–131. doi: 10.1016/j.chaos.2013.07.006 CrossRefGoogle Scholar
  15. Komarov AS, Palenova MM, Smirnova OV (2003) The concept of discrete description of plant ontogenesis and cellular automata models of plant populations. Ecol Model 170:427–439. doi: 10.1016/S0304-3800(03)00243-6 CrossRefGoogle Scholar
  16. Kroll A (2000) Grey-box models: concepts and application. New frontiers in computational intelligence and its applications. IOS Press, Amsterdam, pp 42–51Google Scholar
  17. Lehman CL, Tilman D (1997) Spatial ecology: the role of space in population dynamics and interspecific interactions. In: Tilman D, Kareiva PM (eds) Monographs in population biology, vol 30., Princeton University PressPrinceton, N.J., pp 185–203Google Scholar
  18. Letichevskii AA, Reshod’ko LV (1972) N. Wiener’s theory of the activity of excitable media. Cybern Syst Anal 8:856–864. doi: 10.1007/bf01068458 CrossRefGoogle Scholar
  19. Nee S (2002) Biodiversity: thinking big in ecology. Nature 417:229–230. doi: 10.1038/417229a CrossRefGoogle Scholar
  20. Palmer MW (1994) Variation in species richness: towards a unification of hypotheses. Folia Geobot Phytotax 29:511–530. http://www.jstor.org/stable/4181308
  21. Silvertown J, Holtier S, Johnson J, Dale P (1992) Cellular automaton models of interspecific competition for space—the effect of pattern on process. J Ecol 80:527–534. http://www.jstor.org/stable/2260696
  22. Sommer U (1999) Ecology—competition and coexistence. Nature 402:366–367. doi: 10.1038/46453 CrossRefGoogle Scholar
  23. Tansley AG (1935) The use and abuse of vegetational concepts and terms. Ecology 16:284–307. doi: 10.2307/1930070 CrossRefGoogle Scholar
  24. Tilman D (1987) The importance of the mechanisms of interspecific competition. Am Nat 129:769–774. doi: 10.1086/284672 CrossRefGoogle Scholar
  25. Tilman D, Reich PB, Knops JMH (2006) Biodiversity and ecosystem stability in a decade-long grassland experiment. Nature 441:629–632. doi: 10.1038/nature04742 CrossRefGoogle Scholar
  26. Vitousek PM, Mooney HA, Lubchenco J, Melillo JM (1997) Human domination of earth’s ecosystems science 277:494–499. doi: 10.1126/science.277.5325.494 Google Scholar
  27. Watt AS (1947) Pattern and process in the plant community. J Ecol 35:1–22. doi: 10.2307/2256497 CrossRefGoogle Scholar
  28. Wiener N (1948) Cybernetics; or, control and communication in the animal and the machine. M I T Technology Press Publications, Technology Press, CambridgeGoogle Scholar
  29. Wiener N, Rosenblueth A (1946) The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch Inst Cardiol Mex 16:205–265Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute of Theoretical and Experimental BiophysicsRussian Academy of SciencesPushchinoRussian Federation
  2. 2.Institute of Cell BiophysicsRussian Academy of SciencesPushchinoRussian Federation
  3. 3.Pushchino State Institute of Natural SciencesPushchinoRussian Federation

Personalised recommendations