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


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.


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



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.


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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

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