A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata
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A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata Lev V. Kalmykov1 • Vyacheslav L. Kalmykov2,3
Received: 14 August 2014 / Accepted: 4 May 2015 Springer Science+Business Media Dordrecht 2015
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 twospecies 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
& Vyacheslav L. Kalmykov [email protected] 1
Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation
2
Institute of Cell Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russian Federation
3
Pushchino State Institute of Natural Sciences, Pushchino, Moscow Region 142290, Russian Federation
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L. V. Kalmykov, V. L. Kalmykov
1 Introduction There is a long-standing question in theoretical ecology—How can so many superficially similar species coexist together (Craze 2012; Palmer 1994; Sommer 1999)? Trying to answer this question, ecologists came to the biodiversity paradox (Clark et al. 2007; Hutchinson 1961; Lehman and Tilman 1997; Sommer 1999). In theory, according to the competitive exclusion principle, complete competitors cannot coexist (Hardin 1959, 1960). In practice, there are many examples of such coexistence: rain forests (Hubbell 2001), coral reefs (Dornelas et al. 2006), grasslands (Tilman et al. 2006), plankton communities (Hutchinson 1961). The paradox consists in the contradiction between the competitive exclusion principle and the observed natural biodiversity. ‘‘Resolving the diversity paradox became the central issue in theoretical ecology’’ (Lehman and Tilman 1997). ‘‘The apparent contradiction between competitive exclusion and the species richness found in nature has been a longstanding enig
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