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The Multicomponent Gause Principle in Models of Biological Communities

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Abstract

A refinement is proposed for Gause’s principle of competitive exclusion, which guarantees the disappearance of at least one species in a community with a species number that exceeds the number of resources. Theorems revealing the disappearance of at least n – m components have been developed for a general finite-dimensional system of differential equations that simulates the dynamics of a community with n species in a rough case, i.e., in the absence of a finite number of coincidences defined by relations of the equality type, provided that the Malthusian vector-valued function only assumes values on the hyperplane of the dimension m, which does not contain the origin. It is proposed that the constructed theory can be used for a Lotka–Volterra type system with a Malthusian vector-function, which is a linear combination of the quantities of the available resources.

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ACKNOWLEDGMENTS

The present work was supported by the Russian Foundation for Basic Research, project 15-07-06947.

COMPLIANCE WITH ETHICAL STANDARDS

Сonflict of interests. The authors declare that they have no conflict of interest.

Statement on the welfare of animals. This article does not contain any studies with animals performed by any of the authors.

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  1. Dorodnitsyn Computing Center, Russian Academy of Sciences, 119333, Moscow, Russia

    V. N. Razzhevaikin

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  1. V. N. Razzhevaikin
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Correspondence to V. N. Razzhevaikin.

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Translated by S. Semenova

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Razzhevaikin, V.N. The Multicomponent Gause Principle in Models of Biological Communities. Biol Bull Rev 8, 421–430 (2018). https://doi.org/10.1134/S2079086418050067

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  • DOI: https://doi.org/10.1134/S2079086418050067

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