The Multicomponent Gause Principle in Models of Biological Communities

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.