Mathematical model allowing the coexistence of closely related competitors at the initial stage of evolution

Abstract

The mathematical model presented here aims to elucidate the essential mechanisms of coexistence of species, especially those of closely related forms, as a result of competition in the same environment. It describes a system where the fate of the competitors or mutants is observed at the initial stage of evolution. The model encompasses both the external variables and the internal state of the competitors, which differ only in one of the metabolic rate constants. Results of simulations, even with the simplified form of the model, show that stable coexistence of closely related forms in a uniform environment is possible. In addition, the model allows the analysis of the limitations on the level of differences and similarities among the competitors for achieving a state of coexistence. The essential mechanisms for the coexistence of closely related competitors are proposed to be the involvement of the metabolic network in allowing the same growth rate of competitors which have different internal states, and the interplay between the internal states of the competitors and the external variables of their environment.