Competitive exclusion principle and Droop's model

The situations of fulfillment or violation of the principle of competitive exclusion are investigated. The principle of competitive exclusion is a well-known principle of G.F. Gause. The principle means that each species has its own ecological niche, and no two different species can occupy the same ecological niche. In general, the principle of competitive exclusion states that long-term coexistence of species is impossible if their number exceeds the number of density-dependent factors controlling growth. However, the principle of competitive exclusion is not a repeatedly confirmed law of the physical type; it is only a principle-hypothesis. The fact of its violation is not something outstanding, since numerous examples of such violations are now known. But each such case draws attention to the possible causes of such violations. After all, compliance with the principle of competitive exclusion creates clear characteristics of ecological niches, their similarities or differences. And violation, on the contrary, blurs these differences. We will trace the correspondence of this principle to microbial communities in phytoplankton. The study is of a model nature, conducted on the well-known Droop model. Modeling the vital activity of microorganisms occupies a significant place in the study of biological processes in cultivated conditions. The corresponding dependencies and equations are also applied to natural systems. The model is represented by a system of nonlinear differential equations, in which the properties of the solutions are investigated. This model is also applied to the analysis of phytoplankton in water bodies using laboratory methods of experimental determination of parameters. Equilibrated stationary solutions, called equilibria, are considered. The existence and stability of such solutions are investigated. It turns out that these solutions characterize the phase portrait of the system of differential equations in sufficient detail. Computational experiments in examples illustrate the properties of the solutions.