How Clustering Promotes Biodiversity: A Solution to the Plankton Paradox

From a mathematical perspective, randomly assembled species-rich competitive communities exhibit a high degree of instability, as described by Mays stability theorem. This suggests that actual ecological communities should possess a significant level of organization in their competitive network structure, often with a modular topology, to withstand Mays instability. It is also known that a species-saturated ecological community driven by competitive Lotka-Volterra equations, following a path of competitive exclusion, lingers in a long-term state with species congregated in niche space into well-separated clusters, thereby competing in a modular manner. Without regard to origin, we characterize the modular network topology of interspecific competition in such a community as a hierarchical one, representing interspecific competition and the associated fragmentation of niche space among community species as a two-tiered process. That is, in pairs between species within individual groups (clusters) of ecologically related species, on the one hand, and collectively between these groups as holistic ecological units - ecological species, on the other hand. To illustrate this hierarchical organization, we introduce a generalized multi-resource multi-species competition model that recognizes this topology at the basis of its own network structure of interrelated governing equations of species dynamics. This kind of generalization substantially reduces the competitive exclusion constraints on species coexistence, offering promising potential for a conceptual resolution of the plankton paradox.