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Explaining biodiversity in nature is a fundamental problem in ecology. An outstanding challenge is embodied in the so-called Competitive Exclusion Principle: two species competing for one limiting resource cannot coexist at constant population densities, or more generally, the number of consumer species in steady coexistence cannot exceed that of resources. The fact that competitive exclusion is rarely observed in natural ecosystems has not been fully understood. Here we show that by forming chasing triplets among the consumers and resources in the consumption process, the Competitive Exclusion Principle can be naturally violated. The modeling framework developed here is broadly applicable and can be used to explain the biodiversity of many consumer-resource ecosystems and hence deepens our understanding of biodiversity in nature.
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How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open question in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and Physics. In this context, modeling the stable coexistence of different species competing for limited resources is a particularly demanding task. From the mathematical point of view, coexistence in competitive dynamics can be achieved when dominance among species forms intransitive loops. However, these relationships usually lead to species densities neutrally cycling without converging to a stable equilibrium and, although in recent years several mechanisms have been proposed, models able to explain the robust persistence of competitive ecosystems are lacking. Here we show that stable coexistence in large communities can be achieved when the locality of interactions is taken into account. We consider a simplified ecosystem where individuals of each species lay on a spatial network and interactions are possible only between nodes at a certain distance. Varying such distance allows to interpolate between local and global competition. Our results demonstrate that when two conditions are met: individuals are embedded in space and can only interact with other individuals within a short distance, species coexist reaching a stable equilibrium. On the contrary, when one of these ingredients is missing large fluctuations and neutral cycles emerge.
Microbial electrolysis cells (MECs) employ electroactive bacteria to perform extracellular electron transfer, enabling hydrogen generation from biodegradable substrates. In previous work, we developed and analyzed a differential-algebraic equation (DAE) model for MECs. The model resembles a chemostat with ordinary differential equations (ODEs) for concentrations of substrate, microorganisms, and an extracellular mediator involved in electron transfer. There is also an algebraic constraint for electric current and hydrogen production. Our goal is to determine the outcome of competition between methanogenic archaea and electroactive bacteria, because only the latter contribute to electric current and resulting hydrogen production. We investigate asymptotic stability in two industrially releva
Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity and niche partitioning, are based on competitive exclusion. However, this classical paradigm in ecology relies on implications derived from simple, deterministic models. Here we show how the predictions of a symmetric, deterministic model about the way extinctions proceed can be utterly different from the results derived from the same model when ecological drift (demographic stochasticity) is explicitly considered. Using analytical approximations to the steady-state conditional probabilities for assemblages with two and three species, we demonstrate that stochastic competitive exclusion leads to a cascade of extinctions, whereas the symmetric, deterministic model predicts a multiple collapse of species. To test the robustness of our results, we have studied the effect of environmental stochasticity and relaxed the species symmetry assumption. Our conclusions highlight the crucial role of stochasticity when deriving reliable theoretical predictions for species community assembly.
In his seminal work in the 1970s Robert May suggested that there was an upper limit to the number of species that could be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors making an ecosystem stable or unstable continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turings work on pattern formation with Mays random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with two trophic levels can become unstable with the introduction of dispersal in space. Conversely, we show that Turing instabilities can occur more easily in complex ecosystems with many species than in the case of only a few species. Our work shows that adding more details to the model of May gives rise to more ways in which an equilibrium can become unstable. Making Mays simple model more realistic is therefore unlikely to remove the upper bound on complexity.
Forty years ago, Robert May questioned a central belief in ecology by proving that sufficiently large or complex ecological networks have probability of persisting close to zero. To prove this point, he analyzed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (e.g., predator-prey, mutualistic or competitive). Here we extend Mays results to these relationships and find remarkable differences between predator-prey interactions, which increase stability, and mutualistic and competitive, which are destabilizing. We provide analytic stability criteria for all cases. These results have broad applicability in ecology. For example, we show that, surprisingly, the probability of stability for predator-prey networks is decreased when we impose realistic food web structure or we introduce a large preponderance of weak interactions. Similarly, stability is negatively impacted by nestedness in bipartite mutualistic networks.
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