Overcome Competitive Exclusion in Ecosystems

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.Comment: Manuscript 13 pages, 10 figures; SI 15 pages, 8 figure

Strong violation of the competitive exclusion principle

Bacteria and plants are able to form population waves as a result of their consumer behaviour and propagation. A soliton-like interpenetration of colliding population waves was assumed but not proved earlier. Here we show how and why colliding population waves of trophically identical but fitness different species can interpenetrate through each other without delay. We have hypothesized and revealed here that the last mechanism provides a stable coexistence of two, three and four species, competing for the same limiting resource in the small homogeneous habitat under constant conditions and without any fitness trade-offs. We have explained the mystery of biodiversity mechanistically because (i) our models are bottom-up mechanistic, (ii) the revealed interpenetration mechanism provides strong violation of the competitive exclusion principle and (iii) we have shown that the increase in the number of competing species increases the number of cases of coexistence. Thus the principled assumptions of fitness neutrality (equivalence), competitive trade-offs and competitive niches are redundant for fundamental explanation of species richness

A unified mechanistic model of niche, neutrality and violation of the competitive exclusion principle

The origin of species richness is one of the most widely discussed questions in ecology. The absence of unified mechanistic model of competition makes difficult our deep understanding of this subject. Here we show such a two-species competition model that unifies (i) a mechanistic niche model, (ii) a mechanistic neutral (null) model and (iii) a mechanistic violation of the competitive exclusion principle. Our model is an individual-based cellular automaton. We demonstrate how two trophically identical and aggressively propagating species can stably coexist in one stable homogeneous habitat without any trade-offs in spite of their 10% difference in fitness. Competitive exclusion occurs if the fitness difference is significant (approximately more than 30%). If the species have one and the same fitness they stably coexist and have similar numbers. We conclude that this model shows diffusion-like and half-soliton-like mechanisms of interactions of colliding population waves. The revealed mechanisms eliminate the existing contradictions between ideas of niche, neutrality and cases of violation of the competitive exclusion principle

Strong and weak competitors can coexist in the same niche

The competitive exclusion principle postulates that two trophically identical but fitness different species can not stably coexist in the same niche. However, this principle contradicts the observed nature's species richness. This fact is known as the biodiversity paradox. Here, using a simple cellular automaton model, we mechanistically show how two trophically identical, but fitness different species may stably coexist in the same niche. As environment is stable and any trade-offs are absent in this model, it strongly violates the competitive exclusion principle

Competitive exclusion for chemostat equations with variable yields

In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. The model was studied by Fiedler and Hsu [J. Math. Biol. (2009) 59:233-253]. These authors prove the nonexistence of periodic orbits, by means of a multi-dimensional Bendixon-Dulac criterion. Our approach is based on the construction of Lyapunov functions. The Lyapunov functions extend those used by Hsu [SIAM J. Appl. Math. (1978) 34:760-763] and by Wolkowicz and Lu [SIAM J. Appl. Math. (1997) 57:1019-1043] in the case when growth rates are proportional to food uptakes

Does a population with the highest turnover coefficient win competition?

We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We give sufficient conditions for competitive exclusion and the existence of periodic solutions related to the classical logistic, Beverton-Holt and Ricker models.Comment: The final version will be published in Journal of Difference Equations and Application

Economic associations among causes of species endangerment in the United States.

Associations among causes of species endangerment in the United States reflect the integration of economic sectors, supporting the theory and evidence that economic growth proceeds at the competitive exclusion of nonhuman species in the aggregate.economic growth; biodiversity; endangered species