Competitive exclusion in a vector-host model for the dengue fever

 We study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each induces host immunity but only certain degree of cross-immunity to heterologous serotypes. Our model has been constructed to study both the epidemiological trends of the disease and conditions that permit coexistence in competing strains. Dengue is in the Americas an epidemic disease and our model reproduces this kind of dynamics. We consider two viral strains and temporary cross-immunity. Our analysis shows the existence of an unstable endemic state (‘saddle’ point) that produces a long transient behavior where both dengue serotypes cocirculate. Conditions for asymptotic stability of equilibria are discussed supported by numerical simulations. We argue that the existence of competitive exclusion in this system is product of the interplay between the host superinfection process and frequency-dependent (vector to host) contact rates. Received 4 December 1995; received in revised form 5 March 1996     

Competitive exclusion and coexistence of pathogens in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373-390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable.     

Competitive exclusion and coexistence for a quasilinear size-structured population model

We present a quasilinear size-structured model which describes the dynamics of a population with n competing ecotypes. We assume that the vital rates of each subpopulation depend on the total population due to competition. We provide conditions on the individual rates which guarantee competitive exclusion in the case of closed reproduction (offspring always belongs to the same ecotype as the parent). In particular, our results suggest that the ratio of the reproduction and mortality rates is a good measure to determine the winning ecotype. Meanwhile, we show that in the case of open reproduction all ecotypes coexist.     

Coexistence and invasibility in a two-species competition model with habitat-preference

The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference—generating spatial niches—strongly stabilizes the coexistence of the two species. Eliminating habitat preference—neutral dynamics—the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.     

Global dynamics of a discrete two-species Lottery-Ricker competition model

In this article, we study the global dynamics of a discrete two-dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show that for a certain parameter range, there exists a compact interior attractor that attracts all interior points except Lebesgue measure zero set. This result gives a weaker form of coexistence which is referred to as relative permanence. This new concept of coexistence combined with numerical simulations strongly suggests that the basin of attraction of the locally asymptotically stable interior period-2 orbit is an infinite union of connected components. This idea may apply to many other ecological models. Finally, we discuss the generic dynamical structure that gives relative permanence.     

Competitive exclusion through reproductive interference

A simple differential equation model was developed to describe the competitive interaction that may occur between species through reproductive interference. The model has the form comparable to Volterra's competition equations, and the graphical analysis of the outcome of the two-species interaction based on its zero-growth isoclines proved that: (1) The possible outcome in this model, as in usual models of resource competition, is either stable coexistence of both species or gradual exclusion of one species by the other, depending critically upon the values of the activity overlapping coefficient c_ij; (2) but, for the same c_ij-values, competitive exclusion is much more ready to occur here than in resource competition; (3) and moreover, the final result of the competition is always dependent on the initial-condition due to its non-linear isoclines, i.e., even under the parameter condition that generally allows both species to coexist, an extreme bias in intial density to one species can readily cause subsequent complete exclusion of its counterparts. Thus, it may follow that the reproductive interference is likely to be working in nature as an efficient mechanism to bring about habitat partitioning in either time or space between some closely related species in insect communities, even though they inhabit heterogeneous habitats where resource competition rarely occurs so that they could otherwise attain steady coexistence.     

Diffusion-mediated persistence in two-species competition Lotka-Volterra model

We consider a system composed of two Lotka-Volterra patches connected by diffusion. Each patch has two competitors. Conditions for persistence of the system are given. It is proved that the system can be made persistent under appropriate diffusion coefficients ensuring the instability of boundary equilibria, even if each species is not persistent within each patch. The choice of the coefficients depends closely on the patch dynamics without diffusion.     

Global dynamics of a discrete two-species Lottery-Ricker competition model

In this article, we study the global dynamics of a discrete two-dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show that for a certain parameter range, there exists a compact interior attractor that attracts all interior points except Lebesgue measure zero set. This result gives a weaker form of coexistence which is referred to as relative permanence. This new concept of coexistence combined with numerical simulations strongly suggests that the basin of attraction of the locally asymptotically stable interior period-2 orbit is an infinite union of connected components. This idea may apply to many other ecological models. Finally, we discuss the generic dynamical structure that gives relative permanence.     

Competitive exclusion and limiting similarity: a unified theory

Robustness of coexistence against changes of parameters is investigated in a model-independent manner by analyzing the feedback loop of population regulation. We define coexistence as a fixed point of the community dynamics with no population having zero size. It is demonstrated that the parameter range allowing coexistence shrinks and disappears when the Jacobian of the dynamics decreases to zero. A general notion of regulating factors/variables is introduced. For each population, its impact and sensitivity niches are defined as the differential impact on, and the differential sensitivity towards, the regulating variables, respectively. Either the similarity of the impact niches or the similarity of the sensitivity niches results in a small Jacobian and in a reduced likelihood of coexistence. For the case of a resource continuum, this result reduces to the usual "limited niche overlap" picture for both kinds of niche. As an extension of these ideas to the coexistence of infinitely many species, we demonstrate that Roughgarden's example for coexistence of a continuum of populations is structurally unstable.     

Dynamics in a discrete two-species competition model: coexistence and over-compensation

The dynamic features of an over-compensating discrete two-species competition system with stable coexistence are recaptured, and it is shown how the probabilities of the different possible ecological scenarios, e.g. coexistence, may be calculated when the assumption of no over-compensation is loosened. A Bayesian methodology for calculating the probability that stable oscillations or chaos may occur in plant populations or communities is outlined. The methodology is exemplified using an experimental population of Arabidopsis thaliana. It is concluded that, when making ecological predictions it is preferable and possibly important to test for the possibility of chaotic population dynamics due to over-compensation rather than assuming a priori that over-compensation does not occur.     

Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.     

Competitive exclusion and the No‐Interaction model operate simultaneously in microcosm plant communities

Question: Is the relation between productivity and species richness due to an increase in plant size and hence a reduced plant density? Location: Glasshouse experiment. Methods: Productivity was manipulated with fertilizer and irrigation in a microcosm experiment. The ‘sampling effect’ was removed using rarefaction to a common density of individual plants per pot. Results: Fertility increased community biomass towards an asymptotic maximum, and reduced the light passing through plant canopies towards an asymptotic minimum. As biomass increased, so did species richness. However, this did not seem to be a direct effect of productivity on species richness, but rather one mediated by plant density, since: (1) the richness/ density relation was stronger than the richness/biomass one; (2) adding biomass to the richness/density regression did not increase its predictivity; (3) the richness/biomass relation was removed by rarefaction to 200 individuals per pot. It is therefore concluded that the richness/biomass relation observed was due to the sampling effect. Rarefaction to a small number of plants gave a quite different trend: lower richness at high biomass. This seems to be due to an increased number of subordinate species at high community biomass, and a more uneven distribution of abundance. Conclusion: The Competitive Exclusion and No‐Interaction hypotheses have been seen as alternatives. We suggest that they can operate simultaneously.     

Stability analysis of a two-species model with transitions between population interactions

Stability of a simple two-species system is investigated. This model assumes that the kind of inter-specific interactions is not fixed, and that it depends on the system state, i.e., undergoes transitions between different population interactions due to variation in population densities. The main goal is to show the effects of the transitions between different population interactions on the two-species coexistence, and on the stability conditions of multiple equilibria.     

Competitive exclusion,coexistence and community structure

Studies of coexistence are based ultimately on the assumption that competitive exclusion is a general and accredited phenomenon in nature. However, the ecological and evolutionary impact of interspecific competition is of questionable significance. Review of three reputed examples of competitive exclusion in the field (Aphytis wasps, red and grey squirrels, and triclads) demonstrates that the widely-accepted competition-based interpretations are unlikely, that alternative explanations are overlooked, and that all other reported cases need critical reinvestigation. Although interspecific competition does undoubtedly occur, the evidence suggests it is usually too weak and intermittent a force to achieve competitive exclusion or any other ecologically-significant result, except perhaps rarely and on a minor scale. Coexistence and community structure are therefore not ecological conditions to be especially accounted for, especially since their inherently comparative methods generate information that is largely superficial. Alternative questions that relate directly to species, the units of diversity, are discussed and they emphasize the primary habitat requirements of species, which are fixed during speciation. Neither the comparative approach of coexistence studies, nor the investigation of pattern is likely to be profitable, since the acquisition of species-specific characteristics during speciation requires historical research. At least one alternative theory of ecology, based on the close adaptation of organisms to the environment, is available.     

Competitive exclusion and coexistence of universal grammars

Universal grammar (UG) is a list of innate constraints that specify the set of grammars that can be learned by the child during primary language acquisition. UG of the human brain has been shaped by evolution. Evolution requires variation. Hence, we have to postulate and study variation of UG. We investigate evolutionary dynamics and language acquisition in the context of multiple UGs. We provide examples for competitive exclusion and stable coexistence of different UGs. More specific UGs admit fewer candidate grammars, and less specific UGs admit more candidate grammars. We will analyze conditions for more specific UGs to outcompete less specific UGs and vice versa. An interesting finding is that less specific UGs can resist invasion by more specific UGs if learning is more accurate. In other words, accurate learning stabilizes UGs that admit large numbers of candidate grammars.     

Competitive exclusion of heterologous Campylobacter spp. in chicks

Chicken and human isolates of Campylobacter jejuni were used to provide oral challenge of day-old broiler chicks. The isolation ratio of the competing challenge strains was monitored and varied, depending upon the isolates used. A PCR-restriction fragment length polymorphism assay of the flagellin gene (flaA) was used to discriminate between the chick-colonizing isolates. Our observations indicated that the selected C. jejuni colonizers dominated the niche provided by the chicken ceca. Chicken isolates from the flaA type 7 grouping generally had numerical superiority over the human isolates when they were administered in our 1-day-old chick model. Our results suggest that it is possible to use combinations of C. jejuni chicken isolates as a defined bacterial preparation for the competitive exclusion of human-pathogenic C. jejuni in poultry.     

Competitive exclusion in Cladocera through elevated mortality of adults

The population dynamics of two cladocerans, Ceriodaphnia pulchellaand Diaphanosoma brachyurum competing under laboratory conditionsin lake water was analysed using cross-correlations. Both mixedand isolated populations of the two cladocerans showed delayeddensity-dependence in the death rates of juveniles and adultsas well as in fecundity rate. The regressions for each of thethree rates on total density of competitors were compared betweenthe two species. There were no significant differences in theslopes of regressions for fecundity rates and the death ratesof juveniles. However, in the inferior competitor (Diaphanosoma)which went extinct in all treatments, the death rate of adultsincreased with total density much more quickly than in the superiorcompetitor (Ceriodaphnia). The intraspecific comparisons indicatedthat while Ceriodaphnia adults survived better than juvenilesunder conditions of crowding, in Diaphanosoma, juveniles werebetter survivors than adults. These data suggest that the contentionof higher vulnerability of cladoceran juveniles than adultsto starvation and crowding may prove to be not a universal phenomenon.