Influence of predation on species coexistence in Volterra models

The possibility of predator-mediated coexistence of all species in model ecosystems of the Volterra type is discussed, that is, asymptotic behaviors of systems of two competing species are analyzed when one or two predators are added. All species in the communities can coexist in two distinct ways mathematically, that is, the species may coexist at equilibrium or may coexist in persistent oscillations. The stability of all species at equilibrium increases when one or two predators are added. The conditions for oscillatory coexistence in limit cycles or in chaotic behaviors of two-predator systems are more complicated than in those of one-predator systems. It is concluded that predator-mediated coexistence can be promoted by an intimate relationship between the competitive ability of the prey and the diet preference of the predators.     

Competing species model with behavioral adaptation

This paper studies the properties of a modified Lotka-Volterra model for two competing species, in which the coefficients of the interaction terms are time-dependent averages of the level of interaction over the entire past. For this model, it is shown that (1) competitive exclusion does not occur, (2) there are two possible stable equilibrium points, and (3) in a certain region of parameter space numerical simulations suggest the existence of interesting oscillatory solutions.     

Competition and stoichiometry: coexistence of two predators on one prey

The competitive exclusion principle (CEP) states that no equilibrium is possible if n species exploit fewer than n resources. This principle does not appear to hold in nature, where high biodiversity is commonly observed, even in seemingly homogenous habitats. Although various mechanisms, such as spatial heterogeneity or chaotic fluctuations, have been proposed to explain this coexistence, none of them invalidates this principle. Here we evaluate whether principles of ecological stoichiometry can contribute to the stable maintenance of biodiverse communities. Stoichiometric analysis recognizes that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P) that are present in various proportions in organisms. We incorporate these principles into a standard predator-prey model to analyze competition between two predators on one autotrophic prey. The model tracks two essential elements, C and P, in each species. We show that a stable equilibrium is possible with two predators on this single prey. At this equilibrium both predators can be limited by the P content of the prey. The analysis suggests that chemical heterogeneity within and among species provides new mechanisms that can support species coexistence and that may be important in maintaining biodiversity.     

Kleptoparasitism and complexity in a multi-trophic web

In this work the effects of kleptoparitism in a multi-trophic food-web, in which an omnivorous species scavenges the kills of a top predator, are investigated. Scavengers are assumed to be able to steal predators’ kills by direct interference and aggression. The amount of prey shared depends on the relative competitive abilities of omnivores and predators and on their abundances. To make the proposed model consistent, scavenging is accompanied by other features. First, the predator can prey only on the juvenile life stage of scavengers (i.e. not on adult individuals) as well as on a different species of herbivores. Hence, an age structure is enforced within scavengers, so that they belong to the guild of preys when they are young and vulnerable. Second, predators can switch between prey species selecting the most abundant one. This condition grants the competitive exclusion of the two vegetation eaters, allowing them to co-exist: the omnivore and the herbivore compete for the same vegetation pool but pure herbivores are indeed assumed to be more efficient in its exploitation. The omnivorous species is not able to kill the herbivores, but nonetheless it may exploit their carcasses after they have been killed by predators. Finally, the juvenile/adult ratio of omnivores varies depending on the available resources and predators’ amount. In such a scenario it is shown that kleptoparasitism can modify to a large extent the stability of the system, leading either to a regularization or to chaos, depending both on the scavenger's and the predator's functional response. Moreover, an excess of kleptoparasitism is shown to compromise the whole trophic web, making extinct both predators and scavengers. As far as the authors are aware of, this paper is the first one to explicitly introduce kleptoparasitism in trophic web models.     

Dynamical behavior of two predators competing over a single prey

Dynamical behavior of a food web comprising two predators competing over a single prey has been investigated. The analysis of the food web model shows that the persistence is not possible for two competing predators sharing a single prey species in the cases when any one of the boundary prey–predator planes has a stable equilibrium point. The principle of competitive exclusion holds in such cases. However, numerical simulations exhibit persistence in the presence of periodic solutions in the boundary planes. The system exhibits quasi-periodic behavior in the positive octant. The co-existence in the form of a limit cycle is also possible in some cases.     

Switching effect of predation on competitive prey species

The fact that the predation pressure has a stabilizing effect on the community of competitive species is demonstrated by a mathematical model of two-preys and one-predator system which has the switching property of predation. By analyzing a dynamical system for these three species populations, it is shown that, in a wide range of parameter space, the system has stable coexisting equilibrium states and the manifold of stable stationary points exhibits a cusp catastrophe and there exist two stable stationary points in the cusp region in the parameter space. Thus, it has been shown that Cause's competitive exclusion is actually relaxed by the switching mechanism of predation.     

Dynamical behavior of two predators competing over a single prey

Dynamical behavior of a food web comprising two predators competing over a single prey has been investigated. The analysis of the food web model shows that the persistence is not possible for two competing predators sharing a single prey species in the cases when any one of the boundary prey–predator planes has a stable equilibrium point. The principle of competitive exclusion holds in such cases. However, numerical simulations exhibit persistence in the presence of periodic solutions in the boundary planes. The system exhibits quasi-periodic behavior in the positive octant. The co-existence in the form of a limit cycle is also possible in some cases.     

Analysis of a competitive prey–predator system with a prey refuge

Gauss's competitive exclusive principle states that two competing species having analogous environment cannot usually occupy the same space at a time but in order to exploit their common environment in a different manner, they can co-exist only when they are active in different times. On the other hand, several studies on predators in various natural and laboratory situations have shown that competitive coexistence can result from predation in a way by resisting any one prey species from becoming sufficiently abundant to outcompete other species such that the predator makes the coexistence possible. It has also been shown that the use of refuges by a fraction of the prey population exerts a stabilizing effect in the interacting population dynamics. Further, the field surveys in the Sundarban mangrove ecosystem reveal that two detritivorous fishes, viz. Liza parsia and Liza tade (prey population) coexist in nature with the presence of the predator fish population, viz. Lates calcarifer by using refuges.     

State selection in coupled identical biochemical systems with coexisting stable states

This work examines state selection for coupled biochemical systems with coexisting stable states. For biochemically identical biochemical systems, different coupled systems are examined for the coexistence of (a) one steady state and one oscillatory state or (b) two oscillatory states. For case (a), it is revealed that state selection is always governed by two key factors: the values of kinetic parameters and the coupling strength. When the coupling strength is small, the coupled systems remain in the basin of attraction of their original states. When it is sufficiently large, all coupled systems are always entrained, independently of their original states. Furthermore, for the entrainment, which of the two coexisting states is selected depends sensitively on the activity of recycling enzyme (one of kinetic parameters). It is shown that this is because changing the activity of recycling enzyme alters the size of basin of attraction of each state. When both systems in the same oscillatory state are coupled, an additional factor, namely phase shift between two oscillations, may also affect state selection, and coupling may cause the systems to select either the original oscillatory state or the coexisting steady state. In addition to the features of case (a), case (b) also supports quasiperiodic oscillations and synchronisation of two periodic oscillations. Implications of the results for understanding state selection during the evolution of coupled biochemical systems with coexisting stable states are discussed.     

Competition and coexistence with multiple life-history stages

Do complex life histories affect the conditions under which competitors can coexist? We investigated this using a two-species, two-stage Ricker model. With complex life cycles, the competition coefficients associated with each life-history stage suggest one of three competitive outcomes-coexistence, alternate stable states, or competitive exclusion-that depend on the relative magnitudes of intraspecific and interspecific competition. When the two stages suggest the same outcome, only that outcome can occur. When the stages suggest different outcomes, either one may prevail. It is also possible to have emergent outcomes, in which the outcome is not suggested by either stage. This can occur when the two stages suggest competitive exclusion by opposite species or when one stage suggests alternate stable states and the other suggests coexistence. Therefore, determining the mechanisms of coexistence in species with complex life histories may require consideration of competitive interactions within all life-history stages.     

Modeling of oscillatory scenarios of the coexistence of competing populations

The scenarios of the formation of population distributions have been analyzed for a system of nonlinear reaction–diffusion–advection equations to describe the spatiotemporal distribution of predators and prey. The conditions that must be fulfilled for the model to belong to the class of cosymmetric systems were identified using an analytical approach. Computer simulations of a system with prey and two predators showed that the emergence of families of stationary distributions and oscillatory modes is possible when these conditions are met. The initial distributions of predators were shown to determine the character of the scenario (stationary or non-stationary) at certain combinations of parameters.     

Do wild dogs exclude foxes? Evidence for competition from dietary and spatial overlaps

Abstract The management of wild canids (wild dogs/dingoes and foxes) presents a conservation dilemma for land managers across Australia. These canids are predators of wildlife and domestic stock but dingoes are considered native and anecdotal reports suggest that they may suppress foxes such that dingo/dog conservation may have a net benefit to wildlife. This study examines dietary and spatial interactions between wild dogs and foxes in the Greater Blue Mountains region of NSW to address the possibility of suppression through competitive exclusion by dogs on foxes. Predator diets were compared using faecal analysis as well as an analysis of 19 dietary studies from similar forest habitats in eastern Australia. Spatial relationships were examined using data from an extensive canid control programme. Diets of wild dogs and foxes showed a high degree of overlap in species taken, indicating potential for competition. But there was also evidence of resource partitioning with the size and arboreality of mammalian prey differing between the two predators. Wild dogs and foxes responded to different landscape‐scale variation in the physical environment, but there was no clear evidence of large‐scale differences in their distribution. At the fine scale there was a negative association between these predators that indicated possible temporal avoidance or localized habitat shifts. Therefore, there is evidence for dietary competition and fine‐scale exclusion, but no support for landscape‐scale exclusion of foxes by wild dogs in the Blue Mountains.     

A discrete, size-structured model of microbial growth and competition in the chemostat

A nonlinear matrix model of a size-structured microbial population growing on a scarce nutrient in a chemostat, derived by Gage et al. [6], is modified to include two competing populations. It is shown that competitive exclusion results. The winner is the population able to grow at the lower nutrient concentration.Research partially supported by NSF Grant DMS 9300974     

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.     

Environmental fluctuations,productivity, and species diversity: An experimental study

Seemingly opposing hypotheses concerning the effects of environmental fluctuations on species diversity were shown to complement one another. Studies were made on naturally occurring microbial communities growing in continuous cultures, under both low and high productivity levels. The communities consisted of species of bacteria, protozoan flagellates, and protozoan predators (sarcodinians and ciliates). Fluctuations were imposed by periodically removing a portion of the culture and refilling with sterilized medium. They were designed to mimic the effect of fluctuations periodically decreasing the demand/supply ratio of the community for the available resources. It was found that when growth rates were low (either because of low productivity levels or because of low intrinsic growth rates of the organisms concerned), fluctuations decreased species diversity, whereas when growth rates were high, fluctuations increased species diversity. It is suggested that fluctuations decrease diversity when growth rates are low because they prevent slower growing species from surviving, and increase diversity when growth rates are high because they decrease the extent of competitive domination and exclusion.     

Phage and bacteria support mutual diversity in a narrowing staircase of coexistence

The competitive exclusion principle states that phage diversity M should not exceed bacterial diversity N. By analyzing the steady-state solutions of multistrain equations, we find a new constraint: the diversity N of bacteria living on the same resources is constrained to be M or M+1 in terms of the diversity of their phage predators. We quantify how the parameter space of coexistence exponentially decreases with diversity. For diversity to grow, an open or evolving ecosystem needs to climb a narrowing ‘diversity staircase'' by alternatingly adding new bacteria and phages. The unfolding coevolutionary arms race will typically favor high growth rate, but a phage that infects two bacterial strains differently can occasionally eliminate the fastest growing bacteria. This context-dependent fitness allows abrupt resetting of the ‘Red-Queen''s race'' and constrains the local diversity.     

Cooperative hunting in a discrete predator–prey system II

ABSTRACT

We investigate a discrete-time predator–prey system with cooperative hunting in the predators proposed by Chow et al. by determining local stability of the interior steady states analytically in certain parameter regimes. The system can have either zero, one or two interior steady states. We provide criteria for the stability of interior steady states when the system has either one or two interior steady states. Numerical examples are presented to confirm our analytical findings. It is concluded that cooperative hunting of the predators can promote predator persistence but may also drive the predator to a sudden extinction.     

The diffusive Lotka-Volterra system with three species can have a stable non-constant equilibrium solution

Three examples of the diffusive 3-species Lotka-Volterra system with constant interaction parameters are given, and by bifurcation techniques shown to have stable spatially non-constant equilibrium solutions. One example is competitive; the second one predator-two-competing prey and the third involves two predators and a single prey.     

Competitive exclusion and persistence in models of resource and sexual competition

 We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model. Received 1 November 1995; received in revised form 13 January 1996     

Predation, competition, and nutrient recycling: a stoichiometric approach with multiple nutrients

A model for two competing prey species and one predator is formulated in which three essential nutrients can limit growth of all populations. Prey take up dissolved nutrients and predators ingest prey, assimilating a portion of ingested nutrients and recycling or respiring the balance. For all species, the nutrient contents of individuals vary and growth is coupled to increasing content of the limiting nutrient. This model was parameterized to describe a flagellate preying on two bacterial species, with carbon (C), nitrogen (N), and phosphorus (P) as nutrients. Parameters were chosen so that the two prey species would stably coexist without predators under some nutrient supply conditions. Using numerical simulations, the long-term outcomes of competition and predation were explored for a gradient of N:P supply ratios, varying C supply, and varying preference of the predator for the two prey. Coexistence and competitive exclusion both occurred under some conditions of nutrient supply and predator preference. As in simpler models of competition and predation these outcomes were largely governed by apparent competition mediated by the predator, and resource competition for nutrients whose effective supply was partly governed by nutrient recycling also mediated by the predator. For relatively small regions of parameter space, more complex outcomes with multiple attractors or three-species limit cycles occurred. The multiple constraints posed by multiple nutrients held the amplitudes of these cycles in check, limiting the influence of complex dynamics on competitive outcomes for the parameter ranges explored.