Coexistence of two competitors on one resource and one inhibitor: a chemostat model based on bacteria and antibiotics

We present a continuous time model of the dynamics of two species competing for a single limiting resource in the presence of a substance that inhibits the growth of one of the species. Resource and inhibitor are both derived from external sources. These inputs, and all other model parameters, are assumed to be constant in space and time. There exist conditions that permit the stable coexistence of the competitors, provided that the sensitive species is more efficient in exploiting the limiting resource, and the resistant species removes the inhibitor from the environment. There exists a subset of these conditions wherein the sensitive species can become established if and only if the resistant species is already established. If the resistant species does not remove the inhibitor from the environment, then coexistence of sensitive and resistant species is structurally unstable. If the resistant species produces the inhibitor, then coexistence is dynamically unstable. We review several studies of bacterial competition in the presence of antibiotics that support these conclusions.     

Coexistence of two types on a single resource in discrete time

Armstrong and McGehee (1980) have shown that two species modeled in continuous time can coexist on a single resource provided that one species oscillates autonomously. This paper demonstrates the parallel result in discrete time. I consider a deterministic model of two asexual types in a single patch competing for a single resource, and show that such systems generically produce oscillatory coexistence or bistability if one of the types displays periodic or chaotic behavior in isolation. The conditions for coexistence or bistability are derived in terms of the convexity of the functions describing fitness as a function of resource availability. I also analyze whether or not a stable type, a type with a stable equilibrium population size when considered in isolation, can invade a periodic orbit of an unstable type, and show that the same convexity condition distinguishes these two cases. The widely considered exponential or Ricker model for population dynamics lies on the boundary between the two cases and is highly degenerate in this context.     

Coexistence and emergent neutrality generate synchrony among competitors in fluctuating environments

Many competitive communities exhibit a puzzling amount of species diversity. In this study, we model a community of symmetric competitors in a fluctuating environment. We use biologically realistic temperature-dependent growth curves with a widely hypothesized trade-off between maximum growth and nice breadth to control the shapes of the curves of different species. We perform three analyses of the community dynamics to investigate the role of environmental fluctuations in community composition and species diversity. We initiate communities with equal abundances of all species and randomize the temperature fluctuations so that there is no correlation between species responses, only noise. We initiate single populations and allow other species to randomly invade the community. We also knock out extant species one by one from an established community and allow them to reinvade after the remaining species have adjusted. We find that competitors with sufficiently different temperature niches coexist via temporal niche differentiation. We also find long-term persistence of species that are very similar to a dominant competitor. This creates communities with species clumped along a temperature niche axis, with stable coexistence between groups and near neutrality within groups. The near neutrality results in interspecific synchrony within the groups, providing an explanation for the maintenance of high diversity in competitive communities where synchrony is commonly observed.     

Coexistence of two microbial populations competing for a renewable resource in a non-predator-prey system

If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.     

A stochastic model of the distribution of unequal competitors between resource patches

We present a stochastic model of individuals' movements between two patches of resources. The population is made up of two types of individual with differing competitive abilities, and two types of movements occur, with individuals moving either to increase their intake rate or at random. Several previous models have used simulations to evaluate the likely distribution of individuals. We instead derive equations for the equilibrium distribution of the population, which can be solved numerically. This avoids the need to choose an initial distribution for the population, and enables us to obtain the probability with which rare events occur. This may not be possible when simulations are used, since a rare event may not occur at all. We find that when random movements are rare, an increase in the rate of random movements out of a patch can increase the number of individuals on that patch. We consider an approximation to the model with rare random movements, which provides an explanation for this phenomenon.     

Integrating nested spatial scales: implications for the coexistence of competitors on a patchy resource

1. Intraspecific aggregation at a single spatial scale can promote the coexistence of competitors. This paper demonstrates how this same mechanism can be applied to the many systems that are patchy at two scales, with patches nested within 'superpatches'.
2. Data are presented from a field study showing that insects living in rotting fruits have aggregated distributions in the fruits under a single tree, and that the mean density and degree of aggregation varies significantly among trees. Observations in this system motivate the following models.
3. A model of competition has been developed between two species which explicitly represents spatial variation at two scales. By integrating the probability distributions for each scale, the marginal distributions of competitors over all patches can be found and used to calculate coexistence criteria. This model assumes global movement of the competitors.
4. Although spatial variation at a single scale may not be sufficient for coexistence, the total variation over all patches can allow coexistence. Variation in mean densities among superpatches and variation in the degree of aggregation among superpatches both promote coexistence, but act in different ways.
5. A second model of competition between two species is described which incorporates the effects of limited movement among superpatches. Limited movement among superpatches generally promotes coexistence, and also leads to correlations among aggregation and the mean densities of competitors.     

Coexistence of similar species: evidence of a resource and microhabitat sharing in two intertidal hermit crab species

Hydrobiologia - Theory predicts that species can only coexist if they are sufficiently different in their resource and/or microhabitat utilization; if their needs are too similar, the stronger...     

Increasing resource specialization among competitors shifts control of diversity from local to spatial processes

We argue that an increase in the number of specialized consumers can shift the control of ecological dynamics from local to spatial processes. When there are only a few specialized types, local dynamics maintains most types within each patch. As the number of types increases, the probability of local extinction rises. Subsequent colonizations perturb local dynamics, setting off another round of extinctions and the potential for later recolonization. Global processes of colonization and extinction reduce local diversity and increase differentiation among patches. We draw an analogy between the specificity of host-parasite genetics and the specificity of consumer–resource pairs.     

Coexistence of two termite-eating specialists (Araneae)

1. Competition among closely-related specialist predators has rarely been studied, and thus the mechanism of their coexistence remains enigmatic. Interspecific competition among specialised co-occurring predators capturing termites should be high.
2. Here we investigated various niche dimensions, namely temporal, spatial and trophic, of a couple of jumping spider species of the genus Stenaelurillus (Stenaelurillus guttiger and S. modestus) from South Africa, to find whether these two species co-exist and along which niche dimension(s) they differentiate.
3. The two species co-occurred in two out of five study sites. Body size was not significantly different between the species. The phenology was shifted so that one species matured earlier. Circadian activity was not different, as both species were diurnal and active at similar times. Both species preyed almost exclusively on termites. The fundamental trophic niche was very similar and rather narrow. The realised trophic niche at the prey order level of both species was similar, but at the genus level it was different. In S. modestus it was narrower, as it captured mainly Odontotermes, while S. guttiger exploited a few termite species. The size of prey captured was also similar between the two species. The frequency of intraguild predation was negligible.
4. We conclude that both Stenaelurillus species are specialised termitophagous predators. The two species can coexist across broad spatial scales due to spatial segregation on the landscape. At the sites where they co-occur, the two species specialise on different termite prey, promoting local coexistence.

     

Coexistence of competing microbial species in a chemostat where one population feeds on another

In this paper, we consider a model for a chemostat in which two microbial species compete for a single rate-limiting nutrient, while one of the species feeds on another. Under certain simplifying hypotheses, such a chemostat can be described by a system of three nonlinear ordinary differential equations. A theoretical study is conducted to characterize the possible types of solutions. A limit cycle solution was obtained for some parametric values of the system indicating that coexistence of the two species is possible in a significant range of the operating parameters.     

Coexistence and community structure in a consumer resource model with implicit stoichiometry

We combine stoichiometry theory and optimal foraging theory into the MacArthur consumer-resource model. This generates predictions for diet choice, coexistence, and community structure of heterotroph communities. Tradeoffs in consumer resource-garnering traits influence community outcomes. With scarce resources, consumers forage opportunistically for complementary resources and may coexist via tradeoffs in resource encounter rates. In contrast to single currency models, stoichiometry permits multiple equilibria. These alternative stable states occur when tradeoffs in resource encounter rates are stronger than tradeoffs in elemental conversion efficiencies. With abundant resources consumers exhibit partially selective diets for essential resources and may coexist via tradeoffs in elemental conversion efficiencies. These results differ from single currency models, where adaptive diet selection is either opportunistic or selective. Interestingly, communities composed of efficient consumers share many of the same properties as communities based on substitutable resources. However, communities composed of relatively inefficient consumers behave similarly to plant communities as characterized by Tilman’s consumer resource theory. The results of our model indicate that the effects of stoichiometry theory on community ecology are dependent upon both consumer foraging behavior and the nature of resource garnering tradeoffs.     

Coexistence of competitors in spatially and temporally varying environments: A look at the combined effects of different sorts of variability

A stochastic model is developed for competition among organisms living in a patchy and varying environment. The model is designed to be suitable for species with sedentary adults and widely dispersing larvae or propagules, and applies best to marine systems but may also be adequate for some terrestrial systems. Three kinds of environmental variation are incorporated simultaneously in the model. These are pure spatial variation, pure temporal variation, and the space × time interaction. All three kinds of variation can promote coexistence, and when variation is restricted to immigration rates, all three kinds act very similarly. Moreover, for long-lived organisms their action is nearly identical, and their effects, when present together, combine equivalently. For short-lived organisms, however, pure temporal variation is a less effective promoter of coexistence. Variation in death rates acts quite differently from variation in birth rates for it may demote coexistence in some circumstances, while promoting coexistence in other circumstances. Furthermore, pure spatial variation in death rates has quite different effects than other kinds of death-rate variation. In addition to conditions for coexistence, information is given on population fluctuations, convergence to stationary distributions, and asymptotic distributions for long-lived organisms. While the model is presented as an ecological model, a genetical interpretation is also possible. This leads to new suggested mechanisms for the maintenance of polymorphisms in populations.     

Coexistence via resource partitioning fails to generate an increase in community function

Classic ecological theory suggests that resource partitioning facilitates the coexistence of species by reducing inter-specific competition. A byproduct of this process is an increase in overall community function, because a greater spectrum of resources can be used. In contrast, coexistence facilitated by neutral mechanisms is not expected to increase function. We studied coexistence in laboratory microcosms of the bactivorous ciliates Paramecium aurelia and Colpidium striatum to understand the relationship between function and coexistence mechanism. We quantified population and community-level function (biomass and oxygen consumption), competitive interactions, and resource partitioning. The two ciliates partitioned their bacterial resource along a size axis, with the larger ciliate consuming larger bacteria than the smaller ciliate. Despite this, there was no gain in function at the community level for either biomass or oxygen consumption, and competitive effects were symmetrical within and between species. Because other potential coexistence mechanisms can be ruled out, it is likely that inter-specific interference competition diminished the expected gain in function generated by resource partitioning, leading to a system that appeared competitively neutral even when structured by niche partitioning. We also analyzed several previous studies where two species of protists coexisted and found that the two-species communities showed a broad range of biomass levels relative to the single-species states.     

The other ocean acidification problem: CO2 as a resource among competitors for ecosystem dominance

Predictions concerning the consequences of the oceanic uptake of increasing atmospheric carbon dioxide (CO₂) have been primarily occupied with the effects of ocean acidification on calcifying organisms, particularly those critical to the formation of habitats (e.g. coral reefs) or their maintenance (e.g. grazing echinoderms). This focus overlooks direct and indirect effects of CO₂ on non-calcareous taxa that play critical roles in ecosystem shifts (e.g. competitors). We present the model that future atmospheric [CO₂] may act as a resource for mat-forming algae, a diverse and widespread group known to reduce the resilience of kelp forests and coral reefs. We test this hypothesis by combining laboratory and field CO₂ experiments and data from ‘natural’ volcanic CO₂ vents. We show that mats have enhanced productivity in experiments and more expansive covers in situ under projected near-future CO₂ conditions both in temperate and tropical conditions. The benefits of CO₂ are likely to vary among species of producers, potentially leading to shifts in species dominance in a high CO₂ world. We explore how ocean acidification combines with other environmental changes across a number of scales, and raise awareness of CO₂ as a resource whose change in availability could have wide-ranging community consequences beyond its direct effects.     

Coevolution between crossbills and black pine: the importance of competitors,forest area and resource stability

Studies of predator‐prey interactions have found that geographically structured coevolution has played an important role in the adaptive diversification of crossbills (Loxia spp.). We extend those studies by considering common crossbills (L. curvirostra) in the Mediterranean where they rely on seeds in the cones of black pine (Pinus nigra). On the continent, where tree squirrels (Sciurus vulgaris) are present, enhanced defenses against crossbills were most evident in larger areas of pine forest. On islands in the absence of tree squirrels, crossbills and black pine have coevolved in a predator‐prey arms race on Cyprus but not Corsica. In contrast to other conifers that island endemic crossbills rely upon, black pine does not hold seeds in its cones year round. Consequently, key to the strong crossbill–pine interaction on Cyprus is likely the presence of an alternative conifer that provides seeds during early summer when black pine seeds are scarce.     

Competition of two microbial populations for a single resource in a chemostat when one of them exhibits wall attachment

It is known that two microbial populations competing for a single resource in a homogeneous environment with time-invariant inputs cannot coexist in a steady state. The case where two microbial populations compete for a single resource in a chemostat but one of them exhibits attachment to the chemostat walls is studied theoretically. Because of the cells' attachment to the walls, the environment is no longer homogeneous. The present article considers the case where the attached cells form no more than a monolayer. Other situations occur, often frequently, but we do not consider them here. Two models are used to represent the attachment to the walls: the Topiwala-Hamer model and a model which assumes that the attachment of microbial cells to the solid surfaces is a reversible process. The first model does not allow the population that exhibits wall attachment to wash out from the chemostat, in contrast to the second model (which nevertheless reduces to the first one in the limit). It has been found that in most of the possible cases for both models, the two competitors can coexist in a stable steady state for a wide range of the operating parameters space. The results of the stability analysis are discussed and analytical expressions for the conditions and the boundaries of the domains of stable coexistence are given for all the possible situations that may arise.