Body size mediated coexistence of consumers competing for resources in space

Body size is a major phenotypic trait of individuals that commonly differentiates co-occurring species. We analyzed inter-specific competitive interactions between a large consumer and smaller competitors, whose energetics, selection and giving-up behaviour on identical resource patches scaled with individual body size. The aim was to investigate whether pure metabolic constraints on patch behaviour of vagile species can determine coexistence conditions consistent with existing theoretical and experimental evidence. We used an individual-based spatially explicit simulation model at a spatial scale defined by the home range of the large consumer, which was assumed to be parthenogenic and semelparous. Under exploitative conditions, competitive coexistence occurred in a range of body size ratios between 2 and 10. Asymmetrical competition and the mechanism underlying asymmetry, determined by the scaling of energetics and patch behaviour with consumer body size, were the proximate determinant of inter-specific coexistence. The small consumer exploited patches more efficiently, but searched for profitable patches less effectively than the larger competitor. Therefore, body-size related constraints induced niche partitioning, allowing competitive coexistence within a set of conditions where the large consumer maintained control over the small consumer and resource dynamics. The model summarises and extends the existing evidence of species coexistence on a limiting resource, and provides a mechanistic explanation for decoding the size-abundance distribution patterns commonly observed at guild and community levels.     

Dispersal-mediated coexistence of competing predators

Models of metapopulations have often ignored local community dynamics and spatial heterogeneity among patches. However, persistence of a community as a whole depends both on the local interactions and the rates of dispersal between patches. We study a mathematical model of a metacommunity with two consumers exploiting a resource in a habitat of two different patches. They are the exploitative competitors or the competing predators indirectly competing through depletion of the shared resource. We show that they can potentially coexist, even if one species is sufficiently inferior to be driven extinct in both patches in isolation, when these patches are connected through diffusive dispersal. Thus, dispersal can mediate coexistence of competitors, even if both patches are local sinks for one species because of the interactions with the other species. The spatial asynchrony and the competition-colonization trade-off are usual mechanisms to facilitate regional coexistence. However, in our case, two consumers can coexist either in synchronous oscillation between patches or in equilibrium. The higher dispersal rate of the superior prompts rather than suppresses the inferior. Since differences in the carrying capacity between two patches generate flows from the more productive patch to the less productive, loss of the superior by emigration relaxes competition in the former, and depletion of the resource by subsidized consumers decouples the local community in the latter.     

The invasion and coexistence of competing Wolbachia strains

Cytoplasmic incompatibility between arthropods infected with different strains of Wolbachia has been proposed as an important mechanism for speciation. However, a basic requirement for this mechanism is the coexistence of different strains in neighbouring populations. Here we test whether this required coexistence is possible in a spatial context. Continuous-time models for the behaviour of one and two strains of Wolbachia within a single well-mixed population demonstrate the Allee effect and founder control, such that one strain is always driven extinct. In contrast, discretised spatial models show patchy persistence of the two strains although coexistence within the same habitat is rare. A simplified model of such founder control suggests that it is fragmentation of (or barriers within) the habitat rather than space itself that leads to persistence.     

Herbivore-induced coexistence of competing plant species

We study a series of spatially implicit lottery models in which two competing plant species, with and without defensive traits, are grazed by a herbivore in a homogeneous habitat. One species (palatable) has no defensive traits, while the other (defended) has defensive traits but suffers reduced reproduction as the result of an assumed trade-off. Not surprisingly, coexistence of these plants cannot occur when the herbivore density is very low (the palatable plant always wins) or very high (the defended plant wins). At intermediate densities, however, herbivory can mediate plant coexistence, even in a homogeneous environment. If the herbivore eats several plants per bite, and its forage-selection depends on the average palatability of the plants it eats, then palatable species in the immediate neighbourhood of defended plants may be more likely to persist (associational resistance) even at higher grazing pressure. If the herbivore shows a positive numerical response to the average palatability of the habitat as a whole, then both plant populations are stabilized and coexistence is promoted, because both species obtain a minority advantage through the negative feedback caused by herbivory. If the herbivore exhibits both of these traits, the system may have at most two non-trivial equilibria, one of which is stable and the other unstable. This means that coexistence in such a system is vulnerable to large fluctuations in herbivore density and identity, and this has implications for conservation in systems where large herbivores are managed to promote plant diversity.     

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.     

Dissecting the role of transitivity and intransitivity on coexistence in competing species networks

It is well established that intransitively assembled interaction networks can support the coexistence of competing species, while transitively assembled (hierarchical) networks are prone to species loss through competitive exclusion. However, as the number of species grows, the complexity of ecological interaction networks grows disproportionately, and species can get involved simultaneously in transitive and intransitive groups of interactions. In such complex networks, the effects of intransitivity on species persistence are not straightforward. Dissecting networks into intransitive/transitive components can help us to understand the complex role that intransitivity may play in supporting species diversity. We show through simulations that those species participating in the largest group of intransitive interactions (the core of the network) have high probabilities of persisting in the long term. However, participation in a group of intransitive interactions other than the core does not always improve persistence. Likewise, participating in transitive interactions does not always decrease persistence because certain species (the satellites) transitively linked to the core have also a high persistence probability. Therefore, when networks contain transitive and intransitive structures, as it can be expected in real ecological networks, the existence of a large intransitive core of species can have a disproportionate positive effect on species richness.     

Variability in resource consumption rates and the coexistence of competing species

A model which incorporates random temporal variation in resource consumption rates is used to investigate the effects that such variation has on the coexistence of competitors. The analysis of the model and several extensions of it suggests that such variation in consumption rates will often allow two or more competitors to coexist while limited by the same resource. For variability to promote coexistence, it is necessary that the time scale of resource population dynamics be fast relative to the time scale of environmental change. Variability is especially likely to promote coexistence if there is a large variance in consumption rates, negative correlation between the consumption rates of different species, and a linear or concave relationship between resource consumption and per capita population growth. Many previous studies which have found coexistence of two or more species on one resource can be interpreted as examples of coexistence due to varying resource consumption rates.     

Epitope down-modulation as a mechanism for the coexistence of competing T-cells

Efficient immune responses against pathogens are frequently characterized by the simultaneous targeting of multiple epitopes. However, it remains unclear how the targeting of multiple epitopes is maintained in the face of competition for antigenic stimulation. Here, we investigate this question by using mathematical models of the population dynamics of a viral pathogen, antigen presentation sites and T-cells. We first show that direct competition for access to antigen presenting sites and indirect competition through killing of the pathogen select for dominance of the T-cell response with the highest affinity for its epitope. We then incorporate in our model that epitopes can become down-modulated following interaction with epitope specific T-cells. We demonstrate that epitope down-modulation leads to differentiation of epitope presentation on antigen presenting sites. This differentiation promotes the coexistence of multiple epitope specific responses. Hence, we propose that the functional relevance of epitope down-modulation may be to enable the persistence of a broad immune response despite competition for antigenic stimulation.     

Spatial patterns of coexistence of competing species in patchy habitat

The single-species spatially realistic patch occupancy metapopulation model is, in this study, extended to a metacommunity of many competing species. Competition is assumed to reduce the local carrying capacity (effective patch area), which in turn increases local extinction rates and reduces colonization rates because of smaller population sizes. Each species is described by three parameters: pre-competitive abundance (equilibrium incidence of patch occupancy, which reflects the rate of colonization in relation to extinction rate), the spatial range of migration, and competitive ability. The model ignores spatio–temporal correlations caused by interspecific interactions, because in metacommunities of unequal competitors inhabiting heterogeneous landscapes, correlations in the occurrence of species are driven more by patch heterogeneity than by competition. The model allows the calculation of multispecies equilibria in patchy habitats without simulations. In general, the number of coexisting species in the metacommunity increases with decreasing strength of competition, increasing rate of colonization, and decreasing range of migration. Habitat heterogeneity in the form of spatial variation in patch areas tends to facilitate coexistence. Poor competitors may coexist with superior competitors in the patch network if the former have higher colonization rates (competition–colonization trade-off). When migration distances are short, competition leads to spatial pattern formation: Species tend to have restricted spatial distributions in the network, but contrary to intuitive expectations, often the distributions of many species are nested. Having more dispersive species enhances both local and global diversity, whereas more local migration decreases local but increases global diversity.     

Desiccation and thermal tolerance of eggs and the coexistence of competing mosquitoes

We tested the hypothesis that differences in temperature and desiccation tolerances of eggs of the container-dwelling mosquitoes Aedes albopictus and Aedes aegypti influence whether invading A. albopictus coexist with or exclude A. aegypti in Florida. In the laboratory, egg mortality through 30 days for A. albopictus was strongly temperature and humidity dependent, with low humidity and high temperature producing greatest mortality. In contrast, mortality through 30 days and through 60 days for A. aegypti was very low and independent of temperature and humidity. Mortality through 90 days for A. aegypti showed significant effects of both temperature and humidity. In the field, the proportion of vases occupied by A. albopictus was significantly lower at four of six sites at the start of the wet season (after a dry period) versus well into the wet season (after containers had held water for weeks). The proportion of vases occupied by A. aegypti was independent of when during the wet season vases were sampled. These results imply that dry periods cause disproportionately greater mortality of A. albopictus eggs compared to A. aegypti eggs. Container occupancy at tire and cemetery sites was significantly related to two principal components derived from long-term average climate data. Occupancy of containers by A. albopictus was greatest at cool sites with little or no dry season, and decreased significantly with increasing mean temperature and increasing number of dry months. In contrast, occupancy of containers by A. aegypti was lowest at cool sites with little or no dry season, and increased significantly with increasing mean temperature and increasing dry season length, and decreased significantly with total precipitation and number of wet months. We suggest that local coexistence of these species is possible because warm, dry climates favor A. aegypti and alleviate effects of competition from A. albopictus via differential mortality of A. albopictus eggs.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Temperature fluctuation facilitates coexistence of competing species in experimental microbial communities

1. Temperature fluctuation is a general phenomenon affecting many, if not all, species in nature. While a few studies have shown that temperature fluctuation can promote species coexistence, little is known about the effects of different regimes of temperature fluctuation on coexistence. 2. We experimentally investigated how temperature fluctuation and different regimes of temperature fluctuation ('red' environments in which temperature series exhibited positive temporal autocorrelation vs. 'white' environments in which temperature series showed little autocorrelation) affected the coexistence of two ciliated protists, Colpidium striatum Stein and Paramecium tetraurelia Sonneborn, which competed for bacterial resources. 3. We have previously shown that the two species differed in their growth responses to changes in temperature and in their resource utilization patterns. The two species were not always able to coexist at constant temperatures (22, 24, 26, 28 and 30 degrees C), with Paramecium being competitively excluded at 26 and 28 degrees C. This indicated that resource partitioning was insufficient to maintain coexistence at these temperatures. 4. Here we show that in both red and white environments in which temperature varied between 22 and 32 degrees C, Paramecium coexisted with Colpidium. Consistent with the differential effects of temperature on their intrinsic growth rates, Paramecium population dynamics were largely unaffected by temperature regimes, and Colpidium showed more variable population dynamics in the red environments. 5. Temperature-dependent competitive effects of Colpidium on Paramecium, together with resource partitioning, appeared to be responsible for the coexistence in the white environments; resource partitioning and the storage effect appeared to account for the coexistence in the red environments. 6. These results suggest that temperature fluctuation may play important roles in regulating species coexistence and diversity in ecological communities.     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Limited diffusive fluxes of substrate facilitate coexistence of two competing bacterial strains

Soils are known to support a great bacterial diversity down to the millimeter scale, but the mechanisms by which such a large diversity is sustained are largely unknown. A feature of unsaturated soils is that water usually forms thin, poorly-connected films, which limit solute diffusive fluxes. It has been proposed, but never unambiguously experimentally tested, that a low substrate diffusive flux would impact bacterial diversity, by promoting the coexistence between slow-growing bacteria and their potentially faster-growing competitors. We used a simple experimental system, based on a Petri dish and a perforated Teflon membrane to control diffusive fluxes of substrate (benzoate) whilst permitting direct observation of bacterial colonies. The system was inoculated with prescribed strains of Pseudomonas, whose growth was quantified by microscopic monitoring of the fluorescent proteins they produced. We observed that substrate diffusion limitation reduced the growth rate of the otherwise fast-growing Pseudomonas putida KT2440 strain. This strain out-competed Pseudomonas fluorescens F113 in liquid culture, but its competitive advantage was less marked on solid media, and even disappeared under conditions of low substrate diffusion. Low diffusive fluxes of substrate, characteristic of many unsaturated media (e.g. soils, food products), can thus promote bacterial coexistence in a competitive situation between two strains. This mechanism might therefore contribute to maintaining the noncompetitive diversity pattern observed in unsaturated soils.     

Periodic coexistence in the chemostat with three species competing for three essential resources

A chemostat model of three species of microorganisms competing for three essential, growth-limiting nutrients is considered. J. Husiman and F.J. Weissing [Nature 402 (1999) 407] show numerically that this model can generate periodic oscillations. The present contribution is concerned with rigorous analysis regarding the existence of periodic oscillations in this model. Our analysis is based on the following observation made by Huisman and Weissing: there is a cyclic replacement of species, if each species becomes limited by the resource for which it is the intermediate competitor. Using a permanence theory, an index theory, and a Poincaré-Bendixson theory for three-dimensional competitive systems, we analytically succeed to give sufficient conditions for the existence of periodic orbits in the limit sets in this model. The results in this paper suggest that with a wide range of parameter values, sustained periodic oscillations of species abundances for the model are possible, without involving external disturbances. Our results also suggest that competition is not necessarily destructive, i.e., in the case of existence of sustained periodic oscillations, if one of three competitors is absent, one of the other two rivals cannot survive.     

The impact of density-independent mortality on species coexistence: an experimental test with zooplankton

Mortality (e.g. predation, disturbance) is often thought to lower the intensity of interspecific competition and thereby promote the coexistence of competing species. However, surprisingly few tests of this idea exist, especially for metazoans feeding on a self-renewing resource. Here we examined the effect of density-independent mortality on the coexistence of four species of pond zooplankton (microcrustacean grazers) in a series of laboratory microcosms. Across the experimental mortality gradient, consumer biomass decreased and resource abundance increased with an increase in mortality. Thus, the treatments resulted in an increase in resource availability per consumer (one measure of reduced competitive intensity). There was no significant effect of mortality treatment on species relative abundances or species evenness, and the zooplankter Diaphanosoma dominated community biomass at all mortality levels. Mortality rate did have a marginally significant effect on species richness (p<0.07), but richness did not increase monotonically with mortality level. Instead, richness tended to be highest in the low- and no-mortality treatments.     

Dynamics and responses to mortality rates of competing predators undergoing predator-prey cycles

Two or more competing predators can coexist using a single homogeneous prey species if the system containing all three undergoes internally generated fluctuations in density. However, the dynamics of species that coexist via this mechanism have not been extensively explored. Here, we examine both the nature of the dynamics and the responses of the mean densities of each predator to mortality imposed upon it or its competitor. The analysis of dynamics uncovers several previously undescribed behaviors for this model, including chaotic fluctuations, and long-term transients that differ significantly from the ultimate patterns of fluctuations. The limiting dynamics of the system can be loosely classified as synchronous cycles, asynchronous cycles, and chaotic dynamics. Synchronous cycles are simple limit cycles with highly positively correlated densities of the two predator species. Asynchronous cycles are limit cycles, frequently of complex form, including a significant period during which prey density is nearly constant while one predator gradually, monotonically replaces the other. Chaotic dynamics are aperiodic and generally have intermediate correlations between predator densities. Continuous changes in density-independent mortality rates often lead to abrupt transitions in mean population sizes, and increases in the mortality rate of one predator may decrease the population size of the competing predator. Similarly, increases in the immigration rate of one predator may decrease its own density and increase the density of the other predator. Proportional changes in one predator's birth and death rate functions can have significant effects on the dynamics and mean densities of both predator species. All of these responses to environmental change differ from those observed when competitors coexist stably as the result of resource (prey) partitioning. The patterns described here occur in many other competition models in which there are cycles and differences in the linearity of the responses of consumers to their resources.     

Pattern recognition in neural networks with competing dynamics: coexistence of fixed-point and cyclic attractors

We study the properties of the dynamical phase transition occurring in neural network models in which a competition between associative memory and sequential pattern recognition exists. This competition occurs through a weighted mixture of the symmetric and asymmetric parts of the synaptic matrix. Through a generating functional formalism, we determine the structure of the parameter space at non-zero temperature and near saturation (i.e., when the number of stored patterns scales with the size of the network), identifying the regions of high and weak pattern correlations, the spin-glass solutions, and the order-disorder transition between these regions. This analysis reveals that, when associative memory is dominant, smooth transitions appear between high correlated regions and spurious states. In contrast when sequential pattern recognition is stronger than associative memory, the transitions are always discontinuous. Additionally, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of the same set of patterns, there is a discontinuous transition between associative memory and sequential pattern recognition. In contrast, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of independent sets of patterns, the network is able to perform both associative memory and sequential pattern recognition for a wide range of parameter values.