A new hypothesis to explain the coexistence of n species in the presence of a single resource

This paper presents a hypothesis allowing us to explain the coexistence of several species (here micro-organisms) in competition on a single resource (called a substrate) in a chemostat. We introduce a new class of kinetics that does not only depend on the substrate concentration in the medium, but also on the biomass concentration. From the study of elementary interactions (i) between micro-organisms, (ii) between micro-organisms and their environment in which they grow and from simulations, we show that this modelling approach can be interpreted in terms of substrate diffusion phenomena. A rigorous study of this new class of models allows us to hypothesize that abiotic parameters can explain the fact that an arbitrarily large number of species can coexist in the presence of a unique substrate.     

Coexistence introducing regulation of environmental conditions

Interactions between environmental conditions and environment-affecting species have not been investigated extensively. In this study, the population dynamics of species yielding regulative feedback between temperature (a representative of environmental condition) and species with a temperature-altering trait was examined. We considered a simple closed model that described the population of two species (at least one of them had a temperature-altering trait) competing for one resource. The long-term outcomes of the competition and changes of temperature were explored against increasing background temperature. As a result of simulations, the regulation of temperature was accompanied by the coexistence of two species, which was contrary to the 'Gause's exclusion principle'. The steady-state analysis showed that (i) the temperature-altering trait allowed species to coexist and (ii) the coexistence of species with the trait could introduce the regulation of temperature. A 'trade-off' in their ability to utilize a resource plays a key role in this coexistence and homeostasis of temperature. This may imply that actual environmental conditions can be automatically stabilized by resource competition among species in natural ecosystems.     

Changes in Individual Allometry Can Lead to Species Coexistence without Niche Separation

The principle of competitive exclusion is a fundamental tenet of ecology. Commonly used competition models predict that at most only one species per limiting resource can coexist in the same environment at steady state; hence, the upper limit to species diversity depends only on the number of limiting resources and not on the rates of resource supply. We demonstrate that such model behavior is the result of both the growth and biomass turnover functions being proportional to the population biomass. We argue that at least the growth function should be a nonlinear, concave downward function of biomass. This form for the growth function should arise simply because of changes in the allometry of individuals in the population. With this change in model structure, we show that any number of species can coexist at an asymptotically stable steady state, even where there is only one limiting resource. Furthermore, if growth increases nonlinearly with biomass, the steady-state resource concentration and hence the potential for biodiversity increases as the resource supply rate increases. Received 31 August 2001; accepted 10 April 2002.     

Interspecific Resource Competition Effects on Fisheries Revenue

In many fisheries multiple species are simultaneously caught while stock assessments and fishing quota are defined at species level. Yet species caught together often share habitat and resources, resulting in interspecific resource competition. The consequences of resource competition on population dynamics and revenue of simultaneously harvested species has received little attention due to the historical single stock approach in fisheries management. Here we present the results of a modelling study on the interaction between resource competition of sole (Solea solea) and slaice (Pleuronectus platessa) and simultaneous harvesting of these species, using a stage-structured population model. Three resources were included of which one is shared with a varied competition intensity. We find that plaice is the better competitor of the two species and adult plaice are more abundant than adult sole. When competition is high sole population biomass increases with increasing fishing effort prior to plaice extinction. As a result of this increase in the sole population, the revenue of the stocks combined as function of effort becomes bimodal with increasing resource competition. When considering a single stock quota for sole, its recovery with increasing effort may result in even more fishing effort that would drive the plaice population to extinction. When sole and plaice compete for resources the highest revenue is obtained at effort levels at which plaice is extinct. Ignoring resource competition promotes overfishing due to increasing stock of one species prior to extinction of the other species. Consequently, efforts to mitigate the decline in one species will not be effective if increased stock in the other species leads to increased quota. If a species is to be protected against extinction, management should not only be directed at this one species, but all species that compete with it for resource as well.     

Untangling the mechanisms of cryptic species coexistence in a nematode community through individual-based modelling

Cryptic species are morphologically identical but genetically distinct, and are prominent across numerous phyla. The coexistence of such closely related species on local scales would seem to run counter to traditional coexistence and competition theory; it has been hypothesized as a consequence of differences in their resource use or tolerances to environmental conditions. We developed an individual-based model of a community of three cryptic Litoditis marina (nematode) species, to understand how individual-level interspecific and intraspecific interactions might explain the coexistence of these closely related species. The model incorporates individuals' reproduction, competition, dispersal and resource use. Data characterizing the cryptic species (growth rates, dispersal ability, competitive interactions and responses to changing environmental conditions) were obtained from laboratory experiments involving both mono- and multispecific nematode cultures, and are used to parameterize the model. Simulation studies are used to investigate which individual-level mechanisms of dispersal and interaction lead to the characteristic population-level patterns observed experimentally. Our results highlight the key role of intraspecific competition in mediating dispersal and therefore co-occurrence of the cryptic species. The differences in dispersal also influence the response of the cryptic species to competition, a combination of factors that provides an explanation for their co-occurrence. These results provide insights into how changes in individual-level processes can be amplified to affect population-level co-occurrence.     

Species coexistence under resource competition with intraspecific and interspecific direct competition in a chemostat

Competition theory has developed separately for direct competition and for exploitative competition. However, the combined effects of the two types of competition on species coexistence remain unclear. To examine how intraspecific and interspecific direct competition contributes to the coexistence of species competing for a single resource, we constructed a chemostat-type resource competition model. With general functions for intraspecific and interspecific direct competition, we derived necessary and sufficient conditions (except for a critical case that rarely occurs in a biological sense) that determine the number of stably coexisting species. From these conditions, we found that the number of coexisting species is determined just by the invasibility of each species into subcommunities with a smaller number of species. In addition, using a combination of rigorous mathematical theory and a simple graphical method, we can demonstrate how the stronger intraspecific direct competition facilitates species invasion, leading to a larger number of coexisting species.     

Interference competition and species coexistence

Interference competition is ubiquitous in nature. Yet its effects on resource exploitation remain largely unexplored for species that compete for dynamic resources. Here, I present a model of exploitative and interference competition with explicit resource dynamics. The model incorporates both biotic and abiotic resources. It considers interference competition both in the classical sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, and interference on, the other species) and in the broad sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, but can experience an increase in growth rate via interference on, the other species). Coexistence cannot occur under classical interference competition even when the species inferior at resource exploitation is superior at interference. Such a trade-off can, however, change the mechanism of competitive exclusion from dominance by the superior resource exploiter to a priority effect. Now the inferior resource exploiter can exclude the superior resource exploiter provided it has a higher initial abundance. By contrast, when interference is beneficial to the interacting species, coexistence is possible via a trade-off between exploitation and interference. These results hold regardless of whether the resource is biotic or abiotic, indicating that the outcome of exploitative and interference competition does not depend on the exact nature of resource dynamics. The model makes two key predictions. First, species that engage in costly interference mechanisms (e.g. territoriality, overgrowth or undercutting, allelopathy and other forms of chemical competition) should not be able to coexist unless they also engage in beneficial interference mechanisms (e.g. predation or parasitism). Second, exotic invasive species that displace native biota should be superior resource exploiters that have strong interference effects on native species with little or negative cost. The first prediction provides a potential explanation for patterns observed in several natural systems, including plants, aquatic invertebrates and insects. The second prediction is supported by data on invasive plants and vertebrates.     

Facilitation versus competition in grazing herbivore assemblages

The importance of facilitation versus competition in structuring herbivore species assemblages is a critical issue in theoretical ecology as well as for practical wildlife management. This paper examines the evidence for facilitation and clarifies our understanding in relation to the mechanisms and the spatial and temporal scales where they occur. Evidence for facilitation through stimulation of grass regrowth during the growing season appears stronger than that for increased resource access through removal of obstructing grass structures during the dormant season. Although facilitation may benefit the nutritional gains obtained by certain species in the short term, these benefits do not appear to be translated into the expected population consequences. We suggest this could be due to seasonal tradeoffs between facilitation and competition, as well as to restrictions on the spatial extent of trophic overlap.     

Biodiversity,habitat area,resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.     

Alternatives to Lotka-Volterra competition: Models of intermediate complexity

A family of one-level differential-equation competition models in which two populations are limited by the energy flowing into the system generates the following results. For competitors on the same and only resource: 1) Purely exploitative competition leads to exclusion; which species wins depends on relative abilities to appropriate and extract energy from the resource, and the relative death and maintenance rates. 2) If conspecific interference (e.g., deaths or energy loss from fighting, cannibalism, or display) is sufficiently high relative to abilities to exploit the common resource, competition for the same resource can lead to coexistence. 3) If heterospecific interference is sufficiently high relative to abilities to exploit the common resource, competition for the same resource can lead to a priority effect, in which the outcome depends on initial population sizes. 4) Depending on whether situation (2) or (3) prevails, an increase in the amount of the common resource can convert an outcome in which one species always wins into one giving coexistence (2) or a priority effect (3). 5) If species are similar to one another in their abilities to appropriate and extract energy from the common resource and show reciprocity in intererence costs, competition can have multiple outcomes; either one species wins or the species coexist, depending on initial values.For competition on the same resource, but with each species monopolizing an exclusive resource as well: 1) Purely exploitative competition always leads to a unique point coexistence. 2) If interference is added to the system described in (1), two points of coexistence, separated by a saddle (an “unstable equilibrium”) are possible. This is favored by a) a small yield from the exclusive resources relative to the common one; and b) strong interspecific relative to intraspecific interference.     

Direct competition results from strong competition for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka–Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur in, Theor Popul Biol 1:1–11, 1970). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional.     

The nutrient-load hypothesis: patterns of resource limitation and community structure driven by competition for nutrients and light

Resource competition theory predicts that the outcome of competition for two nutrients depends on the ratio at which these nutrients are supplied. Yet there is considerable debate whether nutrient ratios or absolute nutrient loads determine the species composition of phytoplankton and plant communities. Here we extend the classical resource competition model for two nutrients by including light as additional resource. Our results suggest the nutrient-load hypothesis, which predicts that nutrient ratios determine the species composition in oligotrophic environments, whereas nutrient loads are decisive in eutrophic environments. The underlying mechanism is that nutrient enrichment shifts the species interactions from competition for nutrients to competition for light, which favors the dominance of superior light competitors overshadowing all other species. Intermediate nutrient loads can generate high biodiversity through a fine-grained patchwork of two-species and three-species coexistence equilibria. Depending on the species traits, however, competition for nutrients and light may also produce multiple alternative stable states, suppressing the predictability of the species composition. The nutrient-load hypothesis offers a solution for several discrepancies between classical resource competition theory and field observations, explains why eutrophication often leads to diversity loss, and provides a simple conceptual framework for patterns of biodiversity and community structure observed in nature.     

病原体感染对物种间资源竞争的影响——基于资源竞争理论

病原体感染对种间竞争的影响可能是因为改变了宿主的资源利用过程,然而竞争模型（Lotka-Volterra）由于参数化竞争系数而忽略了资源的动态变化过程,因此基于此类模型的研究无法揭示病原体对宿主资源利用的影响。基于Tilman的资源竞争理论构建了病原体感染一个物种的资源竞争模型,通过分析宿主物种资源利用效率的变化探讨了病原体对种间竞争的影响。结果表明：（1）病原体降低了宿主对资源的消耗率（消费矢量变短）,抬高了对资源的最低需求（零等倾线上移）,这意味着宿主的竞争力减弱;（2）虽然感染影响了竞争物种的密度,但不会改变共存物种的共存状态;（3）病原体可以使宿主物种的竞争对手更容易入侵,形成共存局面,极大地扩大了竞争物种共存的参数范围,本质上促进了物种多样性维持;（4）病原体的传播率和毒性也复杂地影响了竞争物种共存,传播率越大越能促进物种共存,而中等强度毒性最能促进物种共存。研究结果明确了病原体对物种资源利用模式的潜在改变,强调了病原体在物种共存和生物多样性维持中的重要性。     

Ingredients for protist coexistence: competition, endosymbiosis and a pinch of biochemical interactions

1. The interaction between mutualism, facilitation or interference and exploitation competition is of major interest as it may govern species coexistence. However, the interplay of these mechanisms has received little attention. This issue dates back to Gause, who experimentally explored competition using protists as a model [Gause, G.F. (1935) Vérifications expérimentales de la théorie mathématique de la lutte pour la vie. Actualités Scientifiques et Industrielles, 277]. He showed the coexistence of Paramecium caudatum with a potentially allelopathic species, Paramecium bursaria. 2. Paramecium bursaria hosts the green algae Chlorella vulgaris. Therefore, P. bursaria may benefit from carbohydrates synthesised by the algae. Studying endosymbiosis with P. bursaria is possible as it can be freed of its endosymbiont. In addition, C. vulgaris is known to produce allelochemicals, and P. bursaria may benefit also from allelopathic compounds. 3. We designed an experiment to separate the effects of resource exploitation, endosymbiosis and allelopathy and to assess their relative importance for the coexistence of P. bursaria with a competitor that exploits the same resource, bacteria. The experiment was repeated with two competitors, Colpidium striatum or Tetrahymena pyriformis. 4. Results show that the presence of the endosymbiont enables the coexistence of competitors, while its loss leads to competitive exclusion. These results are in agreement with predictions based on resource equilibrium density of monocultures (R*) supporting the idea that P. bursaria's endosymbiont is a resource provider for its host. When P. bursaria and T. pyriformis coexist, the density of the latter shows large variation that match the effects of culture medium of P. bursaria. Our experiment suggests these effects are because of biochemicals produced in P. bursaria culture. 5. Our results expose the hidden diversity of mechanisms that underlie competitive interactions. They thus support Gauses's speculation (1935) that allelopathic effects might have been involved in his competition experiments. We discuss how a species engaged both in competition for a resource and in costly interference such as allelopathy may counterbalance these costs with a resource-provider endosymbiont.     

Advantages and disadvantages of interference‐competitive ability and resource‐use efficiency when invading established communities

Invaders into established communities must overcome low resource availability. To establish, invaders must either appropriate resources from existing individuals through interference competition or efficiently use the small amount of resource that remains. Although both strategies may be important, they are rarely considered together and, in particular, resource‐use efficiency is often ignored in systems dominated by interference competition. To identify the traits that confer invasion success, we experimentally invaded resource patches in established communities with multiple species from two functional groups that differ in interference competitive ability and resource‐use efficiency. In contrast to previous assessments, we show that resource‐use efficiency can facilitate invasion in systems dominated by interference competition. Furthermore, large resource requirements can be a liability when establishing because interference competition is inherently costly and so cannot fully compensate for limitations in the primary resource. However, we also show that there is a tradeoff in performance among functional groups between small and large resource gaps. Our results suggest we modify the way we view and manage species invasion in systems dominated by interference competition.     

Density-dependent habitat selection: evaluating isoleg theory with a Lotka-Volterra model

Contemporary models of density-dependent habitat selection generally focus on long-term evolutionary consequences of intraspecific or interspecific competition and/or patterns of resource use in patchy environments. A primary goal of such studies often is to elucidate evolutionary stable strategies based on steady-state dynamics of population growth. In contrast, we developed a simulation model to explore short-term movements of interspecific competitors among fine-grained habitats of differing attributes, as might result from field manipulations of habitat quality or population densities. In this model, habitat quality is expressed in terms of mean individual fitness, represented by average per capita growth rate calculated according to the Lotka-Volterra equations describing interspecific competition. This model provides a mechanism for quantifying the effects of habitat quality, patterns of resource use and competition on distributions of individuals. Results demonstrate the heuristic value of this model in corroborating predictions derived from the ideal free distribution and isodar theory, and in generating isolegs to test the predictions of isoleg theory. Results indicate that small changes in model parameters have substantial impacts on patterns of habitat use and co-occurrence between species. The model identifies a variety of conditions under which isolegs for a given type of community organization deviate from predictions of contemporary isoleg theory, potentially expanding the universe of possible interspecific behaviors underlying the development of evolutionary stable strategies.     

An Experimental Approach to the Effects of Predictability on Community Structure

This paper considers the effects of different levels of resourcepredictability on niche widths, competition and diversity ina community of three hummingbird species. Three pairs of hypothesesare tested: whether decreasing predictability (a) increasesor decreases niche width, (b) increases or decreases competitionand (c) increases or decreases diversity. The results show thatcomplementary increases and decreases in niche width occur withdecreasing predictability, while competition and diversity decrease,at least with extreme unpredictability. A model, which assumesthe species to have similar resource preferences, and its predictionsare examined. The dominant species, Lampornis clemenciae, excludes a subordinatespecies, Archilochus alexandri, from preferred resources. Thisdefense becomes unprofitable with decreasing predictabilityand Archilochus invades the resources once vigorously defendedby Lampornis. When the spectrum of resources is altered in thedirection of decreasing suitability for both species, Lampornisbecomes even more specialized and sensitive to the effects ofunpredictability. A third species, Eugenes fulgens, steals resourcesundefended by Lampornis. These characteristics seem to be commonto a number of communities in very different taxonomic groups,and characteristic of communities in which species share a commonpreferred resource. The question of how a community organizedwith distinct resource preferences responds to decreasing predictabilityremains open.     

Evolution of species trait through resource competition

To understand the evolution of diverse species, theoretical studies using a Lotka–Volterra type direct competition model had shown that concentrated distributions of species in continuous trait space often occurs. However, a more mechanistic approach is preferred because the competitive interaction of species usually occurs not directly but through competition for resource. We consider a chemostat-type model where species consume resource that are constantly supplied. Continuous traits in both consumer species and resource are incorporated. Consumers utilize resource whose trait values are similar with their own. We show that, even when resource-supply has a continuous distribution in trait space, a positive continuous distribution of consumer trait is impossible. Self-organized generation of distinct species occurs. We also prove global convergence to the evolutionarily stable distribution.     

Timing of resource input and larval competition between invasive and native container-inhabiting mosquitoes (Diptera: Culicidae).

Container-inhabiting mosquito species are subject to both intraspecific and interspecific competition during larval development in resource-limited habitats. The arrival of an invasive species, Aedes albopictus, in the U.S. has altered competitive interactions among container-inhabiting mosquito species and, in some cases, has led to displacement of these species. Resource enrichment of container habitats has been shown to alleviate competitive interactions and to promote species co-existence; however, the importance of the timing of enrichment has yet to be explored. Larval competition between Ae. albopictus and a native species, Ochlerotatus triseriatus, was explored when resources were added either gradually or in a single pulse. Replacement series experiments revealed that Ae. albopictus was able to outcompete and displace Oc. triseriatus via resource monopolization when all resources were made available simultaneously; however, when the same resource amount was added over time, survival was high for both species, leading to co-existence. Timing of resource input also had an effect in monospecific treatments, indicating that intraspecific competition impacts survival as well. Duration of larval development was influenced by both species presence and by timing of resource input for Oc. triseriatus. These results indicate competitive outcome is condition-specific and that timing of resource input can determine whether a dominant invasive competitor displaces a native species, or if the two species are able to co-exist. Both intraspecific and interspecific competition occur at different temporal scales due to species-specific differences in larval developmental time. Timing of resource availability in container habitats can impact mosquito survival via competitive interactions, which can ultimately influence vector population size and behavior, possibly influencing vector-borne disease transmission.     

Species coexistence in resource-limited patterned ecosystems is facilitated by the interplay of spatial self-organisation and intraspecific competition

The exploration of mechanisms that enable species coexistence under competition for a sole limiting resource is widespread across ecology. Two examples of such facilitative processes are intraspecific competition and spatial self-organisation. These processes determine the outcome of competitive dynamics in many resource-limited patterned ecosystems, classical examples of which include dryland vegetation patterns, intertidal mussel beds and subalpine ribbon forests. Previous theoretical investigations have explained coexistence within patterned ecosystems by making strong assumptions on the differences between species (e.g. contrasting dispersal behaviours or different functional responses to resource availability). In this paper, I show that the interplay between the detrimental effects of intraspecific competition and the facilitative nature of self-organisation forms a coexistence mechanism that does not rely on species-specific assumptions and captures coexistence across a wide range of the environmental stress gradient. I use a theoretical model that captures the interactions of two generic consumer species with an explicitly modelled resource to show that coexistence relies on a balance between species' colonisation abilities and their local competitiveness, provided intraspecific competition is sufficiently strong. Crucially, the requirements on species' self-limitation for coexistence to occur differ on opposite ends of the resource input spectrum. For low resource levels, coexistence is facilitated by strong intraspecific dynamics of the species superior in its colonisation abilities, but for larger volumes of resource input, strong intraspecific competition of the locally superior species enables coexistence. Results presented in this paper also highlight the importance of hysteresis in understanding tipping points, in particular extinction events. Finally, the theoretical framework provides insights into spatial species distributions within single patches, supporting verbal hypotheses on coexistence of herbaceous and woody species in dryland vegetation patterns and suggesting potential empirical tests in the context of other patterned ecosystems.