Ultraweak signals can cause synaptic depression and adaptation

Synaptic depression at conventional synapses is usually caused by strong or prolonged stimuli, like tetanic bursts of afferent fiber discharge at high frequencies. In this issue of Neuron, Dunn and Rieke report that, in the retina, even the weakest stimuli, single photons, can lead to synaptic depression at ribbon-type synapses and adaptation of neuronal output to ambient light levels.     

A competitive coexistence principle?

Competitive exclusion – n species cannot coexist on fewer than n limiting resources in a constant and isolated environment – has been a central ecological principle for the past century. Since empirical studies cannot universally demonstrate exclusion, this principle has mainly relied on mathematical proofs. Here we investigate the predictions of a new approach to derive functional responses in consumer/resource systems. Models usually describe the temporal dynamics of consumer/resource systems at a macroscopic level – i.e. at the population level. Each model may be pictured as one time-dependent macroscopic trajectory. Each macroscopic trajectory is, however, the product of many individual fates and from combinatorial considerations can be realized in many different ways at the microscopic – or individual – level. Recently it has been shown that, in systems with large enough numbers of consumer individuals and resource items, one macroscopic trajectory can be realized in many more ways than any other at the individual – or microscopic – level. Therefore, if the temporal dynamics of an ecosystem are assumed to be the outcome of only statistical mechanics – that is, chance – a single trajectory is near-certain and can be described by deterministic equations. We argue that these equations can serve as a null to model consumer-resource dynamics, and show that any number of species can coexist on a single resource in a constant, isolated environment. Competition may result in relative rarity, which may entail exclusion in finite samples of discrete individuals, but exclusion is not systematic. Beyond the coexistence/exclusion outcome, our model also predicts that the relative abundance of any two species depends simply on the ratio of their competitive abilities as computed from – and only from – their intrinsic kinetic and stoichiometric parameters.     

Mechanisms of coexistence in competitive metacommunities

Although there is a large body of theory on spatial competitive coexistence, very little of it involves comparative analyses of alternative mechanisms. We thus have limited knowledge of the conditions under which multiple spatial mechanisms can operate or of emergent properties arising from interactions between mechanisms. Here we present a mathematical framework that allows for comparative analysis of spatial coexistence mechanisms. The basis for comparison is mechanisms operating in spatially homogeneous competitive environments (e.g., life-history trade-offs) versus mechanisms operating in spatially heterogeneous competitive environments (e.g., source-sink dynamics). Our comparative approach leads to several new insights about spatial coexistence. First, we show that spatial variation in the expression of a life-history trade-off leads to a unique regional pattern that cannot be predicted by considering trade-offs or source-sink dynamics alone. This result represents an instance where spatial heterogeneity constrains rather than promotes coexistence, and it illustrates the kind of counterintuitive emergent properties that arise due to interactions between different classes of mechanisms. Second, we clarify the role of dispersal mortality in spatial coexistence. Previous studies have shown that coexistence can be constrained or facilitated by dispersal mortality. Our broader analysis distinguishes situations where dispersal mortality is not necessary for coexistence from those where such mortality is essential for coexistence because it preserves spatial variation in the strength of competition. These results form the basis for two important future directions: evolution of life-history traits in spatially heterogeneous environments and elucidation of the cause and effect relationship(s) between biodiversity and ecosystem functioning.     

Evolution of life-history traits collapses competitive coexistence

Trade-offs between competitive ability and the other life-history traits are considered to be a major mechanism of competitive coexistence. Many theoretical studies have demonstrated the robustness of such a coexistence mechanism ecologically; however, it is unknown whether the coexistence is robust evolutionarily. Here, we report that evolution of life-history traits not directly related to competition, such as longevity, and predator avoidance, easily collapses competitive coexistence in several competition systems: spatially structured, and predator-mediated two-species competition systems. In addition, we found that a superior competitor can be excluded by an inferior one by common mechanisms among the models. Our results suggest that ecological competitive coexistence due to a life-history trait trade-off balance may not be balanced on an evolutionary timescale, that is, it may be evolutionarily fragile.     

Correlations in state space can cause sub-optimal adaptation of optimal feedback control models

Control of our movements is apparently facilitated by an adaptive internal model in the cerebellum. It was long thought that this internal model implemented an adaptive inverse model and generated motor commands, but recently many reject that idea in favor of a forward model hypothesis. In theory, the forward model predicts upcoming state during reaching movements so the motor cortex can generate appropriate motor commands. Recent computational models of this process rely on the optimal feedback control (OFC) framework of control theory. OFC is a powerful tool for describing motor control, it does not describe adaptation. Some assume that adaptation of the forward model alone could explain motor adaptation, but this is widely understood to be overly simplistic. However, an adaptive optimal controller is difficult to implement. A reasonable alternative is to allow forward model adaptation to ‘re-tune’ the controller. Our simulations show that, as expected, forward model adaptation alone does not produce optimal trajectories during reaching movements perturbed by force fields. However, they also show that re-optimizing the controller from the forward model can be sub-optimal. This is because, in a system with state correlations or redundancies, accurate prediction requires different information than optimal control. We find that adding noise to the movements that matches noise found in human data is enough to overcome this problem. However, since the state space for control of real movements is far more complex than in our simple simulations, the effects of correlations on re-adaptation of the controller from the forward model cannot be overlooked.     

Mutual exclusion versus coexistence for discrete competitive systems

Using discrete competition models where the density dependent growth functions are either all exponential or all rational, notwithstanding the complex interactions of the species, we establish an exclusion principle. Moreover, in a 2-species discrete competition model where the growth functions are exponential and rational, an example is given illustrating coexistence when our conditions are satisfied. We obtain an exclusion principle for this 2-species model for some choice of parameters.Research partially supported by funds provided by a Science and Education Grant to the USDA-Forest Service, Southeastern Forest Experiment Station, Population Genetics of Forest Trees Research Unit, Raleigh, North Carolina     

Spatial variation and density-dependent dispersal in competitive coexistence

It is well known that dispersal from localities favourable to a species' growth and reproduction (sources) can prevent competitive exclusion in unfavourable localities (sinks). What is perhaps less well known is that too much emigration can undermine the viability of sources and cause regional competitive exclusion. Here, I investigate two biological mechanisms that reduce the cost of dispersal to source communities. The first involves increasing the spatial variation in the strength of competition such that sources can withstand high rates of emigration; the second involves reducing emigration from sources via density-dependent dispersal. I compare how different forms of spatial variation and modes of dispersal influence source viability, and hence source-sink coexistence, under dominance and pre-emptive competition. A key finding is that, while spatial variation substantially reduces dispersal costs under both types of competition, density-dependent dispersal does so only under dominance competition. For instance, when spatial variation in the strength of competition is high, coexistence is possible (regardless of the type of competition) even when sources experience high emigration rates; when spatial variation is low, coexistence is restricted even under low emigration rates. Under dominance competition, density-dependent dispersal has a strong effect on coexistence. For instance, when the emigration rate increases with density at an accelerating rate (Type III density-dependent dispersal), coexistence is possible even when spatial variation is quite low; when the emigration rate increases with density at a decelerating rate (Type II density-dependent dispersal), coexistence is restricted even when spatial variation is quite high. Under pre-emptive competition, density-dependent dispersal has only a marginal effect on coexistence. Thus, the diversity-reducing effects of high dispersal rates persist under pre-emptive competition even when dispersal is density dependent, but can be significantly mitigated under dominance competition if density-dependent dispersal is Type III rather than Type II. These results lead to testable predictions about source-sink coexistence under different regimes of competition, spatial variation and dispersal. They identify situations in which density-independent dispersal provides a reasonable approximation to species' dispersal patterns, and those under which consideration of density-dependent dispersal is crucial to predicting long-term coexistence.     

General theory of competitive coexistence in spatially-varying environments

A general model of competitive and apparent competitive interactions in a spatially-variable environment is developed and analyzed to extend findings on coexistence in a temporally-variable environment to the spatial case and to elucidate new principles. In particular, coexistence mechanisms are divided into variation-dependent and variation-independent mechanisms with variation-dependent mechanisms including spatial generalizations of relative nonlinearity and the storage effect. Although directly analogous to the corresponding temporal mechanisms, these spatial mechanisms involve different life history traits which suggest that the spatial storage effect should arise more commonly than the temporal storage effect and spatial relative nonlinearity should arise less commonly than temporal relative nonlinearity. Additional mechanisms occur in the spatial case due to spatial covariance between the finite rate of increase of a local population and its local abundance, which has no clear temporal analogue. A limited analysis of these additional mechanisms shows that they have similar properties to the storage effect and relative nonlinearity and potentially may be considered as enlargements of the earlier mechanisms. The rate of increase of a species perturbed to low density is used to quantify coexistence. A general quadratic approximation, which is exact in some important cases, divides this rate of increase into contributions from the various mechanisms above and admits no other mechanisms, suggesting that opportunities for coexistence in a spatially-variable environment are fully characterized by these mechanisms within this general model. Three spatially-implicit models are analyzed as illustrations of the general findings and of techniques using small variance approximations. The contributions to coexistence of the various mechanisms are expressed in terms of simple interpretable formulae. These spatially-implicit models include a model of an annual plant community, a spatial multispecies version of the lottery model, and a multispecies model of an insect community competing for spatially-patchy and ephemeral food.     

Evolution of the maturation rate collapses competitive coexistence

Most theoretical studies on character displacement and the coexistence of competing species have focused attention on the evolution of competitive traits driven by inter-specific competition. We investigated the evolution of the maturation rate which is not directly related to competition and trades off with the birth rate and how it influences competitive outcomes. Evolution may result in the superior competitor becoming extinct if, initially, the inferior competitor has a lower, and the superior one a higher, maturation rate at the coexistence equilibrium. This counterintuitive result is explained by an explosive increase in the adult population of the inferior competitor as a result of the more rapid evolution of its maturation rate, which is caused by differences in the intensity and direction of selection on the maturation rates of the two species and in their adult densities, which are related to differences in their life histories. Thus, a life history trait trade-off with a competitive trait may cause a competitive ecological coexistence to collapse.     

Mutualism can mediate competition and promote coexistence

Mutualistic interactions are not believed to promote coexistence of competitors because mutualisms produce positive feedbacks on abundances whereas coexistence requires negative feedbacks. Here we show that a mutualism between an anemonefish (Amphiprion) and its sea anemone host mediates the effect of asymmetrical competition for space between the anemonefish and another damselfish (Dascyllus) in a manner that fosters their coexistence. Amphiprion stimulates increases in host area, the shared resource, but social interactions cap the number of anemonefish to two adults per host. Space generated by the mutualism becomes differentially available to Dascyllus because the effectiveness of an anemonefish in excluding its competitor declines with increases in the area it defends. This alters Amphiprion's ratio of per capita intra‐ to interspecific effects and thus facilitates coexistence of the fishes. This mechanism may be prevalent in nature, adding another major pathway by which mutualism can enhance diversity.     

Population size dependence, competitive coexistence and habitat destruction

1. Spatial dynamics can lead to coexistence of competing species even with strong asymmetric competition under the assumption that the inferior competitor is a better colonizer given equal rates of extinction. Patterns of habitat fragmentation may alter competitive coexistence under this assumption.
2. Numerical models were developed to test for the previously ignored effect of population size on competitive exclusion and on extinction rates for coexistence of competing species. These models neglect spatial arrangement.
3. Cellular automata were developed to test the effect of population size on competitive coexistence of two species, given that the inferior competitor is a better colonizer. The cellular automata in the present study were stochastic in that they were based upon colonization and extinction probabilities rather than deterministic rules.
4. The effect of population size on competitive exclusion at the local scale was found to have little consequence for the coexistence of competitors at the metapopulation (or landscape) scale. In contrast, population size effects on extinction at the local scale led to much reduced landscape scale coexistence compared to simulations not including localized population size effects on extinction, especially in the cellular automata models. Spatially explicit dynamics of the cellular automata vs. deterministic rates of the numerical model resulted in decreased survival of both species. One important finding is that superior competitors that are widespread can become extinct before less common inferior competitors because of limited colonization.
5. These results suggest that population size–extinction relationships may play a large role in competitive coexistence. These results and differences are used in a model structure to help reconcile previous spatially explicit studies which provided apparently different results concerning coexistence of competing species.     

How competitive intransitivity and niche overlap affect spatial coexistence

Competitive intransitivity is mostly considered outside the main body of coexistence theories that rely primarily on the role of niche overlap and differentiation. How the interplay of competitive intransitivity and niche overlap jointly affects species coexistence has received little attention. Here, we consider a rock–paper–scissors competition system where interactions between species can represent the full spectra of transitive–intransitive continuum and niche overlap/differentiation under different levels of competition asymmetry. By comparing results from pair approximation that only considers interference competition between neighbouring cells in spatial lattices, with those under the mean-field assumption, we show that 1) species coexistence under transitive competition is only possible at high niche differentiation; 2) in communities with partial or pure intransitive interactions, high levels of niche overlap are not necessary to beget species extinction; and 3) strong spatial clustering can widen the condition for intransitive loops to facilitate species coexistence. The two mechanisms, competitive intransitivity and niche differentiation, can support species persistence and coexistence, either separately or in combination. Finally, the contribution of intransitive loops to species coexistence can be enhanced by strong local spatial correlations, modulated and maximised by moderate competition asymmetry. Our study, therefore, provides a bridge to link intransitive competition to other generic ecological theories of species coexistence.     

Environmental variation, stochastic extinction, and competitive coexistence

Understanding how environmental fluctuations affect population persistence is essential for predicting the ecological impacts of expected future increases in climate variability. However, two bodies of theory make opposite predictions about the effect of environmental variation on persistence. Single-species theory, common in conservation biology and population viability analyses, suggests that environmental variation increases the risk of stochastic extinction. By contrast, coexistence theory has shown that environmental variation can buffer inferior competitors against competitive exclusion through a storage effect. We reconcile these two perspectives by showing that in the presence of demographic stochasticity, environmental variation can increase the chance of extinction while simultaneously stabilizing coexistence. Our stochastic simulations of a two-species storage effect model reveal a unimodal relationship between environmental variation and coexistence time, implying maximum coexistence at intermediate levels of environmental variation. The unimodal pattern reflects the fact that the stabilizing influence of the storage effect accumulates rapidly at low levels of environmental variation, whereas the risk of extinction due to the combined effects of environmental variation and demographic stochasticity increases most rapidly at higher levels of variation. Future increases in environmental variation could either increase or decrease an inferior competitor's expected persistence time, depending on the distance between the present level of environmental variation and the optimal level anticipated by this theory.     

An integrative framework of coexistence mechanisms in competitive metacommunities

Species distribution in a metacommunity varies according to their traits, the distribution of environmental conditions and connectivity among localities. These ingredients contribute to coexistence across spatial scales via species sorting, patch dynamics, mass effects and neutral dynamics. These mechanisms however seldom act in isolation and the impact of landscape configuration on their relative importance remains poorly understood. We present a new model of metacommunity dynamics that simultaneously considers these four possible mechanisms over spatially explicit landscapes and propose a statistical approach to partition their contribution to species distribution. We find that landscape configuration can induce dispersal limitations that have negative consequences for local species richness. This result was more pronounced with neutral dynamics and mass effect than with species sorting or patch dynamics. We also find that the relative importance of the four mechanisms varies not only among landscape configurations, but also among species, with some species being mostly constrained by dispersal and/or drift and others by sorting. Changes in landscape properties might lead to a shift in coexistence mechanisms and, by extension, to a change in community composition. This confirms the importance of considering landscape properties for conservation and management. Our results illustrate the idea that ecological communities are the results of multiple mechanisms acting at the same time and complete our understanding of spatial processes in competitive metacommunities.     

Dispersal network heterogeneity promotes species coexistence in hierarchical competitive communities

Understanding the mechanisms of biodiversity maintenance is a fundamental issue in ecology. The possibility that species disperse within the landscape along differing paths presents a relatively unexplored mechanism by which diversity could emerge. By embedding a classical metapopulation model within a network framework, we explore how access to different dispersal networks can promote species coexistence. While it is clear that species with the same demography cannot coexist stably on shared dispersal networks, we find that coexistence is possible on unshared networks, as species can surprisingly form self‐organised clusters of occupied patches with the most connected patches at the core. Furthermore, a unimodal biodiversity response to an increase in species colonisation rates or average patch connectivity emerges in unshared networks. Increasing network size also increases species richness monotonically, producing characteristic species–area curves. This suggests that, in contrast to previous predictions, many more species can co‐occur than the number of limiting resources.     

How flocculation can explain coexistence in the chemostat

We study a chemostat model in which two microbial species grow on a single resource. We show that species coexistence is possible when the species which would normally win the exclusive competition aggregates in flocs. Our mathematical analysis exploits the fact that flocculation is fast compared to biological growth, a common hypothesis in floc models. A numerical study shows the validity of this approach in a large parameter range. We indicate how our model yields a mechanistic justification for the so-called density-dependent growth.     

外来物种入侵后的多物种竞争共存的集合种群模型

基于多物种竞争共存模型,提出外来物种与本地物种竞争共存途径的两种假想:外来物种通过插队竞争与本地物种实现共存;外来物种通过等位竞争与本地物种实现共存.并提出根据外来物种在两种竞争共存模式下占据生境斑块比例的稳定值大小来判断外来物种和本地物种的竞争共存途径.根据两种假想,分别建立了外来物种插队竞争共存模型和等位竞争共存模型.通过应用数学软件Mathematica 4.0对两个模型进行了模拟,得出以下结论:在外来物种与本地物种竞争共存状态下,如果外来物种通过插队竞争与本地物种实现共存,当本地物种竞争力差异较大时,外来物种极易对本地稀少物种构成危害.虽然外来物种不会直接造成本地稀少物种的灭绝,但是会使本地稀少物种的生境斑块急剧减少,增加本地稀少物种灭绝的可能性,而当本地物种竞争力差异较小时,外来物种对本地所有物种的影响都较小.如果外来物种通过等位竞争与本地物种实现共存,无论本地物种竞争力差异大小与否,外来物种只是影响到与其生态位相同的本地物种,影响程度取决于外来物种侵入时所占据生境斑块的比例大小.     

How flocculation can explain coexistence in the chemostat

We study a chemostat model in which two microbial species grow on a single resource. We show that species coexistence is possible when the species which would normally win the exclusive competition aggregates in flocs. Our mathematical analysis exploits the fact that flocculation is fast compared to biological growth, a common hypothesis in floc models. A numerical study shows the validity of this approach in a large parameter range. We indicate how our model yields a mechanistic justification for the so-called density-dependent growth.     

Superinfections can induce evolutionarily stable coexistence of pathogens

Parasites reproduce and are subject to natural selection at several different, but intertwined, levels. In the recent paper, Gilchrist and Coombs (Theor. Popul. Biol. 69:145–153, 2006) relate the between-host transmission in the context of an SI model to the dynamics within a host. They demonstrate that within-host selection may lead to an outcome that differs from the outcome of selection at the host population level. In this paper we combine the two levels of reproduction by considering the possibility of superinfection and study the evolution of the pathogen’s within-host reproduction rate p. We introduce a superinfection function φ = φ(p,q), giving the probability with which pathogens with trait q, upon transmission to a host that is already infected by pathogens with trait p, “take over” the host. We consider three cases according to whether the function q → φ(p,q) (i) has a discontinuity, (ii) is continuous, but not differentiable, or (iii) is differentiable in q = p. We find that in case (i) the within-host selection dominates in the sense that the outcome of evolution at the host population level coincides with the outcome of evolution in a single infected host. In case (iii), it is the transmission to susceptible hosts that dominates the evolution to the extent that the singular strategies are the same as when the possibility of superinfections is ignored. In the biologically most relevant case (ii), both forms of reproduction contribute to the value of a singular trait. We show that when φ is derived from a branching process variant of the submodel for the within-host interaction of pathogens and target cells, the superinfection functions fall under case (ii). We furthermore demonstrate that the superinfection model allows for steady coexistence of pathogen traits at the host population level, both on the ecological, as well as on the evolutionary time scale.