Variation in moisture duration as a driver of coexistence by the storage effect in desert annual plants

Temporal environmental variation is a leading hypothesis for the coexistence of desert annual plants. Environmental variation is hypothesized to cause species-specific patterns of variation in germination, which then generates the storage effect coexistence mechanism. However, it has never been shown how sufficient species differences in germination patterns for multispecies coexistence can arise from a shared fluctuating environment. Here we show that nonlinear germination responses to a single fluctuating physical environmental factor can lead to sufficient differences between species in germination pattern for the storage effect to yield coexistence of multiple species. We derive these nonlinear germination responses from experimental data on the effects of varying soil moisture duration. Although these nonlinearities lead to strong species asymmetries in germination patterns, the relative nonlinearity coexistence mechanism is minor compared with the storage effect. However, these asymmetries mean that the storage effect can be negative for some species, which then only persist in the face of interspecific competition through average fitness advantages. This work shows how a low dimensional physical environment can nevertheless stabilize multispecies coexistence when the species have different nonlinear responses to common conditions, as supported by our experimental data.     

生态群落物种共存的进化机制

本文概述了目前对生态群落的物种共存研究中存在的若干问题及动、植物群落物种共存机制的研究进展。植物群落的物种共存主要介绍与环境、种子再迁移、生态位分化、竞争平衡理论、种库假设、再生生态位等有关的几种假设、生态学上相似种的共存及“原”群落概念等。动物群落的物种共存机制主要从以下几方面叙述：（1）异质环境中的资源分割,主要指动物斑状滋养的不同利用;（2）避免竞争排斥的行为机制,如边缘效应、聚群效应、扩散行为、相互作用和干扰;（3）特化者和泛化者的共存,包括：竞争是物种向多功能进化的作用力、最佳觅食理论与生态学特化及特化概念的发展。最后指出进一步研究的方向。     

Evolutionary coexistence in a fluctuating environment by specialization on resource level

Microbial communities in fluctuating environments, such as oceans or the human gut, contain a wealth of diversity. This diversity contributes to the stability of communities and the functions they have in their hosts and ecosystems. To improve stability and increase production of beneficial compounds, we need to understand the underlying mechanisms causing this diversity. When nutrient levels fluctuate over time, one possibly relevant mechanism is coexistence between specialists on low and specialists on high nutrient levels. The relevance of this process is supported by the observations of coexistence in the laboratory, and by simple models, which show that negative frequency dependence of two such specialists can stabilize coexistence. However, as microbial populations are often large and fast growing, they evolve rapidly. Our aim is to determine what happens when species can evolve; whether evolutionary branching can create diversity or whether evolution will destabilize coexistence. We derive an analytical expression of the invasion fitness in fluctuating environments and use adaptive dynamics techniques to find that evolutionarily stable coexistence requires a special type of trade-off between growth at low and high nutrients. We do not find support for the necessary evolutionary trade-off in data available for the bacterium Escherichia coli and the yeast Saccharomyces cerevisiae on glucose. However, this type of data is scarce and might exist for other species or in different conditions. Moreover, we do find evidence for evolutionarily stable coexistence of the two species together. Since we find this coexistence in the scarce data that are available, we predict that specialization on resource level is a relevant mechanism for species diversity in microbial communities in fluctuating environments in natural settings.     

The storage effect due to frequency-dependent predation in multispecies plant communities

Frequency-dependent seed predation (FDP) has been shown to be a powerful coexistence mechanism in models of annual plant communities. However, FDP undermines the competition-based coexistence mechanism called the storage effect (SEc), which relies on temporal environmental fluctuations that drive fluctuations in competition. Although environmental fluctuations also drive fluctuations in predation, a storage effect due to predation (SEp) may not arise due to a time lag between a change in the environment and the resulting change in the predation rate. Here we show how SEp can arise with multispecies FDP, and in a two-species setting with density-dependent frequency-dependence, partially compensating for the reduction in SEc, in the presence of predation. These outcomes occur when predatory behavior is flexible, and can accommodate to changes in prey abundances on a within-year time scale, leading to changes in predator preferences in response to prey abundances in a given year. When predator preferences are determined by average prey abundances over several years, FDP is still a strong coexistence mechanism but undermines SEc without creating SEp.     

Interacting coexistence mechanisms in annual plant communities: Frequency-dependent predation and the storage effect

We study frequency-dependent seed predation (FDP) in a model of competing annual plant species in a variable environment. The combination of a variable environment and competition leads to the storage-effect coexistence mechanism (SE), which is a leading hypothesis for coexistence of desert annual plants. However, seed predation in such systems demands attention to coexistence mechanisms associated with predation. FDP is one such mechanism, which promotes coexistence by shifting predation to more abundant plant species, facilitating the recovery of species perturbed to low density. When present together, FDP and SE interact, undermining each other’s effects. Predation weakens competition, and therefore weakens mechanisms associated with competition: here SE. However, the direct effect of FDP in promoting coexistence can compensate or more than compensate for this weakening of SE. On the other hand, the environmental variation necessary for SE weakens FDP. With high survival of dormant seeds, SE can be strong enough to compensate, or overcompensate, for the decline in FDP, provided predation is not too strong. Although FDP and SE may simultaneously contribute to coexistence, their combined effect is less than the sum of their separate effects, and is often less than the effect of the stronger mechanism when present alone.     

Competition and coexistence in flowing habitats with a hydraulic storage zone

This paper examines a model of a flowing water habitat with a hydraulic storage zone in which no flow occurs. In this habitat, one or two microbial populations grow while consuming a single nutrient resource. Conditions for persistence of one population and coexistence of two competing populations are derived from eigenvalue problems, the theory of bifurcation and the theory of monotone dynamical systems. A single population persists if it can invade the trivial steady state of an empty habitat. Under some conditions, persistence occurs in the presence of a hydraulic storage zone when it would not in an otherwise equivalent flowing habitat without such a zone. Coexistence of two competing species occurs if each can invade the semi-trivial steady state established by the other species. Numerical work shows that both coexistence and enhanced persistence due to a storage zone occur for biologically reasonable parameters.     

Spatial heterogeneity and the stability of host-parasite coexistence

Spatially heterogeneous environments can theoretically promote more stable coexistence of hosts and parasites by reducing the risk of parasite attack either through providing permanent spatial refuges or through providing ephemeral refuges by reducing dispersal. In experimental populations of Pseudomonas aeruginosa and the bacteriophage PP7, spatial heterogeneity promoted stable coexistence of host and parasite, while coexistence was significantly less stable in the homogeneous environment. Phage populations were found to be persisting on subpopulations of sensitive bacteria. Transferring populations to fresh microcosms every 24 h prevented the development of permanent spatial refuges. However, the lower dispersal rates in the heterogeneous environment were found to reduce parasite transmission thereby creating ephemeral refuges from phage attack. These results suggest that spatial heterogeneity can stabilize an otherwise unstable host-parasite interaction even in the absence of permanent spatial refuges.     

The effect of room-temperature storage on the stability of compounds in DMSO

The stability of approximately 7200 compounds stored as 20-mM DMSO solutions under ambient conditions was monitored for 1 year. Compound integrity was measured by flow injection analysis using positive and negative electrospray ionization mass spectrometry. Each sample was assessed at the beginning of the study, after 12 months of storage, and at a randomized time point between the initial and final time points of the study. The relationship between length of storage and the probability of observing the compound was described by a repeated-measures logistic regression model. The probability of observing the compound was 92% after 3 months of storage at room temperature, 83% after 6 months, and 52% after 1 year in DMSO. An acceptable limit for compound loss and corresponding maximum storage time for samples in DMSO can be determined based on these results.     

Autophagic dysfunction in a lysosomal storage disorder due to impaired proteolysis

Alterations in macroautophagy (hereafter referred to as “autophagy”) are a common feature of lysosomal storage disorders, and have been hypothesized to play a major role in the pathogenesis of these diseases. We have recently reported multiple defects in autophagy contributing to the lysosomal storage disorder Niemann-Pick type C (NPC). These include increased formation of autophagosomes, slowed turnover of autophagosomes secondary to impaired lysosomal proteolysis, and delivery of stored lipids to the lysosome via autophagy. The study summarized here describes novel methods for the interrogation of individual stages of the autophagic pathway, and suggests mechanisms by which lipid storage may result in broader lysosomal dysfunction.     

Evolutionary stability in Lotka-Volterra systems

The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.     

Evolutionary stability in a 400-million-year-old heritable facultative mutualism

Many eukaryotes interact with heritable endobacteria to satisfy diverse metabolic needs. Some of these interactions are facultative symbioses, in which one partner is not essential to the other. Facultative symbioses are expected to be transitional stages along an evolutionary trajectory toward obligate relationships. We tested this evolutionary theory prediction in Ca. Glomeribacter gigasporarum, nonessential endosymbionts of arbuscular mycorrhizal fungi (Glomeromycota). We found that heritable facultative mutualisms can be both ancient and evolutionarily stable. We detected significant patterns of codivergence between the partners that we would only expect in obligate associations. Using codiverging partner pairs and the fungal fossil record, we established that the Glomeromycota-Glomeribacter symbiosis is at least 400 million years old. Despite clear signs of codivergence, we determined that the Glomeribacter endobacteria engage in recombination and host switching, which display patterns indicating that the association is not evolving toward reciprocal dependence. We postulate that low frequency of recombination in heritable endosymbionts together with host switching stabilize facultative mutualisms over extended evolutionary times.     

Species coexistence by permanent spatial heterogeneity in a lottery model

We studied the effect of permanent spatial heterogeneity in promoting species coexistence in a lottery model. The system consisted of multiple habitats, each composed of a number of sites occupied by adults of two species. Larvae produced from different habitats were mixed in a common pool. When an adult died, the vacant site became occupied by an individual randomly chosen from the larval pool. If there were n habitats, there could be up to n-1 internal equilibria with both species in addition to two single-species equilibria. These equilibria and their local stability can be calculated from a single function, indicating the difference among species in their average lifetime reproductive success. Our main result is that between-habitat variation in the ratio of mortalities of two species promotes coexistence, while that of reproductive rates does not. This conclusion is the opposite of the role of temporal variation in the standard lottery model, in which between-year variation in the reproductive rate, but not that in the mortalities, promotes coexistence.     

Oscillatory coexistence in a food chain model with competing predators

A food chain model with two predators feeding on a single prey in a chemostat is studied. Using a multiparameter bifurcation analysis, we find parameters values for which there is stable oscillatory coexistence of the predators. It is also shown how these coexistent states provide a transition between two possible states of competitive exclusion. It is shown that the competitive exclusion principle need not hold if one or more of the predators has oscillatory behavior in the absence of other predators.This work was partially supported by National Science Foundation Grant MCS 83-01881     

Evolutionary stability and the rarity of grandmothering

The provision of intergenerational care, via the Grandmother Hypothesis, has been implicated in the evolution of postfertile longevity, particularly in humans. However, if grandmothering does provide fitness benefits, a key question is why has it evolved so infrequently? We investigate this question with a combination of life‐history and evolutionary game theory. We derive simple eligibility and stability thresholds, both of which must be satisfied if intergenerational care is first to evolve and then to persist in a population. As one threshold becomes easier to fulfill, the other becomes more difficult, revealing a conflict between the two. As such, we suggest that, in fact, we should expect the evolution of grandmothering to be rare.     

Evolutionary branching of virulence in a single-infection model

This study explores the evolutionary dynamics of pathogen virulence in a single-infection model with density-dependent mortality. Although virulence is not an adaptation of the pathogen per se, it is generally believed to be an inevitable by-product of a pathogen's need to propagate and transmit to new hosts: an increase in virulence will parallel an increase in transmission efficacy. The exact characteristics of the trade-off curve defined by this relationship are important with respect to possible evolutionary scenarios. We conduct a critical function analysis, a method that exposes the evolutionary outcome resulting from trade-offs of arbitrary shape, and find that this simple model can display a wide variety of evolutionary dynamics; comprising multiple stable attractors, evolutionary repellors, and most notably, evolutionary branching points. We identify the conditions under which the different evolutionary outcomes are realised. Our analysis furthermore considers the evolution of coexisting strains, and identifies the trade-off characteristics that will support an evolutionarily stable dimorphic state. We find that an evolutionarily stable dimorphism may exist also in the absence of a branching point in the monomorphic state. The analysis reveals that an evolutionarily stable dimorphism will always be attracting and that no further branching is possible under this model. We discuss our results in relation to the dimension of the environmental feedback inherent in the model, and to results from previous studies and models of evolution of virulence.     

Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion

This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which determine the ability of each strain to invade the single-strain equilibrium of the other strain. The main question that we address is whether the presence of spatial structure would allow the two strains to coexist, as the corresponding spatially homogeneous model leads to competitive exclusion. We show analytically that if both invasion numbers are larger than one, then there is a coexistence equilibrium. We devise a finite element numerical method to numerically confirm the stability of the coexistence equilibrium and investigate various competition scenarios between the strains. Finally, we show that the numerical scheme preserves the positive cone and converges of first order in the time variable and second order in the space variables.     

Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion

This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which determine the ability of each strain to invade the single-strain equilibrium of the other strain. The main question that we address is whether the presence of spatial structure would allow the two strains to coexist, as the corresponding spatially homogeneous model leads to competitive exclusion. We show analytically that if both invasion numbers are larger than one, then there is a coexistence equilibrium. We devise a finite element numerical method to numerically confirm the stability of the coexistence equilibrium and investigate various competition scenarios between the strains. Finally, we show that the numerical scheme preserves the positive cone and converges of first order in the time variable and second order in the space variables.     

Competitive exclusion and coexistence of pathogens in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373-390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable.     

Reduction of species coexistence through mixing in a spatial competition model

Many ecological systems exhibit self-organized spatial patterns due to local interactions. Such patterns can promote species diversity and therefore serve as an important mechanism for biodiversity maintenance. Previous work has shown that when species interactions occurred at local spatial scales, species diversity was greatest when robust mosaic spatial patterns formed. Also, intransitive interactions led to the emergence of spiral patterns, frequently resulting in multispecies coexistence. In some instances, intransitive interactions reduced species diversity as the consequence of competitive hierarchies. Here, we extend and broaden this line of investigation and examine the role of global competition along a continuum ranging from spatial mosaics to spiral patterns. While previous models have predicted that species diversity is reduced when interactions occur over larger spatial scales, our model considers the effects of various levels of mixing on species diversity, in the context of various network structures as measured by the covariance of row and column sums of the competition matrix. First, we compare local competition (unmixed system) versus global competition (mixed systems) and show that greater species diversity is maintained under a positive covariance. Second, we show that under various levels of mixing, species diversity declines more rapidly under a negative covariance. Lastly, we demonstrate that time to extinction in our model occurs much more rapidly under a negative covariance.     

Stability and coexistence in a lawn community: experimental assessment of the stability of the actual community

Calculation of a community matrix for a lawn, based on pairwise competition experiments between lawn species, had predicted that the community would be unstable, but that it was close to the stability/instability boundary. To test for stability in the actual community, three types of 'pulse' perturbation were applied: shading for six weeks, mechanical perturbation (removal of vegetation) and a herbicide specific to grasses. Following shade and mechanical perturbation, the abundances of the species recovered towards that of the undisturbed community, although full recovery of the whole community was not realised. For the herbicide perturbation, recovery was still quite incomplete after 4.5 years, apparently because the compensatory growth of dicots made it difficult for the grasses to reinvade. Based on species presence/absence, the lawn fully recovered from all three perturbations. The overall pattern of recovery of the lawn was consistent with the prediction of marginal instability derived from the community matrix analysis. However, care must be taken in the interpretation of these results, as a pre-requisite for valid application of community matrix theory is that the community should be at equilibrium, but in the lawn this assumption was violated. A transitive hierarchy of competitive dominance was identified in the pairwise competition experiments; however, this hierarchy was unrelated to the rankings of the species in field abundance in the undisturbed community. The problems in applying community matrix theory to real communities are reviewed. It is concluded that whilst the theory may have biological relevance to at least simple communities, such as the lawn system used here, difficulties in its practical application, and more importantly, the restrictive assumptions on which the theory is based, will limit its relevance in most natural systems. These results call into question the generality of a large volume of theoretical studies based on these methods.