Lipid domains in giant unilamellar vesicles and their correspondence with equilibrium thermodynamic phases: A quantitative fluorescence microscopy imaging approach

We report a novel analytical procedure to measure the surface areas of coexisting lipid domains in giant unilamellar vesicles (GUVs) based on image processing of 3D fluorescence microscopy data. The procedure involves the segmentation of lipid domains from fluorescent image stacks and reconstruction of 3D domain morphology using active surface models. This method permits the reconstruction of the spherical surface of GUVs and determination of the area fractions of coexisting lipid domains at the level of single vesicles. Obtaining area fractions enables the scrutiny of the lever rule along lipid phase diagram's tie lines and to test whether or not the coexistence of lipid domains in GUVs correspond to equilibrium thermodynamic phases. The analysis was applied to DLPC/DPPC GUVs displaying coexistence of lipid domains. Our results confirm the lever rule, demonstrating that the observed membrane domains correspond to equilibrium thermodynamic phases (i.e., solid ordered and liquid disordered phases). In addition, the fact that the lever rule is validated from 11 to 14 randomly selected GUVs per molar fraction indicates homogeneity in the lipid composition among the explored GUV populations. In conclusion, our study shows that GUVs are reliable model systems to perform equilibrium thermodynamic studies of membranes.     

Gause's Principle and the Effect of Resource Partitioning on the Dynamical Coexistence of Replicating Templates

Models of competitive template replication, although basic for replicator dynamics and primordial evolution, have not yet taken different sequences explicitly into account, neither have they analyzed the effect of resource partitioning (feeding on different resources) on coexistence. Here we show by analytical and numerical calculations that Gause''s principle of competitive exclusion holds for template replicators if resources (nucleotides) affect growth linearly and coexistence is at fixed point attractors. Cases of complementary or homologous pairing between building blocks with parallel or antiparallel strands show no deviation from the rule that the nucleotide compositions of stably coexisting species must be different and there cannot be more coexisting replicator species than nucleotide types. Besides this overlooked mechanism of template coexistence we show also that interesting sequence effects prevail as parts of sequences that are copied earlier affect coexistence more strongly due to the higher concentration of the corresponding replication intermediates. Template and copy always count as one species due their constraint of strict stoichiometric coupling. Stability of fixed-point coexistence tends to decrease with the length of sequences, although this effect is unlikely to be detrimental for sequences below 100 nucleotides. In sum, resource partitioning (niche differentiation) is the default form of competitive coexistence for replicating templates feeding on a cocktail of different nucleotides, as it may have been the case in the RNA world. Our analysis of different pairing and strand orientation schemes is relevant for artificial and potentially astrobiological genetics.     

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.     

Species coexistence in a variable world

The contribution of deterministic and stochastic processes to species coexistence is widely debated. With the introduction of powerful statistical techniques, we can now better characterise different sources of uncertainty when quantifying niche differentiation. The theoretical literature on the effect of stochasticity on coexistence, however, is often ignored by field ecologists because of its technical nature and difficulties in its application. In this review, we examine how different sources of variability in population dynamics contribute to coexistence. Unfortunately, few general rules emerge among the different models that have been studied to date. Nonetheless, we believe that a greater understanding is possible, based on the integration of coexistence and population extinction risk theories. There are two conditions for coexistence in the presence of environmental and demographic variability: (1) the average per capita growth rates of all coexisting species must be positive when at low densities, and (2) these growth rates must be strong enough to overcome negative random events potentially pushing densities to extinction. We propose that critical tests for species coexistence must account for niche differentiation arising from this variability and should be based explicitly on notions of stability and ecological drift.     

Does “supersaturated coexistence” resolve the “paradox of the plankton”?

In contradiction with field observations, theory predicts that the number of coexisting plankton species at equilibrium cannot exceed the number of limiting resources, which is called the "paradox of the plankton". Recently, Huisman & Weissing (1999 , 2000 ) showed, in a model study, that the number of coexisting species may exceed the number of limiting resources when internal system feedback induces oscillations or chaos. In this paper, we use the term "supersaturated coexistence" for this phenomenon. On the basis of these findings, they claimed that the paradox of the plankton is solved. We investigated the prerequisites for supersaturated coexistence in the same model. Our results indicate that supersaturated coexistence is a rare phenomenon in parameter space, requires a very precise parameterization of the community members and is sensitive to the introduction of new species and the removal of the present species. This raises the question of whether supersaturated coexistence is likely to occur in nature. We conclude that the claim by Huisman & Weissing (1999 , 2000 ) is premature.     

On the impossibility of coexistence of infinitely many strategies

We investigate the possibility of coexistence of pure, inherited strategies belonging to a large set of potential strategies. We prove that under biologically relevant conditions every model allowing for coexistence of infinitely many strategies is structurally unstable. In particular, this is the case when the "interaction operator" which determines how the growth rate of a strategy depends on the strategy distribution of the population is compact. The interaction operator is not assumed to be linear. We investigate a Lotka-Volterra competition model with a linear interaction operator of convolution type separately because the convolution operator is not compact. For this model, we exclude the possibility of robust coexistence supported on the whole real line, or even on a set containing a limit point. Moreover, we exclude coexistence of an infinite set of equidistant strategies when the total population size is finite. On the other hand, for infinite populations it is possible to have robust coexistence in this case. These results are in line with the ecological concept of "limiting similarity" of coexisting species. We conclude that the mathematical structure of the ecological coexistence problem itself dictates the discreteness of the species.     

Dynamics of seedling populations and tree species coexistence in a forest: a simulation study

Theoretically, temporal variation of reproduction promotes species coexistence of sessile and polycarpic organisms when the reproduction is synchronized within species but independent among species. Monopoly of vacant sites and high relative population growth rate of minor species in the absence of propagules of other species is the essence of this mechanism. The mechanism is expected to work in forests, but persistent populations of seedlings may affect the promotion of coexistence. Using a tree-based simulation model of forest dynamics, it was demonstrated that the number of coexisting tree species was sensitively affected by the seedling establishment rate. The coexistence was not enhanced by temporal variation of reproduction when seedling establishment rate was low. This is because the reproducing minor species fail to monopolize vacant sites and allow the establishment of seedlings of other species in later years. High mortality of established seedlings under shade also suppressed coexistence. This is likely to be the result of a reduced storage effect of the population of seedlings. A forest structure and dynamics pattern that appears when tree species coexistence is promoted by fluctuating reproduction was searched for, and the number of coexisting species was varied by manipulating the seedling establishment rate. No distinct difference other than the species number itself was found between species-rich and species-poor forests. For example, the seedling population size varied, reflecting the temporal variation of reproduction, irrespective of the seedling establishment rate. Further strategy development is needed to validate the proposed mechanisms of species coexistence.     

The presence of generalist plant pathogens might not explain the long-term coexistence of plant species

Pathogens have been shown to contribute to the possibility of coexistence of competing plant species by creating ecological distinction between the coexisting species. This coexistence promoting mechanism resembles intra-specific density dependence as found in Lotka-Volterra models. However, plant species adapt in their level of resistance against pathogen infection and this adaptation has been shown to be traded-off by a reduction in growth rate. A model is developed to show that taking into account the possible adaptation of plant species to increase their resistance against pathogen infection by generalist pathogens has consequences for the coexistence of the plant species. The results show that in systems where plants adapt to the pathogen infection, coexistence becomes impossible. The implication of this finding is that plant pathogens might contribute less to the coexistence of plant species than is commonly thought.     

Enrichment in a stoichiometric model of two producers and one consumer

We consider a stoichiometric population model of two producers and one consumer. Stoichiometry can be thought of as the tracking of food quality in addition to food quantity. Our model assumes a reduced rate of conversion of biomass from producer to consumer when food quality is low. The model is open for carbon but closed for nutrient. The introduction of the second producer, which competes with the first, leads to new equilibria, new limit cycles, and new bifurcations. The focus of this paper is on the bifurcations which are the result of enrichment. The primary parameters we vary are the growth rates of both producers. Secondary variable parameters are the total nutrients in the system, and the producer nutrient uptake rates. The possible equilibria are: no-life, one-producer, coexistence of both producers, the consumer coexisting with either producer, and the consumer coexisting with both producers. We observe limit cycles in the latter three coexistence combinations. Bifurcation diagrams along with corresponding representative time series summarize the behaviours observed for this model.     

Enrichment in a stoichiometric model of two producers and one consumer

We consider a stoichiometric population model of two producers and one consumer. Stoichiometry can be thought of as the tracking of food quality in addition to food quantity. Our model assumes a reduced rate of conversion of biomass from producer to consumer when food quality is low. The model is open for carbon but closed for nutrient. The introduction of the second producer, which competes with the first, leads to new equilibria, new limit cycles, and new bifurcations. The focus of this paper is on the bifurcations which are the result of enrichment. The primary parameters we vary are the growth rates of both producers. Secondary variable parameters are the total nutrients in the system, and the producer nutrient uptake rates. The possible equilibria are: no-life, one-producer, coexistence of both producers, the consumer coexisting with either producer, and the consumer coexisting with both producers. We observe limit cycles in the latter three coexistence combinations. Bifurcation diagrams along with corresponding representative time series summarize the behaviours observed for this model.     

Adaptation in a hybrid world with multiple interaction types: a new mechanism for species coexistence

In ecological communities, numerous species coexist and affect each others’ population levels via various types of interspecific interactions. Previous ecological theory explaining multispecies coexistence tended to focus on a single interaction type, such as antagonism, competition, or mutualism, and its consequences on population dynamics. Hence, it remains unclear what, if any, contribution multiple coexisting interaction types have on the multispecies coexistence. Here, we show that the coexistence of multiple interaction types can be essential for multispecies coexistence. We present a simple model in which the exploiter and mutualist adaptively switch between two competing resource species. An adaptive mutualist, which favors the more abundant species, provides a mechanism of majority-advantage and, thus, potentially inhibits the coexistence of resource species. In the absence of an exploiter, an adaptive mutualist leads to competitive exclusion at the resource species level. However, the coexistence of an adaptive exploiter and a mutualist allows the coexistence of all species in the community, because the mutualist-mediated “winner” tends to be suppressed by the adaptive exploiter. The mutualist indirectly increases the abundance of the exploiter through mutualistic interactions, thereby indirectly supporting this coexistence mechanism. In fact, coexistence may occur even if the exploiter or mutualist alone cannot mediate the coexistence of two resources. We conclude that the coexistence of mutualism and antagonism may be the key to the persistence of the four-species module in the presence of adaptive switching.     

Disappearing refuges in time and space: how environmental change threatens species coexistence

Understanding the impacts of environmental changes on species survival is a major challenge in ecological research, especially when shifting from single- to multispecies foci. Here, we apply a spatially explicit two-species simulation model to analyze the effects of geographic range shifting and habitat isolation on different coexistence mechanisms. The model explicitly considers dispersal, local competition, and growth on a single resource. Results highlight that both range shifting and habitat isolation severely impact coexistence. However, the strength of these impacts depends on the underlying coexistence mechanisms. Neutrally coexisting species are particularly sensitive to habitat isolation, while stabilized coexistence through overcompensatory density regulation is much more sensitive to range shifting. We conclude that, at the community level, the response to environmental change sensitively depends on the underlying coexistence mechanisms. This suggests that predictions and management recommendations should consider differences between neutral versus stabilized community structures whenever possible.     

Positive interactions among competitors can produce species-rich communities

Although positive interactions between species are well documented, most ecological theory for investigating multispecies coexistence remains rooted in antagonistic interactions such as competition and predation. Standard resource-competition models from this theory predict that the number of coexisting species should not exceed the number of factors that limit population growth. Here I show that positive interactions among resource competitors can produce species-rich model communities supported by a single limiting resource. Simulations show that when resource competitors reduce each others' per capita mortality rate (e.g. by ameliorating an abiotic stress), stable multispecies coexistence with a single resource may be common, even while the net interspecific interaction remains negative. These results demonstrate that positive interactions may provide an important mechanism for generating species-rich communities in nature. They also show that focusing on the net interaction between species may conceal important coexistence mechanisms when species simultaneously engage in both antagonistic and positive interactions.     

Fine-scale community and genetic structure are tightly linked in species-rich grasslands

Recent evidence indicates that grassland community structure and species diversity are influenced by genetic variation within species. We review what is known regarding the impact of intraspecific diversity on grassland community structure, using an ancient limestone pasture as a focal example. Two genotype-dependent effects appear to modify community structure in this system. First, the abundance of individual constituent species can depend upon the combined influence of direct genetic effects stemming from individuals within the population. Second, the outcome of localized interspecific interactions occurring within the community can depend on the genotypes of participating individuals (indicating indirect genetic effects). Only genotypic interactions are thought to be capable of allowing the long-term coexistence of both genotypes and species. We discuss the implications of these effects for the maintenance of diversity in grasslands. Next, we present new observations indicating that losses of genotypic diversity from each of two species can be predicted by the abundance of other coexisting species within experimental grassland communities. These results suggest genotype-specific responses to abundance in other coexisting species. We conclude that both direct and indirect genetic effects are likely to shape community structure and species coexistence in grasslands, implying tight linkage between fine-scale genetic and community structure.     

Influence of cholesterol on phospholipid bilayers phase domains as detected by Laurdan fluorescence.

Coexisting gel and liquid-crystalline phospholipid phase domains can be observed in synthetic phospholipid vesicles during the transition from one phase to the other and, in vesicles of mixed phospholipids, at intermediate temperatures between the transitions of the different phospholipids. The presence of cholesterol perturbs the dynamic properties of both phases to such an extent as to prevent the detection of coexisting phases. 6-Lauroyl-2-dimethylaminopahthalene (Laurdan) fluorescence offers the unique advantage of well resolvable spectral parameters in the two phospholipid phases that can be used for the detection and quantitation of coexisting gel and liquid-crystalline domains. From Laurdan fluorescence excitation and emission spectra, the generalized polarization spectra and values were calculated. By the generalized polarization phospholipid phase domain coexistence can be detected, and each phase can be quantitated. In the same phospholipid vesicles where without cholesterol domain coexistence can be detected, above 15 mol% and, remarkably, at physiological cholesterol concentrations, > or = 30 mol%, no separate Laurdan fluorescence signals characteristic of distinct domains can be observed. Consequences of our results on the possible size and dynamics of phospholipid phase domains and their biological relevance are discussed.     

Simulating Fluid–Solid Equilibrium with the Gibbs Ensemble

The Gibbs ensemble is employed to simulate fluid–solid equilibrium for a shifted-force Lennard-Jones system. This is achieved by generating an accurate canonical Helmholtz free-energy model of the (defect-free) solid phase. This free-energy model is easily generated, with accuracy limited only by finite-size effects, by a single isothermal–isobaric simulation at a pressure not too far from coexistence for which the chemical potential is known. We choose to illustrate this method at the known triple-point because the chemical potential is easily calculated from the coexisting gas. Alternatively, our methods can be used to locate fluid–solid coexistence and the triple-point of pure systems if the chemical potential of the solid phase can be efficiently calculated at a pressure not too far from the actual coexistence pressure. Efficient calculation of the chemical potential of solids would also enable the Gibbs ensemble simulation of bulk solid–solid equilibrium and the grand-canonical ensemble simulation of bulk solids.     

Relatedness among arbuscular mycorrhizal fungi drives plant growth and intraspecific fungal coexistence

Arbuscular mycorrhizal fungi (AMF) form symbioses with most plant species. They are ecologically important determinants of plant growth and diversity. Considerable genetic variation occurs in AMF populations. Thus, plants are exposed to AMF of varying relatedness to each other. Very little is known about either the effects of coexisting AMF on plant growth or which factors influence intraspecific AMF coexistence within roots. No studies have addressed whether the genetics of coexisting AMF, and more specifically their relatedness, influences plant growth and AMF coexistence. Relatedness is expected to influence coexistence between individuals, and it has been suggested that decreasing ability of symbionts to coexist can have negative effects on the growth of the host. We tested the effect of a gradient of AMF genetic relatedness on the growth of two plant species. Increasing relatedness between AMFs lead to markedly greater plant growth (27% biomass increase with closely related compared to distantly related AMF). In one plant species, closely related AMF coexisted in fairly equal proportions but decreasing relatedness lead to a very strong disequilibrium between AMF in roots, indicating much stronger competition. Given the strength of the effects with such a shallow relatedness gradient and the fact that in the field plants are exposed to a steeper gradient, we consider that AMF relatedness can have a strong role in plant growth and the ability of AMF to coexist. We conclude that AMF relatedness is a driver of plant growth and that relatedness is also a strong driver of intraspecific coexistence of these ecologically important symbionts.     

The competition-colonization trade-off is dead; long live the competition-colonization trade-off

When applied at the individual patch level, the classic competition-colonization models of species coexistence assume that propagules of superior competitors can displace adults of inferior competitors (displacement competition). But if adults are invulnerable to displacement by propagules (as trees are to seeds), and propagules compete to replace adults that die for reasons independent of the outcome of juvenile competition (a lottery system), a competition-colonization trade-off alone is not able to produce coexistence. However, we show that coexistence is possible if patch density varies spatially, such that it becomes a niche axis. We also show how a dispersal-fecundity trade-off can partition variation in patch density. We discuss the application of these models to empirical systems. An important implication of communities coexisting via variation in patch density is that the amount of habitat loss necessarily interacts with the pattern of loss in affecting extinctions, invasions, and coexistence, in contrast to displacement competition models, for which the spatial pattern of loss is not important or is less important. Finally, with respect to mechanisms promoting coexistence, we suggest that trade-offs between different stages of colonization could be far more common in nature than a trade-off between competitive ability and colonization ability.