Gibbs-Ensemble Molecular Dynamics: Liquid-Gas Equilibria for Lennard-Jones Spheres and n-Hexane

Abstract

We present a novel method to simulate phase equilibria in atomic and molecular systems. The method is a Molecular Dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles (or molecules) in a thermodynamically consistent fashion. Here we pres the derivation of the generalized equations of motion and discuss the relation of the resulting trajectory averages to the relevant ensemble. We test this Gibbs-Ensemble Molecular Dynamics algorithm by applying it to an atomic and a molecular system, i.e. to the liquid-gas coexistence in a Lennard-Jones fluid and in n-hexane. In both cases our results are in good accord with previous mean field and Gibbs-Ensemble Monte Carlo results as well as with the experimental data in the case of hexane. We also show that our Gibbs-Ensemble Molecular Dynamics algorithm like other Molecular Dynamics techniques can be used to study the dynamics of the system. Self-diffusion coefficients calculated with this method are in agreement with the result of conventional constant temperature Molecular Dynamics.     

The Boundary Condition in the Gibbs Ensemble Simulation of a Stockmayer Fluid under an Applied Field

Abstract

We calculate the vapour-liquid coexistence properties of the Stockmayer fluid with reduced permanent dipole μ? = 2.0 under an applied electrostatic field E ₀? = 1.0 for various boundary conditions by the Gibbs ensemble simulation. In contrast to the system under no field, the phase behaviour of the Stockmayer fluid under the applied field calculated in simulation strongly depends on the dielectric constant of the surroundings used in the Hamiltonian. We propose that the value of the dielectric constant of the surroundings for the vapour and the liquid phase used in the simulation should be adjusted to that of the system in the corresponding phase, in order to best represent the thermodynamics of the bulk system under applied field.     

Modelling patterns of coexistence of three congeneric headwater fishes

1. Mechanisms driving patterns of occurrence and co-occurrence among North American freshwater fishes are poorly understood. In particular, the influence of biotic interactions on coexistence among stream reaches and their effects on regional species distribution patterns is not well understood for congeneric headwater fishes.
2. Occupancy models provide a useful framework for examining patterns of co-occurrence while also accounting for imperfect detection. Occupancy models may be extended to test for evidence that a dominant species influences the occurrence of a subordinate species and thus evaluate support for the hypothesis that species interactions drive patterns of coexistence.
3. We examined patterns of occurrence and co-occurrence at the stream-reach scale among three species of darters (Percidae: Etheostomatinae) that occupy headwater streams within a Gulf Coastal Plain drainage in the south-eastern U.S.A. We assessed species occurrences at 97 sites in first- to third-order streams on one occasion each and used data from four sub-reaches sampled with equal effort at each site to estimate species-specific detection probabilities. Following sampling, a suite of habitat variables was collected at three equidistant points along each of the three transects established within a sub-reach. Coarse (stream-segment, catchment, network) scale variables were also incorporated using geospatial data. Single-species and two-species occupancy models were used to examine patterns of occupancy and coexistence.
4. The occupancy of each species was influenced by distinct habitat variables. Goldstripe darters (Etheostoma parvipinne) were constrained by a stream size gradient, groundwater input appeared to influence the occurrence of Yazoo darters (Etheostoma raneyi), and local habitat heterogeneity (e.g. variation in depth and current velocity) appeared to influence the occupancy of redspot darters (Etheostoma artesiae).
5. We found no evidence that the presence of one species influenced the occurrence of another within a stream-reach based on two-species occupancy models. Rather, species co-occurrences were best explained as independent occurrences within a stream-reach according to species-specific habitat associations.
6. Occupancy modelling may provide a suitable framework for evaluating the influence of biotic interactions among congeneric stream fishes along species-specific habitat gradients at the stream reach scale. Our study offers insight into how habitat variation can influence coexistence of potential competitors across a large river system.

     

Rainfall variability maintains grass‐forb species coexistence

Environmental variability can structure species coexistence by enhancing niche partitioning. Modern coexistence theory highlights two fluctuation‐dependent temporal coexistence mechanisms —the storage effect and relative nonlinearity – but empirical tests are rare. Here, we experimentally test if environmental fluctuations enhance coexistence in a California annual grassland. We manipulate rainfall timing and relative densities of the grass Avena barbata and forb Erodium botrys, parameterise a demographic model, and partition coexistence mechanisms. Rainfall variability was integral to grass–forb coexistence. Variability enhanced growth rates of both species, and early‐season drought was essential for Erodium persistence. While theoretical developments have focused on the storage effect, it was not critical for coexistence. In comparison, relative nonlinearity strongly stabilised coexistence, where Erodium experienced disproportionately high growth under early‐season drought due to competitive release from Avena. Our results underscore the importance of environmental variability and suggest that relative nonlinearity is a critical if underappreciated coexistence mechanism.     

Trade-offs and coexistence in microbial microcosms

Trade-offs among the abilities of organisms to respond to different environmental factors are often assumed to play a major role in the coexistence of species. There has been extensive theoretical study of the role of such trade-offs in ecological communities but it has proven difficult to study such trade-offs experimentally. Microorganisms are ideal model systems with which to experimentally study the causes and consequences of ecological trade-offs. In model communities of E. coli B and T-type bacteriophage, a trade-off in E. coli between resistance to bacteriophage and competitive ability is often observed. This trade-off can allow the coexistence of different ecological types of E. coli. The magnitude of this trade-off affects, in predictable ways, the structure, dynamics and response to environmental change of these communities. Genetic factors, environmental factors, and gene-by-environment interactions determine the magnitude of this trade-off. Environmental control of the magnitude of trade-offs represents one avenue by which environmental change can alter community properties such as invasability, stability and coexistence. This revised version was published online in August 2006 with corrections to the Cover Date.     

Competitive interactions and partial displacement of Anastrepha obliqua by Ceratitis capitata in the occupation of host mangoes (Mangifera indica)

1. We examined the competitive interactions between a native fruit fly species (Anastrepha obliqua Macquart) and the invasive medfly (Ceratitis capitata Wiedemann) when these co-occur on a shared mango fruit host (Mangifera indica L.).
2. Using mango fruits of distinct levels of ripeness, we investigated both competition among larvae and among adult females for oviposition. We quantified competition by the numbers of eggs laid and the intensity of agonistic interactions between adult females.
3. Interactions between immature fruit flies led to reduced size and number of emerged adults of both species. These impacts were felt more acutely in the native species.
4. Interspecific competition between females led to fewer eggs laid on semi-ripe fruit by both species, which may be the result of niche overlap associated with oviposition.
5. Intraspecific interactions between A. obliqua individuals led to intense agonistic behaviour, with a concurrent decrease in number of landings on these host fruits.
6. These results suggest that the native species undergoes a partial niche displacement when facing the invasive species. A portion of the fundamental niche of A. obliqua remained unoccupied by the invading C. capitata, which may allow their coexistence under natural conditions.

     

Effects of antagonistic coevolution on parasite‐mediated host coexistence

Parasites can promote diversity by mediating coexistence between a poorer and superior competitor, if the superior competitor is more susceptible to parasitism. However, hosts and parasites frequently undergo antagonistic coevolution. This process may result in the accumulation of pleiotropic fitness costs associated with host resistance, and could breakdown coexistence. We experimentally investigated parasite‐mediated coexistence of two genotypes of the bacterium Pseudomonas fluorescens, where one genotype underwent coevolution with a parasite (a virulent bacteriophage), whereas the other genotype was resistant to the evolving phages at all time points, but a poorer competitor. In the absence of phages, the resistant genotype was rapidly driven extinct in all populations. In the presence of the phages, the resistant genotype persisted in four of six populations and eventually reached higher frequencies than the sensitive genotype. The coevolving genotype showed a reduction in the growth rate, consistent with a cost of resistance, which may be responsible for a decline in its relative fitness. These results demonstrate that the stability of parasite‐mediated coexistence of resistant and susceptible species or genotypes is likely to be affected if parasites and susceptible hosts coevolve.     

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.     

Patterns of coexistence between two mesocarnivores in northern Patagonia in the presence of invasive hares and anthropogenic disturbance

We analysed coexistence patterns between two mesocarnivores, Geoffroy's cat (Leopardus geoffroyi: Felidae) and culpeo fox (Pseudalopex culpaeus: Canidae), in northern Patagonia, Argentina. We examined spatial distribution influenced by land cover, anthropogenic disturbance and invasive hare presence, and analysed temporal activity patterns and dietary composition. If competitive exclusion accounts for carnivore coexistence in this system, we predicted segregation would occur in one or more of these aspects as a mechanism for coexistence. We performed camera trapping in Nahuel Huapi National Park, from February to May 2012 and January to April 2013. Using camera detections, we analysed spatial patterns with co‐occupancy modelling and temporal patterns by fitting kernel density estimates and measuring overlap. We performed a dietary meta‐analysis using available literature and performed a discriminant function analysis of diet categories between species. We observed high spatial and temporal overlap between Geoffroy's cats and culpeo foxes. We found no evidence of segregation in relation to land cover occupancy, anthropogenic disturbance, invasive hare occurrence or activity patterns. Though both species consumed predominantly small and medium mammals, Geoffroy's cats consumed more birds, reptiles and amphibians, and culpeo foxes consumed more large mammals, carrion and plant material; coexistence between these two carnivores in this Patagonian protected area appears to be facilitated by diet segregation.     

Multiple equilibria and exotic behaviour in excitable membranes

The excitation equation for an excitable membrane dV/dt=F(V) may have multiple equilibria where F(V)=0, and these may be stable or unstable. We demonstrate multiple equilibria in the Hodgkin-Huxley equations when either g_K or [Ca²⁺]₀ is lowered in the presence of a hyperpolarising current density. Under these conditions molluscan somata exhibit exotic behaviours-endogenous paroxysmal depolarising shifts and complex multiple spikes reminiscent of the normal complex activity of some mammalian central neurones. Complex discharge waveforms can be an expression of membrane (differential) properties, rather than electrotonic, geometric (partial differential) behaviour.     

Ecophysiological responses to different forest patch type of two codominant tree seedlings

According to gap‐phase dynamics theory, forests can be divided into four distinct patch types: gap patch (G), building patch (B), mature patch (M), and degeneration patch (D). Varying light conditions across patch types are one of the most important factors affecting the coexistence of vegetation. Mechanisms of coexistence can be understood through detailed knowledge of ecophysiological responses of codominant tree seedlings to patch types. The following study was conducted to determine ecophysiological responses of Cyclobalanopsis glauca (an evergreen broad‐leaved species) and Bothrocaryum controversum (a deciduous broad‐leaved species) to four different patch types. During the gap‐phase dynamics, light intensity and the magnitude of change in the four different patches followed the order of: G > B > D > M. Both species had the greatest photosynthetic capacity in the G patch. Dry leaf mass per area (LMA), Chlorophyll a + b concentration (Chl), carotenoids (Car), and nitrogen content per area (N_a) all responded to changes in light across patch type, but B. controversum showed greater sensitivity and changes than C. glauca. From G to M patch, the maximal quantum efficiency of PSII (F_v/F_m) had a larger variation magnitude for B. controversum than for C. glauca. From G to M patch, B. controversum showed significant changes in gas exchange, while C. glauca showed only small changes. Ecophysiological trait partitioning of response to light in different patches provides a possible explanation of a coexistence mechanism.     

How do similarities in spatial distributions and interspecific associations affect the coexistence of Quercus species in the Baotianman National Nature Reserve,Henan, China

Congeneric species often have similar ecological characteristics and use similar resources. These similarities may make it easier for them to co‐occur in a similar habitat but may also lead to strong competitions that limit their coexistence. Hence, how do similarities in congeneric species affect their coexistence exactly? This study mainly used spatial point pattern analysis in two 1 hm² plots in the Baotianman National Nature Reserve, Henan, China, to compare the similarities in spatial distributions and interspecific associations of Quercus species. Results revealed that Quercus species were all aggregated under the complete spatial randomness null model, and aggregations were weaker under the heterogeneous Poisson process null model in each plot. The interspecific associations of Quercus species to non‐Quercus species were very similar in Plot 1. However, they can be either positive or negative in different plots between the co‐occurring Quercus species. The spatial distributions of congeneric species, interspecific associations with non‐Quercus species, neighborhood richness around species, and species diversity were all different between the two plots. We found that congeneric species did have some similarities, and the closely related congeneric species can positive or negative associate with each other in different plots. The co‐occurring congeneric species may have different survival strategies in different habitats. On the one hand, competition among congenerics may lead to differentiation in resource utilization. On the other hand, their similar interspecific associations can strengthen their competitive ability and promote local exclusion to noncongeneric species to obtain more living space. Our results provide new knowledge for us to better understand the coexistence mechanisms of species.     

Using stable isotopes to test for trophic niche partitioning: a case study with stream salamanders and fish

1. Stream salamanders and fish often co‐occur even though fish prey on and outcompete salamanders. However, the mechanisms that allow palatable salamanders to coexist with fish are unknown. 2. We tested mechanisms in the field that promote coexistence between Idaho giant salamanders (Dicamptodon aterrimus) and stream salmonid fishes in headwater streams. Previous research in this system indicated that salamander dispersal did not promote coexistence with fish. We tested the hypothesis that D. aterrimus shift their diet when they occur with fish, facilitating coexistence through local niche partitioning. 3. We used nitrogen and carbon stable isotopes to describe the trophic niche of D. aterrimus and fish in three co‐occurring populations of salamanders and fish and three populations of salamanders without fish. We used two approaches to quantify trophic niche partitioning with stable isotopes: 95% kernel density estimators and isotopic mixing models. 4. We found that salamanders and fish were generalists that consumed aquatic invertebrates primarily, but both species were also cannibalistic and predatory on one another. We also found no support for trophic niche partitioning as a coexistence mechanism because there were no differences in the trophic niche metrics among salamander populations with and without fish. 5. Although we did not identify mechanisms that facilitate salamander and fish coexistence, our empirical data and use of novel approaches to describe the trophic niche did yield important insights on the role of predator–prey interactions and cannibalism as alternative coexistence mechanisms. In addition, we found that 95% kernel estimators are a simple and robust method to describe population‐level measure of trophic structure.     

How does spatio-temporal disturbance influence species diversity in a hierarchical competitive system? Prospective order of species coexistence and extinction

To address how habitat destruction and hierarchical competition among species affect the spatio-temporal dynamics of a multi-species community, we present a compartment model in which multiple species undergo dispersal and competitive interactions in a patchy habitat arranged in a two-dimensional lattice. We assume that disturbances are periodically imposed on some parts of the lattice in a block, followed by a period free of disturbance. For convenience, species are ranked in order of competitive ability. We further assume that the intrinsic growth rate of species i, _i , and the dispersal ability, D _i , increase in decreasing order of rank. Our model can analytically determine the exact number of surviving species when disturbance is absent. In the presence of disturbance, we numerically examine how spatio-temporal changes in environmental heterogeneity affect species coexistence and extinction, for the case in which the value of _i /D _i monotonically increases or decreases with rank. The results demonstrate that (1) when the interspecific competition is smaller than the intraspecific competition, we can provide predictions on the prospective order of species to be driven extinct and the order of potential species to revive with increasing extents of disturbance; (2) when the interspecific competition is stronger than intraspecific competition, a small difference in the disturbance level can lead to drastic changes in the species composition, their densities and the order of species extinction. In addition, comparison with other similar models reveals that differences in species interaction in local population dynamics critically affect the disturbance-mediated species diversity.     

Niche overlap in allotopic and syntopic populations of sexually interacting ground‐hopper species

Abstract There is accumulating evidence that sexual interactions among species (reproductive interference) could have dramatic effects for species’ coexistence. It has been shown that the fitness of individuals can be substantially reduced as a consequence of reproductive interference. This might subsequently lead to displacement of a species (sexual exclusion). On the other hand, some evolutionary and ecological mechanisms might enable species to coexist, such as the divergence of mate recognition systems (reproductive character displacement), habitat partitioning, clumped dispersion patterns or different colonization capabilities. We have previously shown that the two ground‐hopper species Tetrix subulata and Tetrix ceperoi interact sexually in the laboratory as well as in the field. At sites where both species co‐occur niche overlap was high, suggesting that coexistence is maintained by different niche breadths rather than by habitat partitioning. To test the hypothesis that habitat partitioning does not contribute to species’ coexistence, we examined whether allotopic and syntopic populations of these two species differ in niche overlap (competitive release). Our results show that niche overlap is higher in syntopic than in allotopic populations, suggesting that the site‐specific habitat structure (heterogeneity) has a stronger influence on microhabitat utilization than the presence of heterospecifics. Hence, our data do not support the hypothesis that habitat partitioning plays a substantial role for the coexistence of these sexually interacting species.     

Can two species of midge coexist in a single puddle of rain-water?

Larvae of two midge species, Chironomus pulcher and Chironomus imicola normally occur in different puddles of rain-water; C. pulcher in shaded and C. imicola in sunny ones. When the sun/shade signal is unclear, both species can coexist for most of each rainy season. Yet, in the laboratory, C. pulcher shows total competitive exclusion of C. imicola. The puzzle is resolved by experiments and observations which suggest that some naturally occurring puddles possess characteristics not present in laboratory pools. These include a spatial refuge (deep water) and separate shaded and sunny parts. Both variables are normally found only in larger puddles, so coexistence is a function of patch size. On its own, each variable is a necessary but not a sufficient condition for coexistence.     

Assessing niche partitioning of co‐occurring sibling bat species by DNA metabarcoding

Niche partitioning through foraging is a mechanism likely involved in facilitating the coexistence of ecologically similar and co‐occurring animal species by separating their use of resources. Yet, this mechanism is not well understood in flying insectivorous animals. This is particularly true of bats, where many ecologically similar or cryptic species coexist. The detailed analysis of the foraging niche in sympatric, cryptic sibling species provides an excellent framework to disentangle the role of specific niche factors likely involved in facilitating coexistence. We used DNA metabarcoding to determine the prey species consumed by a population of sympatric sibling Rhinolophus euryale and Rhinolophus mehelyi whose use of habitat in both sympatric and allopatric ranges has been well established through radio tracking. Although some subtle dietary differences exist in prey species composition, the diet of both bats greatly overlapped (O_jk = 0.83) due to the consumption of the same common and widespread moths. Those dietary differences we did detect might be related to divergences in prey availabilities among foraging habitats, which prior radio tracking on the same population showed are differentially used and selected when both species co‐occur. This minor dietary segregation in sympatry may be the result of foraging on the same prey‐types and could contribute to reduce potential competitive interactions (e.g., for prey, acoustic space). Our results highlight the need to evaluate the spatial niche dimension in mediating the co‐occurrence of similar insectivorous bat species, a niche factor likely involved in processes of bat species coexistence.     

Foraging behaviour in tadpoles of the bronze frog<Emphasis Type="Italic">Rana temporalis</Emphasis>: Experimental evidence for the ideal free distribution

The ability of bronze frogRana temporalis tadpoles (pure or mixed parental lines) to assess the profitability of food habitats and distribute themselves accordingly was tested experimentally using a rectangular choice tank with a non-continuous input design. Food (boiled spinach) was placed at two opposite ends of the choice tank in a desired ratio (1:1, 1:2 or 1:4) to create habitat A and B. The tadpoles in Gosner stage 28–33, pre-starved for 24 h, were introduced in an open ended mesh cylinder placed in the center of the choice tank, held for 4 min (for acclimation) and then released to allow free movement and habitat selection. The number of tadpoles foraging at each habitat was recorded at 10, 15, 20, 25 and 30 min time intervals. The actual suitability,S _i (the food available in a habitat after colonization of tadpoles) of each habitat was obtained from the equationS _i =B _i−f _i (d _i) whereB _i is basic suitability (amount of food provided at each habitat before release of tadpoles),f _i is the rate of depletion of food (lowering effect) with introduction of each tadpole, andd _i is the density of tadpoles in habitati. The expected number of tadpoles at each habitat was derived from the actual suitability. With no food in the choice tank, movement of the tadpoles in the test arena was random indicating no bias towards any end of the choice tank or the procedure. In tests with a 1:1 food ratio, the observed ratio of tadpoles (11.71: 12.28) was comparable with the expected 12:12 ratio. The observed number of tadpoles in the habitats with a 1:2 food ratio was 8.71:15.29 and 7.87:16.13 for pure and mixed parental lines respectively. In both cases, the observed ratios were close to the expected values (7:17). Likewise, in experiments with a 1:4 food ratio, the observed number of tadpoles in the two habitats (10.78:37.22) did not differ significantly from the expected ratio of 7:41. In all tests, the number ofR. temporalis tadpoles matched ideally with habitat profitability (undermatching indexK ≜ 1. The study shows that tadpoles of the bronze frog exhibit an ideal free distribution while foraging regardless of whether they are siblings or non-siblings in a group, which correlates well with their group living strategy in nature.     

Estimating effects of constraints on plant performance with regression quantiles

Rates of change in final summer densities of two desert annuals, Eriogonum abertianum and Haplopappus gracilis, as constrained by their initial winter germination densities were estimated with regression quantiles and compared with mechanistic fits based on a self‐thinning rule proposed by Guo et al. (1998); Oikos 83: 237–245). The allometric relation used was equivalent to S=Nf (Ni)?1=cf (Ni)?1, where S is the ratio of final to initial densities (survivorship), cf is a constant that is a final density specific to the species and environment, Ni is the initial plant density, and Nf is final plant density. We used regression quantiles to estimate cf assuming the exponent of ?1 was fixed (model 1, Nf (Ni)?1=cf (Ni)?1) and also obtained estimates by treating the exponent as a parameter to estimate (model 2, Nf (Ni)?1=cf (Ni)λ). Regression quantiles allow rates of change to be estimated through any part of a data distribution conditional on some linear function of covariates. We focused on estimates for upper (90–99th) quantiles near the boundary of the summer density distributions where we expected effects of self‐thinning to operate as the primary constraint on plant performance. Allometric functions estimated with regression quantiles were similar to functions fit by Guo et al. (1998) when the exponent was constrained to ?1. However, the data were more consistent with estimates for model (2), where exponents were closer to ?0.4 than ?1, although model fit was not as good at higher initial plant densities as when the exponent was fixed at ?1. An exponential form (model 3, Nf (Ni)?1=cf (Ni)λ eγNi) that is a generalization of the discrete logistic growth function, where estimates of λ were ?0.23 to ?0.28 and estimates of γ were ?0.003 to ?0.006, provided better fit from low to high initial germination densities. Model 3 predictions were consistent with an interpretation that final summer densities were constrained by initial germination densities when these were low (<40 per 0.25 m2 for Eriogonum and <100 per 0.25 m2 for Haplopappus) and were constrained by the self‐thinning process at higher germination densities. Our exponential model (3) estimated with regression quantiles had similar form to the mechanistic relation of Guo et al. (1998) when plotted as a survivorship function, but avoided the unrealistic assumption that all populations attained a similar final density, and was based on a statistical model that has formal rules for estimation and inference.