Colonization-persistence trade-offs in natural bacterial communities.

Fitness equalizing mechanisms, such as trade-offs, are recognized as one of the main factors promoting species coexistence in community ecology. However, they have rarely been explored in microbial communities. Although microbial communities are highly diverse, the coexistence of their multiple taxa is largely attributed to niche differences and high dispersal rates, following the principle 'everything is everywhere, but the environment selects'. We use a dynamical stochastic model based on the theory of island biogeography to study highly diverse bacterial communities over time across three different systems (soils, alpine lakes and shallow saline lakes). Assuming fitness equalization mechanisms, here we newly analytically derive colonization-persistence trade-offs, and report a signal of such trade-offs in natural bacterial communities. Moreover, we show that different subsets of species in the community drive this trade-off. Rare taxa, which are occasional and more likely to follow independent colonization/extinction dynamics, drive this trade-off in the aquatic communities, while the core sub-community did it in the soils. We conclude that equalizing mechanisms may be more important than previously recognized in bacterial communities. Our work also emphasizes the fundamental value of dynamical models for understanding temporal patterns and processes in highly diverse communities.

The Stochastic Nature of Functional Responses.

Functional responses are non-linear functions commonly used to describe the variation in the rate of consumption of resources by a consumer. They have been widely used in both theoretical and empirical studies, but a comprehensive understanding of their parameters at different levels of description remains elusive. Here, by depicting consumers and resources as stochastic systems of interacting particles, we present a minimal set of reactions for consumer resource dynamics. We rigorously derived the corresponding system of ODEs, from which we obtained via asymptotic expansions classical 2D consumer-resource dynamics, characterized by different functional responses. We also derived functional responses by focusing on the subset of reactions describing only the feeding process. This involves fixing the total number of consumers and resources, which we call chemostatic conditions. By comparing these two ways of deriving functional responses, we showed that classical functional response parameters in effective 2D consumer-resource dynamics differ from the same parameters obtained by measuring (or deriving) functional responses for typical feeding experiments under chemostatic conditions, which points to potential errors in interpreting empirical data. We finally discuss possible generalizations of our models to systems with multiple consumers and more complex population structures, including spatial dynamics. Our stochastic approach builds on fundamental ecological processes and has natural connections to basic ecological theory.

Competitive dominance in plant communities: Modeling approaches and theoretical predictions.

Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where some species out-compete or dominate over some others are key to describe natural ecosystems. Here we develop ecological theory using a stochastic, synthetic framework for plant community assembly that leads to predictions amenable to empirical testing. We propose two stochastic, continuous-time Markov models that incorporate competitive dominance through a hierarchy of species heights. The first model, which is spatially implicit, predicts both the expected number of species that survive and the conditions under which heights are clustered in realized model communities. The second one allows spatially-explicit interactions of individuals and alternative mechanisms that can help shorter plants overcome height-driven competition, and it demonstrates that clustering patterns remain, not only locally but also across increasing spatial scales. Moreover, although plants are actually height-clustered in the spatially-explicit model, plant species abundances are not necessarily skewed to taller plants.

Phenotypic variability promotes diversity and stability in competitive communities.

Intraspecific variation is at the core of evolutionary theory, and yet, from an ecological perspective, we have few robust expectations for how this variation should affect the dynamics of large communities. Here, by adapting an approach from evolutionary game theory, we show that the incorporation of phenotypic variability into competitive networks dramatically alters the dynamics across ecological timescales, stabilising the systems and buffering the communities against demographic perturbations. The beneficial effects of phenotypic variability are strongest when there are substantial differences among phenotypes and when phenotypes are inherited with moderately high fidelity; yet even low levels of variation lead to significant increases in diversity, stability, and robustness. By identifying a simple and ubiquitous stabilising force in competitive communities, this work contributes to our core understanding of how biological diversity is maintained in natural systems.

Stochastic competitive exclusion leads to a cascade of species extinctions.

Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity and niche partitioning, are based on competitive exclusion. However, this classical paradigm in ecology relies on implications derived from simple, deterministic models. Here we show how the predictions of a symmetric, deterministic model about the way extinctions proceed can be utterly different from the results derived from the same model when ecological drift (demographic stochasticity) is explicitly considered. Using analytical approximations to the steady-state conditional probabilities for assemblages with two and three species, we demonstrate that stochastic competitive exclusion leads to a cascade of extinctions, whereas the symmetric, deterministic model predicts a multiple collapse of species. To test the robustness of our results, we have studied the effect of environmental stochasticity and relaxed the species symmetry assumption. Our conclusions highlight the crucial role of stochasticity when deriving reliable theoretical predictions for species community assembly.

New patterns in human biogeography revealed by networks of contacts between linguistic groups.

Human languages differ broadly in abundance and are distributed highly unevenly on the Earth. In many qualitative and quantitative aspects, they strongly resemble biodiversity distributions. An intriguing and previously unexplored issue is the architecture of the neighbouring relationships between human linguistic groups. Here we construct and characterize these networks of contacts and show that they represent a new kind of spatial network with uncommon structural properties. Remarkably, language networks share a meaningful property with food webs: both are quasi-interval graphs. In food webs, intervality is linked to the existence of a niche space of low dimensionality; in language networks, we show that the unique relevant variable is the area occupied by the speakers of a language. By means of a range model analogous to niche models in ecology, we show that a geometric restriction of perimeter covering by neighbouring linguistic domains explains the structural patterns observed. Our findings may be of interest in the development of models for language dynamics or regarding the propagation of cultural innovations. In relation to species distribution, they pose the question of whether the spatial features of species ranges share architecture, and eventually generating mechanism, with the distribution of human linguistic groups.

Degree of intervality of food webs: from body-size data to models.

In food webs, the degree of intervality of consumers' diets is an indicator of the number of dimensions that are necessary to determine the niche of a species. Previous studies modeling food-web structure have shown that real networks are compatible with a high degree of diet contiguity. However, current models are also compatible with the opposite, namely that species' diets have relatively low contiguity. This is particularly true when one takes species' body size as a proxy for niche value, in which case the indeterminacy of diet contiguities provided by current models can be large. We propose a model that enables us to narrow down the range of possible values of diet contiguity. According to this model, we find that diet contiguity not only can be high, but must be high when species are ranked in ascending order of body size.

Dropping mortality by increasing connectivity in plant epidemics.

Pathogen introduction in plant communities can cause serious impacts and biodiversity losses that may take a long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance because of its implications in conservation and potential economic losses. Understanding the mechanisms that hinder pathogen propagation is, therefore, crucial. Usual modelization approaches in epidemic spreading are based in compartmentalized models, without keeping track of pathogen concentrations during spreading. In this contribution we present and fully analyze a dynamical model for plant epidemic spreading based on pathogen abundances. The model, which is defined on top of network substrates, is amenable to a deep mathematical analysis in the absence of a limit in the amount of pathogen a plant can tolerate before dying. In the presence of such death threshold, we observe that the fraction of dead plants peaks at intermediate values of network connectivity, and mortality decreases for large average degrees. We discuss the implications of our results as mechanisms to halt infection propagation.

Biological Microbial Interactions from Cooccurrence Networks in a High Mountain Lacustrine District.

A fundamental question in biology is why some species tend to occur together in the same locations, while others are never observed coexisting. This question becomes particularly relevant for microorganisms thriving in the highly diluted waters of high mountain lakes, where biotic interactions might be required to make the most of an extreme environment. We studied a high-throughput gene data set of alpine lakes (>220 Pyrenean lakes) with cooccurrence network analysis to infer potential biotic interactions, using the combination of a probabilistic method for determining significant cooccurrences and coexclusions between pairs of species and a conceptual framework for classifying the nature of the observed cooccurrences and coexclusions. This computational approach (i) determined and quantified the importance of environmental variables and spatial distribution and (ii) defined potential interacting microbial assemblages. We determined the properties and relationships between these assemblages by examining node properties at the taxonomic level, indicating associations with their potential habitat sources (i.e., aquatic versus terrestrial) and their functional strategies (i.e., parasitic versus mixotrophic). Environmental variables explained fewer pairs in bacteria than in microbial eukaryotes for the alpine data set, with pH alone explaining the highest proportion of bacterial pairs. Nutrient composition was also relevant for explaining association pairs, particularly in microeukaryotes. We identified a reduced subset of pairs with the highest probability of species interactions ("interacting guilds") that significantly reached higher occupancies and lower mean relative abundances in agreement with the carrying capacity hypothesis. The interacting bacterial guilds could be more related to habitat and microdispersal processes (i.e., aquatic versus soil microbes), whereas for microeukaryotes trophic roles (osmotrophs, mixotrophs, and parasitics) could potentially play a major role. Overall, our approach may add helpful information to guide further efforts for a mechanistic understanding of microbial interactions in situ. IMPORTANCE A fundamental question in biology is why some species tend to occur together in the same locations, while others are never observed to coexist. This question becomes particularly relevant for microorganisms thriving in the highly diluted waters of high mountain lakes, in which biotic interactions might be required to make the most of an extreme environment. Microbial metacommunities are too often only studied in terms of their environmental niches and geographic barriers since they show inherent difficulties to quantify biological interactions and their role as drivers of ecosystem functioning. Our study highlights that telling apart potential interactions from both environmental and geographic niches may help for the initial characterization of organisms with similar ecologies in a large scope of ecosystems, even when information about actual interactions is partial and limited. The multilayered statistical approach carried out here offers the possibility of going beyond taxonomy to understand microbiological behavior in situ.

Struggle for space: viral extinction through competition for cells.

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms leading to viral extinction. Here we report on infection extinction due to intraspecific competition to infect susceptible hosts. Beneficial mutations increase the production of viral progeny, while the host cell may develop defenses against infection. For an unlimited number of host cells, a feedback runaway coevolution between host resistance and progeny production occurs. However, physical space limits the advantage that the virus obtains from increasing offspring numbers; thus, infection clearance may result from an increase in host defenses beyond a finite threshold. Our results might be relevant to devise improved control strategies in environments with mobility constraints or different geometrical properties.

Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics.

Recently we have introduced a simplified model of ecosystem assembly (Capitán et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper analysis of the model, obtaining analytical results and introducing some approximations which allow us to reconstruct the results of our previous work. In particular, we show that the population dynamics equations of a very general class of trophic-level structured food-web have an unique interior equilibrium point which is globally stable. We show analytically that communities found as end states of the assembly process are pyramidal and we find that the equilibrium abundance of any species at any trophic level is approximately inversely proportional to the number of species in that level. We also find that the per capita growth rate of a top predator invading a resident community is key to understand the appearance of complex end states reported in our previous work. The sign of these rates allows us to separate regions in the space of parameters where the end state is either a single community or a complex set containing more than one community. We have also built up analytical approximations to the time evolution of species abundances that allow us to determine, with high accuracy, the sequence of extinctions that an invasion may cause. Finally we apply this analysis to obtain the communities in the end states. To test the accuracy of the transition probability matrix generated by this analytical procedure for the end states, we have compared averages over those sets with those obtained from the graph derived by numerical integration of the Lotka-Volterra equations. The agreement is excellent.

Species assembly in model ecosystems, II: Results of the assembly process.

In the companion paper of this set (Capitán and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitán et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.

A signal of competitive dominance in mid-latitude herbaceous plant communities.

Understanding the main determinants of species coexistence across space and time is a central question in ecology. However, ecologists still know little about the scales and conditions at which biotic interactions matter and how these interact with the environment to structure species assemblages. Here we use recent theoretical developments to analyse plant distribution and trait data across Europe and find that plant height clustering is related to both evapotranspiration (ET) and gross primary productivity. This clustering is a signal of interspecies competition between plants, which is most evident in mid-latitude ecoregions, where conditions for growth (reflected in actual ET rates and gross primary productivities) are optimal. Away from this optimum, climate severity probably overrides the effect of competition, or other interactions become increasingly important. Our approach bridges the gap between species-rich competition theories and large-scale species distribution data analysis.

The characteristic time of ecological communities.

A simple description of temporal dynamics of ecological communities may help us understand how community assembly proceeds, predict ecological responses to environmental disturbances, and improve the performance of biological conservation actions. Although community changes take place at multiple temporal scales, the variation of species composition and richness over time across communities and habitats shows general patterns that may potentially reveal the main drivers of community dynamics. We used the simplest stochastic model of island biogeography to propose two quantities to characterize community dynamics: the community characteristic time, as a measure of the typical time scale of species-richness change, and the characteristic Jaccard index, as a measure of temporal ß diversity, that is, the variation of community composition over time. In addition, the community characteristic time, which sets the temporal scale at which null, noninteracting species assemblages operate, allowed us to define a relative sampling frequency (to the characteristic time). Here we estimate these quantities across microbial and macroscopic species assemblages to highlight two related results. First, we illustrated both characteristic time and Jaccard index and their relation with classic time-series in ecology, and found that the most thoroughly sampled communities, relative to their characteristic time, presented the largest similarity between consecutive samples. Second, our analysis across a variety of habitats and taxa show that communities span a large range of species turnover, from potentially very fast (short characteristic times) to rather slow (long characteristic times) communities. This was in agreement with previous knowledge, but indicated that some habitats may have been sampled less frequently than required. Our work provides new perspectives to explore the temporal component in ecological studies and highlights the usefulness of simple approximations to the complex dynamics of ecological communities.

Statistical mechanics of ecosystem assembly.

We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows us to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the end state of the process), which is therefore resistant to invasions. This also shows that the end state is independent of the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner.

Phase diagram of a two-dimensional lattice gas model of a ramp system.

Using Monte Carlo simulation and fundamental measure theory we study the phase diagram of a two-dimensional lattice gas model with a nearest neighbor hard core exclusion and a next-to-nearest neighbor finite repulsive interaction. The model presents two competing ranges of interaction and, in common with many experimental systems, exhibits a low density solid phase, which melts back to the fluid phase upon compression. The theoretical approach is found to provide a qualitatively correct picture of the phase diagram of our model system.

A Randomized Trait Community Clustering approach to unveil consistent environmental thresholds in community assembly.

Similarities and differences of phenotypes within local co-occurring species hold the key to inferring the contribution of stochastic or deterministic processes in community assembly. Developing both phylogenetic-based and trait-based quantitative methods to unravel these processes is a major aim in community ecology. We developed a trait-based approach that: (i) assesses if a community trait clustering pattern is related to increasing environmental constraints along a gradient; and (ii) determines quantitative thresholds for an environmental variable along a gradient to interpret changes in prevailing community assembly drivers. We used a regional set of natural shallow saline ponds covering a wide salinity gradient (0.1-40% w/v). We identify a consistent discrete salinity threshold (ca. 5%) for microbial community assembly drivers. Above 5% salinity a strong environmental filtering prevailed as an assembly force, whereas a combination of biotic and abiotic factors dominated at lower salinities. This method provides a conceptual approach to identify consistent environmental thresholds in community assembly and enables quantitative predictions for the ecological impact of environmental changes.

Fundamental-measure density functional for mixtures of parallel hard cylinders.

We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For this purpose we first generalize to multicomponent mixtures the fundamental-measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of those authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step, we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.

Coexistence of many species in random ecosystems.

Rich ecosystems harbour thousands of species interacting in tangled networks encompassing predation, mutualism and competition. Such widespread biodiversity is puzzling, because in ecological models it is exceedingly improbable for large communities to stably coexist. One aspect rarely considered in these models, however, is that coexisting species in natural communities are a selected portion of a much larger pool, which has been pruned by population dynamics. Here we compute the distribution of the number of species that can coexist when we start from a pool of species interacting randomly, and show that even in this case we can observe rich, stable communities. Interestingly, our results show that, once stability conditions are met, network structure has very little influence on the level of biodiversity attained. Our results identify the main drivers responsible for widespread coexistence in natural communities, providing a baseline for determining which structural aspects of empirical communities promote or hinder coexistence.

Fundamental-measure density functional for the fluid of aligned hard hexagons: Further insights in fundamental measure theory.

In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for an admittedly academic model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share "lost cases," i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane x+y+z=0 . The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through an additional term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for further developments of fundamental measure theory.