Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator-prey, mutualistic or competitive). Here we extend May's results to these relationships and find remarkable differences between predator-prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator-prey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator-prey networks can be arbitrarily large and complex, provided that predator-prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.

Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. Here, we report on the observation of two-center interference in the molecular-frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which are measured in coincidence with electrons, allows choosing the symmetry of the residual ion, leading to observation of both, gerade and ungerade, types of interference.

For two competing species, intraspecific competition must exceed interspecific competition for coexistence. To generalize this well-known criterion to multiple competing species, one must take into account both the distribution of interaction strengths and community structure. Here we derive a multispecies generalization of the two-species rule in the context of symmetric Lotka-Volterra competition and obtain explicit stability conditions for random competitive communities. We then explore the influence of community structure on coexistence. Results show that both the most and least stabilized cases have striking global structures, with a nested pattern emerging in both cases. The distribution of intraspecific coefficients leading to the most and least stabilized communities also follows a predictable pattern that can be justified analytically. In addition, we show that the size of the parameter space allowing for feasible communities always increases with the strength of intraspecific effects in a characteristic way that is independent of the interspecific interaction structure. We conclude by discussing possible extensions of our results to nonsymmetric competition.

Sensitivity analysis, the study of how ecological variables of interest respond to changes in external conditions, is a theoretically well-developed and widely applied approach in population ecology. Though the application of sensitivity analysis to predicting the response of species-rich communities to disturbances also has a long history, derivation of a mathematical framework for understanding the factors leading to robust coexistence has only been a recent undertaking. Here we suggest that this development opens up a new perspective, providing advances ranging from the applied to the theoretical. First, it yields a framework to be applied in specific cases for assessing the extinction risk of community modules in the face of environmental change. Second, it can be used to determine trait combinations allowing for coexistence that is robust to environmental variation, and limits to diversity in the presence of environmental variation, for specific community types. Third, it offers general insights into the nature of communities that are robust to environmental variation. We apply recent community-level extensions of mathematical sensitivity analysis to example models for illustration. We discuss the advantages and limitations of the method, and some of the empirical questions the theoretical framework could help answer.

The mutualistic interactions between plants and their pollinators or seed dispersers have played a major role in the maintenance of Earth's biodiversity. To investigate how coevolutionary interactions are shaped within species-rich communities, we characterized the architecture of an array of quantitative, mutualistic networks spanning a broad geographic range. These coevolutionary networks are highly asymmetric, so that if a plant species depends strongly on an animal species, the animal depends weakly on the plant. By using a simple dynamical model, we showed that asymmetries inherent in coevolutionary networks may enhance long-term coexistence and facilitate biodiversity maintenance.

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper, we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227-276). Here we review and generalize this analysis, beyond the

Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k(-alpha), a pattern with broad implications for the structure and dynamics of complex systems. However, the universality of scale-free networks remains controversial. Here, we organize different definitions of scale-free networks and construct a severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks. Across these networks, we find robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws. Furthermore, social networks are at best weakly scale free, while a handful of technological and biological networks appear strongly scale free. These findings highlight the structural diversity of real-world networks and the need for new theoretical explanations of these non-scale-free patterns.

Plants can have positive effects on each other. For example, the accumulation of nutrients, provision of shade, amelioration of disturbance, or protection from herbivores by some species can enhance the performance of neighbouring species. Thus the notion that the distributions and abundances of plant species are independent of other species may be inadequate as a theoretical underpinning for understanding species coexistence and diversity. But there have been no large-scale experiments designed to examine the generality of positive interactions in plant communities and their importance relative to competition. Here we show that the biomass, growth and reproduction of alpine plant species are higher when other plants are nearby. In an experiment conducted in subalpine and alpine plant communities with 115 species in 11 different mountain ranges, we find that competition generally, but not exclusively, dominates interactions at lower elevations where conditions are less physically stressful. In contrast, at high elevations where abiotic stress is high the interactions among plants are predominantly positive. Furthermore, across all high and low sites positive interactions are more important at sites with low temperatures in the early summer, but competition prevails at warmer sites.

Whether species interactions are static or change over time has wide-reaching ecological and evolutionary consequences. However, species interaction networks are typically constructed from temporally aggregated interaction data, thereby implicitly assuming that interactions are fixed. This approach has advanced our understanding of communities, but it obscures the timescale at which interactions form (or dissolve) and the drivers and consequences of such dynamics. We address this knowledge gap by quantifying the within-season turnover of plant-pollinator interactions from weekly censuses across 3 years in a subalpine ecosystem. Week-to-week turnover of interactions (1) was high, (2) followed a consistent seasonal progression in all years of study and (3) was dominated by interaction rewiring (the reassembly of interactions among species). Simulation models revealed that species' phenologies and relative abundances constrained both total interaction turnover and rewiring. Our findings reveal the diversity of species interactions that may be missed when the temporal dynamics of networks are ignored.

A major challenge in community ecology is to understand how species respond to environmental changes. Previous studies have shown that the reorganization of interactions among co-occurring species can modulate their chances to adapt to novel environmental conditions. Moreover, empirical evidence has shown that these ecological dynamics typically facilitate the persistence of groups of species rather than entire communities. However, so far, we have no systematic methodology to identify those groups of species with the highest or lowest chances to adapt to new environments through a reorganization of their interactions. Yet, this could prove extremely valuable for developing new conservation strategies. Here, we introduce a theoretical framework to estimate the effect of the reorganization of interactions on the adaptability of a group of species, within a community, to novel environmental conditions. We introduce the concept of the adaptation space of a group of species based on a feasibility analysis of a population dynamics model. We define the adaptation space of a group as the set of environmental conditions that can be made compatible with its persistence thorough the reorganization of interactions among species within the group. The larger the adaptation space of a group, the larger its likelihood to adapt to a novel environment. We show that the interactions in the community outside a group can act as structural constraints and be used to quantitatively compare the size of the adaptation space among different groups of species within a community. To test our theoretical framework, we perform a data analysis on several pairs of natural and artificially perturbed ecological communities. Overall, we find that the groups of species present in both control and perturbed communities are among the ones with the largest adaptation space. We believe that the results derived from our framework point out towards new directions to understand and estimate the adaptability of species to changing environments.

Environmental factors are important drivers of community dynamics. Yet, despite extensive research, it is still extremely challenging to predict the effect of environmental changes on the dynamics of ecological communities. Equilibrium- and model-based approaches have provided a theoretical framework with which to investigate this problem systematically. However, the applicability of this framework to empirical data has been limited because equilibrium dynamics of populations within communities are seldom observed in nature and exact equations for community dynamics are rarely known. To overcome these limitations, here we develop a data-driven non-parametric framework to estimate the tolerance of non-equilibrium community dynamics to environmental perturbations (that is, their structural stability). Following our approach, we show that in non-equilibrium systems, structural stability can vary significantly across time. As a case study, we investigate the structural stability of a rocky intertidal community with dynamics at the edge of chaos. The structural stability of the community as a whole exhibited a clear seasonal pattern, despite the persistent chaotic dynamics of individual populations. Importantly, we show that this seasonal pattern of structural stability is causally driven by sea temperature. Overall, our approach provides novel opportunities for estimating the tolerance of ecological communities to environmental changes within a non-parametric framework.

A major quest in network and community ecology has been centered on understanding the importance of structural patterns in species interaction networks-the synthesis of who interacts with whom in a given location and time. In the past decades, much effort has been devoted to infer the importance of a particular structure by its capacity to tolerate an external perturbation on its structure or dynamics. Here, we demonstrate that such a perspective leads to inconsistent conclusions. That is, the importance of a network structure changes as a function of the external perturbations acting on a community at any given point in time. Thus, we discuss a research agenda to investigate the relative importance of the structure of ecological networks under an environment-dependent framework. We hypothesize that only by studying systematically the link between network structure and community dynamics under an environment-dependent framework, we can uncover the limits at which communities can tolerate environmental changes.

The net effects of interspecific species interactions on individuals and populations vary in both sign (-, 0, +) and magnitude (strong to weak). Interaction outcomes are context-dependent when the sign and/or magnitude change as a function of the biotic or abiotic context. While context dependency appears to be common, its distribution in nature is poorly described. Here, we used meta-analysis to quantify variation in species interaction outcomes (competition, mutualism, or predation) for 247 published articles. Contrary to our expectations, variation in the magnitude of effect sizes did not differ among species interactions, and while mutualism was most likely to change sign across contexts (and predation least likely), mutualism did not strongly differ from competition. Both the magnitude and sign of species interactions varied the most along spatial and abiotic gradients, and least as a function of the presence/absence of a third species. However, the degree of context dependency across these context types was not consistent among mutualism, competition and predation studies. Surprisingly, study location and ecosystem type varied in the degree of context dependency, with laboratory studies showing the highest variation in outcomes. We urge that studying context dependency per se, rather than focusing only on mean outcomes, can provide a general method for describing patterns of variation in nature.

Community assembly provides a conceptual foundation for understanding the processes that determine which and how many species live in a particular locality. Evidence suggests that community assembly often leads to a single stable equilibrium, such that the conditions of the environment and interspecific interactions determine which species will exist there. In such cases, regions of local communities with similar environmental conditions should have similar community composition. Other evidence suggests that community assembly can lead to multiple stable equilibria. Thus, the resulting community depends on the assembly history, even when all species have access to the community. In these cases, a region of local communities with similar environmental conditions can be very dissimilar in their community composition. Both regional and local factors should determine the patterns by which communities assemble, and the resultant degree of similarity or dissimilarity among localities with similar environments. A single equilibrium in more likely to be realized in systems with small regional species pools, high rates of connectance, low productivity and high disturbance. Multiple stable equilibria are more likely in systems with large regional species pools, low rates of connectance, high productivity and low disturbance. I illustrate preliminary evidence for these predictions from an observational study of small pond communities, and show important effects on community similarity, as well as on local and regional species richness.

Identifying stable coexistence in empirical systems is notoriously difficult. Here, we show how spatiotemporal structure and complex system dynamics can confound two commonly used stability metrics in empirical contexts: response to perturbation and invasion rate when rare. We use these metrics to characterize stable coexistence across a range of spatial and temporal scales for five simulated models in which the ability of species to coexist in the long term is known a priori and for an empirical old field successional time series. We term the resulting multivariate distribution of metrics a

Aim: Species differ in their degree of specialization when interacting with other species, with significant consequences for the function and robustness of ecosystems. In order to better estimate such consequences, we need to improve our understanding of the spatial patterns and drivers of specialization in interaction networks. Methods: Here, we used the extensive environmental gradient of Mt. Kilimanjaro (Tanzania, East Africa) to study patterns and drivers of specialization, and robustness of plant-pollinator interactions against simulated species extinction with standardized sampling methods. We studied specialization, network robustness and other network indices of 67 quantitative plant-pollinator networks consisting of 268 observational hours and 4,380 plant-pollinator interactions along a 3.4 km elevational gradient. Using path analysis, we tested whether resource availability, pollinator richness, visitation rates, temperature, and/or area explain average specialization in pollinator communities. We further linked pollinator specialization to different pollinator taxa, and species traits, that is, proboscis length, body size, and species elevational ranges. Results: We found that specialization decreased with increasing elevation at different levels of biological organization. Among all variables, mean annual temperature was the best predictor of average specialization in pollinator communities. Specialization differed between pollinator taxa, but was not related to pollinator traits. Network robustness against simulated species extinctions of both plants and pollinators was lowest in the most specialized interaction networks, that is, in the lowlands. Conclusions: Our study uncovers patterns in plant-pollinator specialization along elevational gradients. Mean annual temperature was closely linked to pollinator specialization. Energetic constraints, caused by short activity timeframes in cold highlands, may force ectothermic species to broaden their dietary spectrum. Alternatively or in addition, accelerated evolutionary rates might facilitate the establishment of specialization under warm climates. Despite the mechanisms behind the patterns have yet to be fully resolved, our data suggest that temperature shifts in the course of climate change may destabilize pollination networks by affecting network architecture.

Understanding how the natural world will be impacted by environmental change over the coming decades is one of the most pressing challenges facing humanity. Addressing this challenge is difficult because environmental change can generate both population-level plastic and evolutionary responses, with plastic responses being either adaptive or nonadaptive. We develop an approach that links quantitative genetic theory with data-driven structured models to allow prediction of population responses to environmental change via plasticity and adaptive evolution. After introducing general new theory, we construct a number of example models to demonstrate that evolutionary responses to environmental change over the short-term will be considerably slower than plastic responses and that the rate of adaptive evolution to a new environment depends on whether plastic responses are adaptive or nonadaptive. Parameterization of the models we develop requires information on genetic and phenotypic variation and demography that will not always be available, meaning that simpler models will often be required to predict responses to environmental change. We consequently develop a method to examine whether the full machinery of the evolutionarily explicit models we develop will be needed to predict responses to environmental change or whether simpler nonevolutionary models that are now widely constructed may be sufficient.

Traits can provide a window into the mechanisms that maintain coexistence among competing species. Recent theory suggests that competitive interactions will lead to groups, or clusters, of species with similar traits. However, theoretical predictions typically assume complete knowledge of the map between competition and measured traits. These assumptions limit the plausible application of these patterns for inferring competitive interactions in nature. Here, we relax these restrictions and find that the clustering pattern is robust to contributions of unknown or unobserved niche axes. However, it may not be visible unless measured traits are close proxies for niche strategies. We conclude that patterns along single niche axes may reveal properties of interspecific competition in nature, but detecting these patterns requires natural history expertise firmly tying traits to niches.

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.

The structure of ecological communities is usually represented by food webs. In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks. Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs are different from those found in large ones. Furthermore, food webs (except in isolated cases) do not share general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character and a scale-free (power-law) distribution of the degree (the number of links per vertex). Here we propose to describe food webs as transportation networks by extending to them the concept of allometric scaling (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.

The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf's law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks. In this Letter, we discuss how the statistical analysis of these laws are affected by correlations present in the observations, the typical scenario for data from complex systems. We first show how standard maximum-likelihood recipes lead to false rejections of statistical laws in the presence of correlations. We then propose a conservative method (based on shuffling and undersampling the data) to test statistical laws and find that accounting for correlations leads to smaller rejection rates and larger confidence intervals on estimated parameters.

The quest for understanding how species interactions modulate diversity has progressed by theoretical and empirical advances following niche and network theories. Yet, niche studies have been limited to describe coexistence within tropic levels despite incorporating information about multi-trophic interactions. Network approaches could address this limitation, but they have ignored the structure of species interactions within trophic levels. Here we call for the integration of niche and network theories to reach new frontiers of knowledge exploring how interactions within and across trophic levels promote species coexistence. This integration is possible due to the strong parallelisms in the historical development, ecological concepts, and associated mathematical tools of both theories. We provide a guideline to integrate this framework with observational and experimental studies.

Recent hypotheses argue that phylogenetic relatedness should predict both the niche differences that stabilise coexistence and the average fitness differences that drive competitive dominance. These still largely untested predictions complicate Darwin's hypothesis that more closely related species less easily coexist, and challenge the use of community phylogenetic patterns to infer competition. We field parameterised models of competitor dynamics with pairs of 18 California annual plant species, and then related species' niche and fitness differences to their phylogenetic distance. Stabilising niche differences were unrelated to phylogenetic distance, while species' average fitness showed phylogenetic structure. This meant that more distant relatives had greater competitive asymmetry, which should favour the coexistence of close relatives. Nonetheless, coexistence proved unrelated to phylogeny, due in part to increasing variance in fitness differences with phylogenetic distance, a previously overlooked property of such relationships. Together, these findings question the expectation that distant relatives should more readily coexist.

The vast majority of plants obtain an important proportion of vital resources from soil through mycorrhizal fungi. Generally, this happens in exchange of photosynthetically fixed carbon, but occasionally the interaction is mycoheterotrophic, and plants obtain carbon from mycorrhizal fungi. This process results in an antagonistic interaction between mycoheterotrophic plants and their fungal hosts. Importantly, the fungal-host diversity available for plants is restricted as mycoheterotrophic interactions often involve narrow lineages of fungal hosts. Unfortunately, little is known whether fungal-host diversity may be additionally modulated by plant-plant interactions through shared hosts. Yet, this may have important implications for plant competition and coexistence. Here, we use DNA sequencing data to investigate the interaction patterns between mycoheterotrophic plants and arbuscular mycorrhizal fungi. We find no phylogenetic signal on the number of fungal hosts nor on the fungal hosts shared among mycoheterotrophic plants. However, we observe a potential trend toward increased phylogenetic diversity of fungal hosts among mycoheterotrophic plants with increasing overlap in their fungal hosts. While these patterns remain for groups of plants regardless of location, we do find higher levels of overlap and diversity among plants from the same location. These findings suggest that species coexistence cannot be fully understood without attention to the two sides of ecological interactions.

Metacommunity theory provides an understanding of how spatial processes determine the structure and function of communities at local and regional scales. Although metacommunity theory has considered trophic dynamics in the past, it has been performed idiosyncratically with a wide selection of possible dynamics. Trophic metacommunity theory needs a synthesis of a few influential axis to simplify future predictions and tests. We propose an extension of metacommunity ecology that addresses these shortcomings by incorporating variability among trophic levels in 'spatial use properties'. We define 'spatial use properties' as a set of traits (dispersal, migration, foraging and spatial information processing) that set the spatial and temporal scales of organismal movement, and thus scales of interspecific interactions. Progress towards a synthetic predictive framework can be made by (1) documenting patterns of spatial use properties in natural food webs and (2) using theory and experiments to test how trophic structure in spatial use properties affects metacommunity dynamics.

Although the effects of variation between individuals within species are traditionally ignored in studies of species coexistence, the magnitude of intraspecific variation in nature is forcing ecologists to reconsider. Compelling intuitive arguments suggest that individual variation may provide a previously unrecognised route to diversity maintenance by blurring species-level competitive differences or substituting for species-level niche differences. These arguments, which are motivating a large body of empirical work, have rarely been evaluated with quantitative theory. Here we incorporate intraspecific variation into a common model of competition and identify three pathways by which this variation affects coexistence: (1) changes in competitive dynamics because of nonlinear averaging, (2) changes in species' mean interaction strengths because of variation in underlying traits (also via nonlinear averaging) and (3) effects on stochastic demography. As a consequence of the first two mechanisms, we find that intraspecific variation in competitive ability increases the dominance of superior competitors, and intraspecific niche variation reduces species-level niche differentiation, both of which make coexistence more difficult. In addition, individual variation can exacerbate the effects of demographic stochasticity, and this further destabilises coexistence. Our work provides a theoretical foundation for emerging empirical interests in the effects of intraspecific variation on species diversity.

The maximum information entropy (MaxEnt) principle is a successful method of statistical inference that has recently been applied to ecology. Here, we show how MaxEnt can accurately predict patterns such as species-area relationships (SARs) and abundance distributions in macroecology and be a foundation for ecological theory. We discuss the conceptual foundation of the principle, why it often produces accurate predictions of probability distributions in science despite not incorporating explicit mechanisms, and how mismatches between predictions and data can shed light on driving mechanisms in ecology. We also review possible future extensions of the maximum entropy theory of ecology (METE), a potentially important foundation for future developments in ecological theory.

Mutualisms between species play an important role in ecosystem function and stability. However, in some environments, the competitive aspects of an interaction may dominate the mutualistic aspects. Although these transitions could have far-reaching implications, it has been difficult to study the causes and consequences of this mutualistic-competitive transition in experimentally tractable systems. Here, we study a microbial cross-feeding mutualism in which each yeast strain supplies an essential amino acid for its partner strain. We find that, depending upon the amount of freely available amino acid in the environment, this pair of strains can exhibit an obligatory mutualism, facultative mutualism, competition, parasitism, competitive exclusion, or failed mutualism leading to extinction of the population. A simple model capturing the essential features of this interaction explains how resource availability modulates the interaction and predicts that changes in the dynamics of the mutualism in deteriorating environments can provide advance warning that collapse of the mutualism is imminent. We confirm this prediction experimentally by showing that, in the high nutrient competitive regime, the strains rapidly reach a common carrying capacity before slowly reaching the equilibrium ratio between the strains. However, in the low nutrient regime, before collapse of the obligate mutualism, we find that the ratio rapidly reaches its equilibrium and it is the total abundance that is slow to reach equilibrium. Our results provide a general framework for how mutualisms may transition between qualitatively different regimes of interaction in response to changes in nutrient availability in the environment.

Bascompte et al. (Reports, 21 April 2006, p. 431) used network asymmetries to explain mathematical conditions necessary for stability in historic models of mutualism. The Lotka-Volterra equations they used artificially created conditions in which some factor, such as asymmetric interaction strengths, is necessary for community coexistence. We show that a more realistic model incorporating nonlinear functional responses requires no such condition and is consistent with their data.

Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant-pollinator networks, we show that this statement is incorrect. A simpler metric-the number of mutualistic partners a species has-is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.

Motivated by both analytical tractability and empirical practicality, community ecologists have long treated the species pair as the fundamental unit of study. This notwithstanding, the challenge of understanding more complex systems has repeatedly generated interest in the role of so-called higher-order interactions (HOIs) imposed by species beyond the focal pair. Here we argue that HOIs - defined as non-additive effects of density on per capita growth - are best interpreted as emergent properties of phenomenological models (e.g. Lotka-Volterra competition) rather than as distinct 'ecological processes' in their own right. Using simulations of consumer-resource models, we explore the mechanisms and system properties that give rise to HOIs in observational data. We demonstrate that HOIs emerge under all but the most restrictive of assumptions, and that incorporating non-additivity into phenomenological models improves the quantitative and qualitative accuracy of model predictions. Notably, we also observe that HOIs derive primarily from mechanisms and system properties that apply equally to single-species or pairwise systems as they do to more diverse communities. Consequently, there exists a strong mandate for further recognition of non-additive effects in both theoretical and empirical research.

The tremendous diversity of species in ecological communities has motivated a century of research into the mechanisms that maintain biodiversity. However, much of this work examines the coexistence of just pairs of competitors. This approach ignores those mechanisms of coexistence that emerge only in diverse competitive networks. Despite the potential for these mechanisms to create conditions under which the loss of one competitor triggers the loss of others, we lack the knowledge needed to judge their importance for coexistence in nature. Progress requires borrowing insight from the study of multitrophic interaction networks, and coupling empirical data to models of competition.

Most networked systems of scientific interest are characterized by temporal links, meaning the network's structure changes over time. Link temporality has been shown to hinder many dynamical processes, from information spreading to accessibility, by disrupting network paths. Considering the ubiquity of temporal networks in nature, we ask: Are there any advantages of the networks' temporality? We use an analytical framework to show that temporal networks can, compared to their static counterparts, reach controllability faster, demand orders of magnitude less control energy, and have control trajectories, that are considerably more compact than those characterizing static networks. Thus, temporality ensures a degree of flexibility that would be unattainable in static networks, enhancing our ability to control them.

Niche theory is one of the core thoughts in modern ecology. This paper deeply and comprehensively reviewed the process of formation and evolvement, and the latest development of the niche theory, and the main standpoints of the representative genres. The paper also pointed out the most influential genres, and analyzed the differences and the connections, the advantages and the shortcomings among these genres. The developing history of the niche research was classified. The directions and the prospects of the niche theory were deeply discussed.

The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.

The impact of biodiversity loss on the functioning of ecosystems and their ability to provide ecological services has become a central issue in ecology. Several experiments have provided evidence that reduced species diversity may impair ecosystem processes such as plant biomass production. The interpretation of these experiments, however, has been controversial because two types of mechanism may operate in combination. In the 'selection effect', dominance by species with particular traits affects ecosystem processes. In the 'complementarity effect', resource partitioning or positive interactions lead to increased total resource use. Here we present a new approach to separate the two effects on the basis of an additive partitioning analogous to the Price equation in evolutionary genetics. Applying this method to data from the pan-European BIODEPTH experiment reveals that the selection effect is zero on average and varies from negative to positive in different localities, depending on whether species with lower- or higher-than-average biomass dominate communities. In contrast, the complementarity effect is positive overall, supporting the hypothesis that plant diversity influences primary production in European grasslands through niche differentiation or facilitation.

The ecological consequences of biodiversity loss have aroused considerable interest and controversy during the past decade. Major advances have been made in describing the relationship between species diversity and ecosystem processes, in identifying functionally important species, and in revealing underlying mechanisms. There is, however, uncertainty as to how results obtained in recent experiments scale up to landscape and regional levels and generalize across ecosystem types and processes. Larger numbers of species are probably needed to reduce temporal variability in ecosystem processes in changing environments. A major future challenge is to determine how biodiversity dynamics, ecosystem processes, and abiotic factors interact.

A scientific growth area in recent years has been the study of networks of interacting entities within a population, including species in food webs, human or other animals transmitting infection, proteins in cells, cells in organisms (e.g. neuronal networks), the internet and the World Wide Web. Here, I review some of the differing network patterns that arise in theory and in practice, with an emphasis on their dynamical implications, particularly for resistance to deliberate or accidental disturbance. I offer caveats and opinionated comment about some excesses of enthusiasm and suggest some areas where these network ideas might find further application.

Robustness of coexistence against changes of parameters is investigated in a model-independent manner by analyzing the feedback loop of population regulation. We define coexistence as a fixed point of the community dynamics with no population having zero size. It is demonstrated that the parameter range allowing coexistence shrinks and disappears when the Jacobian of the dynamics decreases to zero. A general notion of regulating factors/variables is introduced. For each population, its impact and sensitivity niches are defined as the differential impact on, and the differential sensitivity towards, the regulating variables, respectively. Either the similarity of the impact niches or the similarity of the sensitivity niches results in a small Jacobian and in a reduced likelihood of coexistence. For the case of a resource continuum, this result reduces to the usual

Darwin used the metaphor of a 'tangled bank' to describe the complex interactions between species. Those interactions are varied: they can be antagonistic ones involving predation, herbivory and parasitism, or mutualistic ones, such as those involving the pollination of flowers by insects. Moreover, the metaphor hints that the interactions may be complex to the point of being impossible to understand. All interactions can be visualized as ecological networks, in which species are linked together, either directly or indirectly through intermediate species. Ecological networks, although complex, have well defined patterns that both illuminate the ecological mechanisms underlying them and promise a better understanding of the relationship between complexity and ecological stability.

Understanding species coexistence and the maintenance of biodiversity has long been the central interest of ecologists. The niche-based theory of community assembly has dominated community ecology for nearly a century, yet understanding of the mechanisms of species coexistence has remained elusive. The newly developed neutral theory of biodiversity has offered a promising alternative to the niche paradigm. The analytical elegance and simplicity of the neutral theory and its predictive power have made the theory widely popular. However, it is the very same simplicity of the theory (e.g. the symmetric assumption) that makes the theory vulnerable to stark criticisms. Widespread empirical evidence has shown that species in communities are not functionally symmetric; ecological equivalence is more a conceptual simplicity than a biological real-ism. Recognizing that niche and neutral processes do not have to diametrically oppose each other and a community is likely determined by the interplay of the two processes, ecologists currently are searching to reconcile the two theories by either incorporating drift into niche theory or niche into the neutral framework. However, this reconciliation process is still at its very early stage, we expect this direction will lead to a more complete understanding of community assembly mechanisms. In this paper, we provide a review on the brief histories of the niche and neutral theories, with the focus on comparing the distinct importance of the two theories in explaining community assembly. We discuss in details several integrated models that attempt to unify the niche and neutral theories. We argue that it is an essential step for any successful theory to with-stand substantial experimental and field tests. The experimental tests of neutral theories are an important di-rection that has currently not received due attention.

Neutralizing antibodies (nAbs) hold promise as effective therapeutics against COVID-19. Here, we describe protein engineering and modular design principles that have led to the development of synthetic bivalent and tetravalent nAbs against SARS-CoV-2. The best nAb targets the host receptor binding site of the viral S-protein and its tetravalent versions can block entry with a potency that exceeds the bivalent nAbs by an order of magnitude. Structural studies show that both the bivalent and tetravalent nAbs can make multivalent interactions with a single S-protein trimer, observations consistent with the avidity and potency of these molecules. Significantly, we show that the tetravalent nAbs show much increased tolerance to potential virus escape mutants. Bivalent and tetravalent nAbs can be produced at large-scale and are as stable and specific as approved antibody drugs. Our results provide a general framework for developing potent antiviral therapies against COVID-19 and related viral threats, and our strategy can be readily applied to any antibody drug currently in development.

Simplified mechanistic models in ecology have been criticised for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in ecology to make predictions constrained by just a handful of state variables, like total abundance or species richness. But an outstanding question remains: what principle tells us which state variables to constrain? Here we attempt to solve both problems simultaneously, by translating a given set of mechanisms into the state variables to be used in MaxEnt, and then using this MaxEnt theory as a null model against which to compare mechanistic predictions. In particular, we identify the sufficient statistics needed to parametrise a given mechanistic model from data and use them as MaxEnt constraints. Our approach isolates exactly what mechanism is telling us over and above the state variables alone.

A key question of theoretical ecology is which properties of ecosystems favour their stability and help maintaining biodiversity. This question recently reconsidered mutualistic systems, generating intense controversy about the role of mutualistic interactions and their network architecture. Here we show analytically and verify with simulations that reducing the effective interspecific competition and the propagation of perturbations positively influences structural stability against environmental perturbations, enhancing persistence. Noteworthy, mutualism reduces the effective interspecific competition only when the direct interspecific competition is weaker than a critical value. This critical competition is in almost all cases larger in pollinator networks than in random networks with the same connectance. Highly connected mutualistic networks reduce the propagation of environmental perturbations, a mechanism reminiscent of MacArthur's proposal that ecosystem complexity enhances stability. Our analytic framework rationalizes previous contradictory results, and it gives valuable insight on the complex relationship between mutualism and biodiversity.

Knowledge of species composition and their interactions, in the form of interaction networks, is required to understand processes shaping their distribution over time and space. As such, comparing ecological networks along environmental gradients represents a promising new research avenue to understand the organization of life. Variation in the position and intensity of links within networks along environmental gradients may be driven by turnover in species composition, by variation in species abundances and by abiotic influences on species interactions. While investigating changes in species composition has a long tradition, so far only a limited number of studies have examined changes in species interactions between networks, often with differing approaches. Here, we review studies investigating variation in network structures along environmental gradients, highlighting how methodological decisions about standardization can influence their conclusions. Due to their complexity, variation among ecological networks is frequently studied using properties that summarize the distribution or topology of interactions such as number of links, connectance, or modularity. These properties can either be compared directly or using a procedure of standardization. While measures of network structure can be directly related to changes along environmental gradients, standardization is frequently used to facilitate interpretation of variation in network properties by controlling for some co-variables, or via null models. Null models allow comparing the deviation of empirical networks from random expectations and are expected to provide a more mechanistic understanding of the factors shaping ecological networks when they are coupled with functional traits. As an illustration, we compare approaches to quantify the role of trait matching in driving the structure of plant-hummingbird mutualistic networks, i.e. a direct comparison, standardized by null models and hypothesis-based metaweb. Overall, our analysis warns against a comparison of studies that rely on distinct forms of standardization, as they are likely to highlight different signals. Fostering a better understanding of the analytical tools available and the signal they detect will help produce deeper insights into how and why ecological networks vary along environmental gradients.

Speciation can be gradual or sudden and involve few or many genetic changes. Inferring the processes generating such patterns is difficult, and may require consideration of emergent and non-linear properties of speciation, such as when small changes at tipping points have large effects on differentiation. Tipping points involve positive feedback and indirect selection stemming from associations between genomic regions, bi-stability due to effects of initial conditions and evolutionary history, and dependence on modularity of system components. These features are associated with sudden 'regime shifts' in other cellular, ecological, and societal systems. Thus, tools used to understand other complex systems could be fruitfully applied in speciation research.

Although pairwise interactions have always had a key role in ecology and evolutionary biology, the recent increase in the amount and availability of biological data has placed a new focus on the complex networks embedded in biological systems. The increased availability of computational tools to store and retrieve biological data has facilitated wide access to these data, not just by biologists but also by specialists from the social sciences, computer science, physics and mathematics. This fusion of interests has led to a burst of research on the properties and consequences of network structure in biological systems. Although traditional measures of network structure and function have started us off on the right foot, an important next step is to create biologically realistic models of network formation, evolution, and function. Here, we review recent applications of network thinking to the evolution of networks at the gene and protein level and to the dynamics and stability of communities. These studies have provided new insights into the organization and function of biological systems by applying existing techniques of network analysis. The current challenge is to recognize the commonalities in evolutionary and ecological applications of network thinking to create a predictive science of biological networks.

In theoretical ecology, traditional studies based on dynamical stability and numerical simulations have not found a unified answer to the effect of network architecture on community persistence. Here, we introduce a mathematical framework based on the concept of structural stability to explain such a disparity of results. We investigated the range of conditions necessary for the stable coexistence of all species in mutualistic systems. We show that the apparently contradictory conclusions reached by previous studies arise as a consequence of overseeing either the necessary conditions for persistence or its dependence on model parameterization. We show that observed network architectures maximize the range of conditions for species coexistence. We discuss the applicability of structural stability to study other types of interspecific interactions.

Understanding the effects of biodiversity on community persistence and productivity is key to managing both natural and production systems. Because rare species face greater danger of extinction, species evenness, a measure of how similar abundances are across species in a community, is seen as a key component of biodiversity. However, previous studies have failed to find a consistent association of species evenness with species survival and biomass production. Here we provide a theoretical framework for the relationship among these three elements. We demonstrate that the lack of consistent outcomes is not an idiosyncratic artifact of different studies but can be unified under one common framework. Applying a niche theory approach, we confirm that under demographic stochasticity evenness is a general indicator of the risk of future species extinctions in a community, in accordance with the majority of empirical studies. In contrast, evenness cannot be used as a direct indicator of the level of biomass production in a community. When a single species dominates, as expressed by the constraints imposed by the population dynamics, biomass production depends on the niche position of the dominating species and can increase or decrease with evenness. We demonstrate that high species evenness and an intermediate level of biomass production is the configuration that maximizes the average species survival probability in response to demographic stochasticity.

Many of the observed species interactions embedded in ecological communities are not permanent, but are characterized by temporal changes that are observed along with abiotic and biotic variations. While work has been done describing and quantifying these changes, little is known about their consequences for species coexistence. Here, we investigate the extent to which changes of species composition impact the likelihood of persistence of the predator-prey community in the highly seasonal Bialowieza Primeval Forest (northeast Poland), and the extent to which seasonal changes of species interactions (predator diet) modulate the expected impact. This likelihood is estimated extending recent developments on the study of structural stability in ecological communities. We find that the observed species turnover strongly varies the likelihood of community persistence between summer and winter. Importantly, we demonstrate that the observed seasonal interaction changes minimize the variation in the likelihood of persistence associated with species turnover across the year. We find that these community dynamics can be explained as the coupling of individual species to their environment by minimizing both the variation in persistence conditions and the interaction changes between seasons. Our results provide a homeostatic explanation for seasonal species interactions and suggest that monitoring the association of interactions changes with the level of variation in community dynamics can provide a good indicator of the response of species to environmental pressures.

The foundational concepts behind the persistence of ecological communities have been based on two ecological properties: dynamical stability and feasibility. The former is typically regarded as the capacity of a community to return to an original equilibrium state after a perturbation in species abundances and is usually linked to the strength of interspecific interactions. The latter is the capacity to sustain positive abundances on all its constituent species and is linked to both interspecific interactions and species demographic characteristics. Over the last 40 years, theoretical research in ecology has emphasized the search for conditions leading to the dynamical stability of ecological communities, while the conditions leading to feasibility have been overlooked. However, thus far, we have no evidence of whether species interactions are more conditioned by the community's need to be stable or feasible. Here, we introduce novel quantitative methods and use empirical data to investigate the consequences of species interactions on the dynamical stability and feasibility of mutualistic communities. First, we demonstrate that the more nested the species interactions in a community are, the lower the mutualistic strength that the community can tolerate without losing dynamical stability. Second, we show that high feasibility in a community can be reached either with high mutualistic strength or with highly nested species interactions. Third, we find that during the assembly process of a seasonal pollinator community located at The Zackenberg Research Station (northeastern Greenland), a high feasibility is reached through the nested species interactions established between newcomer and resident species. Our findings imply that nested mutualistic communities promote feasibility over stability, which may suggest that the former can be key for community persistence.

The architecture of mutualistic networks facilitates coexistence of individual participants by minimizing competition relative to facilitation. However, it is not known whether this benefit is received by each participant node in proportion to its overall contribution to network persistence. This issue is critical to understanding the trade-offs faced by individual nodes in a network. We address this question by applying a suite of structural and dynamic methods to an ensemble of flowering plant/insect pollinator networks. Here we report two main results. First, nodes contribute heterogeneously to the overall nested architecture of the network. From simulations, we confirm that the removal of a strong contributor tends to decrease overall network persistence more than the removal of a weak contributor. Second, strong contributors to collective persistence do not gain individual survival benefits but are in fact the nodes most vulnerable to extinction. We explore the generality of these results to other cooperative networks by analysing a 15-year time series of the interactions between designer and contractor firms in the New York City garment industry. As with the ecological networks, a firm's survival probability decreases as its individual nestedness contribution increases. Our results, therefore, introduce a new paradox into the study of the persistence of cooperative networks, and potentially address questions about the impact of invasive species in ecological systems and new competitors in economic systems.

Most ecological processes now show responses to anthropogenic climate change. In terrestrial, freshwater, and marine ecosystems, species are changing genetically, physiologically, morphologically, and phenologically and are shifting their distributions, which affects food webs and results in new interactions. Disruptions scale from the gene to the ecosystem and have documented consequences for people, including unpredictable fisheries and crop yields, loss of genetic diversity in wild crop varieties, and increasing impacts of pests and diseases. In addition to the more easily observed changes, such as shifts in flowering phenology, we argue that many hidden dynamics, such as genetic changes, are also taking place. Understanding shifts in ecological processes can guide human adaptation strategies. In addition to reducing greenhouse gases, climate action and policy must therefore focus equally on strategies that safeguard biodiversity and 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.

Neutralizing antibodies (nAbs) hold promise as effective therapeutics against COVID-19. Here, we describe protein engineering and modular design principles that have led to the development of synthetic bivalent and tetravalent nAbs against SARS-CoV-2. The best nAb targets the host receptor binding site of the viral S-protein and its tetravalent versions can block entry with a potency that exceeds the bivalent nAbs by an order of magnitude. Structural studies show that both the bivalent and tetravalent nAbs can make multivalent interactions with a single S-protein trimer, observations consistent with the avidity and potency of these molecules. Significantly, we show that the tetravalent nAbs show much increased tolerance to potential virus escape mutants. Bivalent and tetravalent nAbs can be produced at large-scale and are as stable and specific as approved antibody drugs. Our results provide a general framework for developing potent antiviral therapies against COVID-19 and related viral threats, and our strategy can be readily applied to any antibody drug currently in development.

Historical contingency broadly refers to the proposition that even random historical events can constrain the ecological and evolutionary pathways of organisms and that of entire communities. Focusing on communities, these pathways can be reflected into specific structural changes within and across trophic levels - how species interact with and affect each other - which has important consequences for species coexistence. Using the registry of the last 2000 years of plant introductions and their novel herbivores encountered in Central Europe, we find that the order of arrival of closely related (but not of distantly related) plant species constrained the structural changes within the trophic level formed by herbivore species across the observation period. Because it is difficult for field and lab experiments to be conducted over hundreds of years to record and replay the assembly history of a community, our study provides an alternative to understand how structural changes have occurred across extensive periods of time.

We present an overlooked but important property of modern coexistence theory (MCT), along with two key new results and their consequences. The overlooked property is that stabilizing mechanisms (increasing species' niche differences) and equalizing mechanisms (reducing species' fitness differences) have two distinct sets of meanings within MCT: one in a two-species context and another in a general multispecies context. We demonstrate that the two-species framework is not a special case of the multispecies one, and therefore these two parallel frameworks must be studied independently. Our first result is that, using the two-species framework and mechanistic consumer-resource models, stabilizing and equalizing mechanisms exhibit complex interdependence, such that changing one will simultaneously change the other. Furthermore, the nature and direction of this simultaneous change sensitively depend on model parameters. The second result states that while MCT is often seen as bridging niche and neutral modes of coexistence by building a niche-neutrality continuum, the interdependence between stabilizing and equalizing mechanisms acts to break this continuum under almost any biologically relevant circumstance. We conclude that the complex entanglement of stabilizing and equalizing terms makes their impact on coexistence difficult to understand, but by seeing them as aggregated effects (rather than underlying causes) of coexistence, we may increase our understanding of ecological dynamics.

The feasibility domain of an ecological community can be described by the set of environmental abiotic and biotic conditions under which all co-occurring and interacting species in a given site and time can have positive abundances. Mathematically, the feasibility domain corresponds to the parameter space compatible with positive (feasible) solutions at equilibrium for all the state variables in a system under a given model of population dynamics. Under specific dynamics, the existence of a feasible equilibrium is a necessary condition for species persistence regardless of whether the feasible equilibrium is dynamically stable or not. Thus, the size of the feasibility domain can also be used as an indicator of the tolerance of a community to random environmental variations. This has motivated a rich research agenda to estimate the feasibility domain of ecological communities. However, these methodologies typically assume that species interactions are static, or that input and output energy flows on each trophic level are unconstrained. Yet, this is different to how communities behave in nature. Here, we present a step-by-step quantitative guideline providing illustrative examples, computational code, and mathematical proofs to study systematically the feasibility domain of ecological communities under changes of interspecific interactions and subject to different constraints on the trophic energy flows. This guideline covers multi-trophic communities that can be formed by any type of interspecific interactions. Importantly, we show that the relative size of the feasibility domain can significantly change as a function of the biological information taken into consideration. We believe that the availability of these methods can allow us to increase our understanding about the limits at which ecological communities may no longer tolerate further environmental perturbations, and can facilitate a stronger integration of theoretical and empirical research.

How likely is it that few species can randomly assemble into a feasible and stable community? Some studies have answered that as long as the community is feasible, it will nearly always be stable. In contrast, other studies have answered that the likelihood is almost null. Here, we show that the origin of this debate has been the underestimation of the association of the parameter space of intrinsic growth rates with the feasibility and stability properties of small randomly-assembled communities. In particular, we demonstrate that not all parameterizations and sampling distributions of intrinsic growth rates lead to the same probabilities of stability and feasibility, which could mistakenly lead to under- or overestimate the stability properties of feasible communities. Additionally, we find that stability imposes a filtering of species abundances

Observational and experimental studies have shown that an interaction class between two species (be it mutualistic, competitive, antagonistic, or neutral) may switch to a different class, depending on the biotic and abiotic factors within which species are observed. This complexity arising from the evidence of context-dependencies has underscored a difficulty in establishing a systematic analysis about the extent to which species interactions are expected to switch in nature and experiments. Here, we propose an overarching theoretical framework, by integrating probabilistic and structural approaches, to establish null expectations about switches of interaction classes across environmental contexts. This integration provides a systematic platform upon which it is possible to establish new hypotheses, clear predictions, and quantifiable expectations about the context-dependency of species interactions.

Understanding how microbial communities develop is essential for predicting and directing their future states. Ecological theory suggests that community development is often influenced by priority effects, in which the order and timing of species arrival determine how species affect one another. Priority effects can have long-lasting consequences, particularly if species arrival history varies during the early stage of community development, but their importance to the human gut microbiota and host health remains largely unknown. Here, we explore how priority effects might influence microbial communities in the gastrointestinal tract during early childhood and how the strength of priority effects can be estimated from the composition of the microbial species pool. We also discuss factors that alter microbial transmission, such as delivery mode, diet and parenting behaviours such as breastfeeding, which can influence the likelihood of priority effects. An improved knowledge of priority effects has the potential to inform microorganism-based therapies, such as prebiotics and probiotics, which are aimed at guiding the microbiota towards a healthy state.

Ecologists are fascinated by the prevalence of nestedness in biogeographic and community data, where it is thought to promote biodiversity in mutualistic systems. Traditionally, nestedness has been treated in a binary sense: species and their interactions are either present or absent, neglecting information on abundances and interaction frequencies. Extending nestedness to quantitative data facilitates the study of species preferences, and we propose a new detection method that follows from a basic property of bipartite networks: large dominant eigenvalues are associated with highly nested configurations. We show that complex ecological networks are binary nested, but quantitative preferences are non-nested, indicating limited consumer overlap of favoured resources. The spectral graph approach provides a formal link to local dynamical stability analysis, where we demonstrate that nested mutualistic structures are minimally stable. We conclude that, within the binary constraint of interaction plausibility, species preferences are partitioned to avoid competition, thereby benefiting system-wide resource allocation.

Identifying causal networks is important for effective policy and management recommendations on climate, epidemiology, financial regulation, and much else. We introduce a method, based on nonlinear state space reconstruction, that can distinguish causality from correlation. It extends to nonseparable weakly connected dynamic systems (cases not covered by the current Granger causality paradigm). The approach is illustrated both by simple models (where, in contrast to the real world, we know the underlying equations/relations and so can check the validity of our method) and by application to real ecological systems, including the controversial sardine-anchovy-temperature problem.

Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants has a key role in the organization of ecological communities. Such networks in ecology have generally evolved a nested architecture independent of species composition and latitude; specialist species, with only few mutualistic links, tend to interact with a proper subset of the many mutualistic partners of any of the generalist species. Despite sustained efforts to explain observed network structure on the basis of community-level stability or persistence, such correlative studies have reached minimal consensus. Here we show that nested interaction networks could emerge as a consequence of an optimization principle aimed at maximizing the species abundance in mutualistic communities. Using analytical and numerical approaches, we show that because of the mutualistic interactions, an increase in abundance of a given species results in a corresponding increase in the total number of individuals in the community, and also an increase in the nestedness of the interaction matrix. Indeed, the species abundances and the nestedness of the interaction matrix are correlated by a factor that depends on the strength of the mutualistic interactions. Nestedness and the observed spontaneous emergence of generalist and specialist species occur for several dynamical implementations of the variational principle under stationary conditions. Optimized networks, although remaining stable, tend to be less resilient than their counterparts with randomly assigned interactions. In particular, we show analytically that the abundance of the rarest species is linked directly to the resilience of the community. Our work provides a unifying framework for studying the emergent structural and dynamical properties of ecological mutualistic networks.

Research on the relationship between the architecture of ecological networks and community stability has mainly focused on one type of interaction at a time, making difficult any comparison between different network types. We used a theoretical approach to show that the network architecture favoring stability fundamentally differs between trophic and mutualistic networks. A highly connected and nested architecture promotes community stability in mutualistic networks, whereas the stability of trophic networks is enhanced in compartmented and weakly connected architectures. These theoretical predictions are supported by a meta-analysis on the architecture of a large series of real pollination (mutualistic) and herbivory (trophic) networks. We conclude that strong variations in the stability of architectural patterns constrain ecological networks toward different architectures, depending on the type of interaction.

Niche and fitness differences control the outcome of competition, but determining their relative importance in invaded communities-which may be far from equilibrium-remains a pressing concern. Moreover, it is unclear whether classic approaches for studying competition, which were developed predominantly for pairs of interacting species, will fully capture dynamics in complex species assemblages. We parameterized a population-dynamic model using competition experiments of two native and three exotic species from a grassland community. We found evidence for minimal fitness differences or niche differences between the native species, leading to slow replacement dynamics and priority effects, but large fitness advantages allowed exotics to unconditionally invade natives. Priority effects driven by strong interspecific competition between exotic species drove single-species dominance by one of two exotic species in 80% of model outcomes, while a complex mixture of nonhierarchical competition and coexistence between native and exotic species occurred in the remaining 20%. Fungal infection, a commonly hypothesized coexistence mechanism, had weak fitness effects and is unlikely to substantially affect coexistence. In contrast to previous work on pairwise outcomes in largely native-dominated communities, our work supports a role for nearly neutral dynamics and priority effects as drivers of species composition in invaded communities.

Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.

Mutualistic networks have been shown to involve complex patterns of interactions among animal and plant species, including a widespread presence of nestedness. The nested structure of these webs seems to be positively correlated with higher diversity and resilience. Moreover, these webs exhibit marked measurable structural patterns, including broad distributions of connectivity, strongly asymmetrical interactions and hierarchical organization. Hierarchical organization is an especially interesting property, since it is positively correlated with biodiversity and network resilience, thus suggesting potential selection processes favouring the observed web organization. However, here we show that all these structural quantitative patterns-and nestedness in particular-can be properly explained by means of a very simple dynamical model of speciation and divergence with no selection-driven coevolution of traits. The agreement between observed and modelled networks suggests that the patterns displayed by real mutualistic webs might actually represent evolutionary spandrels.

One challenge in merging community and ecosystem ecology is to integrate the complexity of natural multitrophic communities into concepts of ecosystem functioning. Here, we combine food-web and allometry theories to demonstrate that primary production, as measured by the total nutrient uptake of the multitrophic community, is determined by vertical diversity (i.e. food web's maximum trophic level) and structure (i.e. distributions of species and their abundances and metabolic rates across trophic levels). In natural ecosystems, the community size distribution determines all these vertical patterns and thus the total nutrient uptake. Our model suggests a vertical diversity hypothesis (VDH) for ecosystem functioning in complex food webs. It predicts that, under a given nutrient supply, the total nutrient uptake increases exponentially with the maximum trophic level in the food web and it increases with its maximum body size according to a power law. The VDH highlights the effect of top-down regulation on plant nutrient uptake, which complements traditional paradigms that emphasised the bottom-up effect of nutrient supply on vertical diversity. We conclude that the VDH contributes to a synthetic framework for understanding the relationship between vertical diversity and ecosystem functioning in food webs and predicting the impacts of global changes on multitrophic ecosystems.

Body size determines a host of species traits that can affect the structure and dynamics of food webs, and other ecological networks, across multiple scales of organization. Measuring body size provides a relatively simple means of encapsulating and condensing a large amount of the biological information embedded within an ecological network. Recently, important advances have been made by incorporating body size into theoretical models that explore food web stability, the patterning of energy fluxes, and responses to perturbations. Because metabolic constraints underpin body-size scaling relationships, metabolic theory offers a potentially useful new framework within which to develop novel models to describe the structure and functioning of ecological networks and to assess the probable consequences of biodiversity change.