Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

Most studies of plant-animal mutualisms involve a small number of species. There is almost no information on the structural organization of species-rich mutualistic networks despite its potential importance for the maintenance of diversity. Here we analyze 52 mutualistic networks and show that they are highly nested; that is, the more specialist species interact only with proper subsets of those species interacting with the more generalists. This assembly pattern generates highly asymmetrical interactions and organizes the community cohesively around a central core of interactions. Thus, mutualistic networks are neither randomly assembled nor organized in compartments arising from tight, parallel specialization. Furthermore, nestedness increases with the complexity (number of interactions) of the network: for a given number of species, communities with more interactions are significantly more nested. Our results indicate a nonrandom pattern of community organization that may be relevant for our understanding of the organization and persistence of biodiversity.

In natural communities, species and their interactions are often organized as nonrandom networks, showing distinct and repeated complex patterns. A prevalent, but poorly explored pattern is ecological modularity, with weakly interlinked subsets of species (modules), which, however, internally consist of strongly connected species. The importance of modularity has been discussed for a long time, but no consensus on its prevalence in ecological networks has yet been reached. Progress is hampered by inadequate methods and a lack of large datasets. We analyzed 51 pollination networks including almost 10,000 species and 20,000 links and tested for modularity by using a recently developed simulated annealing algorithm. All networks with >150 plant and pollinator species were modular, whereas networks with <50 species were never modular. Both module number and size increased with species number. Each module includes one or a few species groups with convergent trait sets that may be considered as coevolutionary units. Species played different roles with respect to modularity. However, only 15% of all species were structurally important to their network. They were either hubs (i.e., highly linked species within their own module), connectors linking different modules, or both. If these key species go extinct, modules and networks may break apart and initiate cascades of extinction. Thus, species serving as hubs and connectors should receive high conservation priorities.coevolution ͉ compartment ͉ module ͉ nestedness ͉ species role B iodiversity encompasses not just species but also interactions among species. Within habitats, species and their interactions assemble into large, complex ecological networks. Such networks are rich in structural heterogeneity (1). Understanding network structure and its underlying causes are essential parts of any study of biodiversity and its responses to disturbances, yet it is a conceptual and methodological challenge to address these problems in highly diversified communities with thousands of interactions.Moving through an ecological network of species and their connecting links, one traverses a heterogeneous universe of link-dense and -sparse areas. Link-dense regions are termed compartments (2) or, here, modules (3), whereas link-sparse regions demarcate their boundaries. Species within a module are linked more tightly together than they are to species in other modules. The extent to which species interactions are organized into modules is termed the modularity of the network. Modularity may reflect habitat heterogeneity, divergent selection regimes, and phylogenetic clustering of closely related species (4, 5), leading to nonrandom patterns of interaction and ultimately contributing to the complexity of ecological networks. Modules with their tightly linked species may even be the long-sought key units of coevolution, in which reciprocal selection leads to trait convergence in unrelated species (6). However, modularity has been notoriously difficult to demonstrate either because of it...

The main drivers of global environmental change (CO 2 enrichment, nitrogen deposition, climate, biotic invasions and land use) cause extinctions and alter species distributions, and recent evidence shows that they exert pervasive impacts on various antagonistic and mutualistic interactions among species. In this review, we synthesize data from 688 published studies to show that these drivers often alter competitive interactions among plants and animals, exert multitrophic effects on the decomposer food web, increase intensity of pathogen infection, weaken mutualisms involving plants, and enhance herbivory while having variable effects on predation. A recurrent finding is that there is substantial variability among studies in both the magnitude and direction of effects of any given GEC driver on any given type of biotic interaction. Further, we show that higher order effects among multiple drivers acting simultaneously create challenges in predicting future responses to global environmental change, and that extrapolating these complex impacts across entire networks of species interactions yields unanticipated effects on ecosystems. Finally, we conclude that in order to reliably predict the effects of GEC on community and ecosystem processes, the greatest single challenge will be to determine how biotic and abiotic context alters the direction and magnitude of GEC effects on biotic interactions.

All Change Research on early warning signals for critical transitions in complex systems such as ecosystems, climate, and global finance systems recently has been gathering pace. At the same time, studies on complex networks are starting to reveal which architecture may cause systems to be vulnerable to systemic collapse. Scheffer et al. (p. 344 ) review how previously isolated lines of work can be connected, conclude that many critical transitions (such as escape from the poverty trap) can have positive outcomes, and highlight how the new approaches to sensing fragility can help to detect both risks and opportunities for desired change.

The main theories of biodiversity either neglect species interactions or assume that species interact randomly with each other. However, recent empirical work has revealed that ecological networks are highly structured, and the lack of a theory that takes into account the structure of interactions precludes further assessment of the implications of such network patterns for biodiversity. Here we use a combination of analytical and empirical approaches to quantify the influence of network architecture on the number of coexisting species. As a case study we consider mutualistic networks between plants and their animal pollinators or seed dispersers. These networks have been found to be highly nested, with the more specialist species interacting only with proper subsets of the species that interact with the more generalist. We show that nestedness reduces effective interspecific competition and enhances the number of coexisting species. Furthermore, we show that a nested network will naturally emerge if new species are more likely to enter the community where they have minimal competitive load. Nested networks seem to occur in many biological and social contexts, suggesting that our results are relevant in a wide range of fields.

Abstract. The mutualistic interactions between plants and the animals that pollinate them or disperse their fruits have molded the organization of Earths's biodiversity. These interactions create networks of interdependence often times involving dozens or hundreds of species. Recent research has used concepts from graph theory to characterize the architecture of these networks. Mutualistic networks are heterogeneous, nested and build upon weak and asymmetric links among species. This network architecture highly affects its robustness to perturbations such as the extinction of a species.Redes mutualistas planta-animal: la arquitectura de la biodiversidad Resumen. Las interacciones de beneficio mutuo entre las plantas y los animales que las polinizan o dispersan sus semillas han jugado un papel muy relevante en la generación de biodiversidad en la Tierra. Estas interacciones crean redes de interdependencia que suelen involucrar decenas o centenares de especies. Investigación reciente ha utilizado conceptos de la teoría de grafos para caracterizar la arquitectura de estas redes. Las redes mutualistas son heterogéneas, anidadas y construidas sobre interacciones débiles y asimétricas entre especies. La arquitectura de estas redes afecta en gran medida su robustez ante perturbaciones como la extinción de una especie.The mutualistic interactions between plants and the animals that pollinate them or disperse their seeds have molded the organization of Earths's biodiversity. Plants have created new niches for insect diversification, which in turn may have increased plant diversification. The importance of these mutually beneficial interactions can be grasped by considering that more than 90% of tree species in the tropical forests need animals to complete their life cycle. Animal extinction would result in the consequent extinction of plants.Historically, the first studies on mutualistic interactions focused on highly specialized, pairwise interactions. These examples of an almost perfect matching between the morphology of a flower and that of an insect have illustrated textbook covers since Darwin's time, but they are probably the exception rather than the norm. Mutualistic interactions may involve dozens or even hundreds of species interacting in complex ways. Progress in coevolutionary studies during the last two decades has been made by studying how small groups of species interact in a community context and how these interactions change through time and space ([9]). More recently, the physics of complex networks has provided tools and concepts to tackle entire plant-animal coevolutionary networks. These results have unambiguously concluded that mutualistic networks are highly heterogeneous (the bulk of species have a few interactions, but a few species have many more interactions than expected by chance, [6]); nested (specialists interact with proper subsets of * This paper is based on a lecture delivered by the author, at the International Symposium Mathematics for the XXIth Century, 221J. Bascompte the species ge...

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. I t is widely acknowledged that mutualistic interactions have molded biodiversity (1, 2). In the past decade, much has been learned about how communities shape coevolutionary interactions across time and space (3). However, although most studies on coevolution focus on pairs or small groups of species, recent work has highlighted the need to understand how broader networks of species coevolve (4-7). Such knowledge is critical to understanding the persistence and coevolution of highly diverse plant-animal assemblages.Recent research on the architecture of plantanimal mutualistic networks has been based mostly on qualitative data, assuming that all realized interactions are equally important (Fig. 1A) (5-7). This has precluded a deeper assessment of network structure (8) and strongly limited our understanding of its dynamic implications. To understand how mutualistic networks are organized and how such an organization affects species coexistence, we compiled from published studies and our own work 19 plantpollinator and 7 plant-frugivore quantitative networks ( Fig. 1 and Database S1). These networks range from arctic to tropical ecosystems and illustrate diverse ecological and biogeographical settings. Each network displays information on the mutual dependence or strength between each plant and animal species, mainly measured as the relative frequency of visits (9). Thus, our networks describe ecological interactions, and evolutionary inferences should be made with caution. However, frequency of visits has been shown to be a surrogate for per capita reproductive performance (10). Our results could be more directly related to coevolution when the reproductive success of one species depends directly on visitation frequency. This seems to be the case when there is a high variation of dependences among species (10). Unlike previous studies on food webs (11-16), for each plant-animal species pair, we have now two estimates of mutual dependence (defined in two adjacency matrices P and A): the dependence d P ij of plant species i on animal species j (i.e., the fraction of all animal visits coming from this particular animal species) and the dependence d A ji of animal species j on plant species i (i.e., the fraction of all visits by this animal species going to this particular plant species) (Fig. 1, B and C). Therefore, one can calcula...