Leveraging advances in machine learning for the robust classification and interpretation of networks

The ability to simulate realistic networks based on empirical data is an important task across scientific disciplines, from epidemiology to computer science. Often, simulation approaches involve selecting a suitable network generative model such as Erdös-Rényi or small-world. However, few tools are available to quantify if a particular generative model is suitable for capturing a given network structure or organization. We utilize advances in interpretable machine learning to classify simulated networks by our generative models based on various network attributes, using both primary features and their interactions. Our study underscores the significance of specific network features and their interactions in distinguishing generative models, comprehending complex network structures and the formation of real-world networks.

Evolutionary history as the main driver of cohesive groups' hierarchical organization in flea-mammal interaction networks

Cohesive species groups (components, sectors, modules, and subgraphs) represent parts of an ecological network with a substantially higher density of interactions than the surrounding parts. We investigated cohesive groups in 108 flea-mammal networks from all over the world and tested whether these groups are hierarchically organized, that is, whether groups at the higher level are composed of groups at the lower level, thus representing a network structure. We measured congruence between groups, using congruence coefficients, and asked whether the extent of hierarchical organization differs between biogeographic realms, different biomes, and different climatic zones. We also tested whether coefficients of congruence between cohesive groups are affected by environmental variables (amount of green vegetation, precipitation, and air temperature). We found that (i) cohesive groups of species in these networks are hierarchically organized and (ii) the strength of this organization differs significantly between networks from different biogeographic realms but is not generally affected by surrounding environmental conditions such as vegetation type and climate. In other words, the structure of flea-mammal networks, in terms of the hierarchical organization of cohesive groups, seems to be determined, first and foremost, by the evolutionary history of flea-mammal interactions, that is, by processes and events of the past. We conclude that the impact of evolutionary history on the network structure appeared to be stronger than that of the contemporary environment.

Potential extinction cascades in a desert ecosystem: Linking food web interactions to community viability

Desert communities are threatened with species loss due to climate change, and their resistance to such losses is unknown. We constructed a food web of the Mojave Desert terrestrial community (300 nodes, 4080 edges) to empirically examine the potential cascading effects of bird extinctions on this desert network, compared to losses of mammals and lizards. We focused on birds because they are already disappearing from the Mojave, and their relative thermal vulnerabilities are known. We quantified bottom-up secondary extinctions and evaluated the relative resistance of the community to losses of each vertebrate group. The impact of random bird species loss was relatively low compared to the consequences of mammal (causing the greatest number of cascading losses) or reptile loss, and birds were relatively less likely to be in trophic positions that could drive top-down effects in apparent competition and tri-tropic cascade motifs. An avian extinction cascade with year-long resident birds caused more secondary extinctions than the cascade involving all bird species for randomized ordered extinctions. Notably, we also found that relatively high interconnectivity among avian species has formed a subweb, enhancing network resistance to bird losses.

DNA barcoding continues to identify endangered species of shark sold as food in a globally significant shark fin trade hub

Shark fins are a delicacy consumed throughout Southeast Asia. The life history characteristics of sharks and the challenges associated with regulating fisheries and the fin trade make sharks particularly susceptible to overfishing. Here, we used DNA barcoding techniques to investigate the composition of the shark fin trade in Singapore, a globally significant trade hub. We collected 505 shark fin samples from 25 different local seafood and Traditional Chinese Medicine shops. From this, we identified 27 species of shark, three species are listed as Critically Endangered, four as Endangered and ten as Vulnerable by the International Union for Conservation of Nature (IUCN). Six species are listed on CITES Appendix II, meaning that trade must be controlled in order to avoid utilization incompatible with their survival. All dried fins collected in this study were sold under the generic term "shark fin"; this vague labelling prevents accurate monitoring of the species involved in the trade, the effective implementation of policy and conservation strategy, and could unwittingly expose consumers to unsafe concentrations of toxic metals. The top five most frequently encountered species in this study are Rhizoprionodon acutus, Carcharhinus falciformis, Galeorhinus galeus, Sphyrna lewini and Sphyrna zygaena. Accurate labelling that indicates the species of shark that a fin came from, along with details of where it was caught, allows consumers to make an informed choice on the products they are consuming. Doing this could facilitate the avoidance of species that are endangered, and similarly the consumer can choose not to purchase species that are documented to contain elevated concentrations of toxic metals.

Organization of the macroinvertebrate community in a tropical annual agroecosystem into modules

The structure of macroinvertebrate communities in agroecosystems has been assumed to be modular and organized around key herbivore pests. We characterized the macroinvertebrate community in the annual organic brassica agroecosystem in tropical central Brazil to determine if the community was a random assemblage of independent populations or was organized into repeatable multi-species components. We sampled 36 macroinvertebrate taxa associated with six organic brassica farms at biweekly intervals during the dry season during two years in the Distrito Federal, Brazil. We used an unconstrained ordination based on latent variable modeling (boral) with negative binomial population counts to analyze community composition independent of variation in sample abundance. We evaluated observed community structure by comparing it with randomized alternatives. We found that the community was not a random assemblage and consistently organized itself into two modules based around the major herbivores; one with lepidoptera and whiteflies and their associated natural enemies which was gradually replaced during the season by one with brassica aphids, aphid parasitoids and coccinellids. This analysis suggests that the historical and present-day focus on pest herbivores and their associated species in agroecosystems may be justified based on community structure.

The Structure of Ecological Networks Across Levels of Organization

Interactions connect the units of ecological systems, forming networks. Individual-based networks characterize variation in niches among individuals within populations. These individual-based networks merge with each other, forming species-based networks and food webs that describe the architecture of ecological communities. Networks at broader spatiotemporal scales portray the structure of ecological interactions across landscapes and over macroevolutionary time. Here, I review the patterns observed in ecological networks across multiple levels of biological organization. A fundamental challenge is to understand the amount of interdependence as we move from individual-based networks to species-based networks and beyond. Despite the uneven distribution of studies, regularities in network structure emerge across scales due to the fundamental architectural patterns shared by complex networks and the interplay between traits and numerical effects. I illustrate the integration of these organizational scales by exploring the consequences of the emergence of highly connected species for network structures across scales.

On neighbourhood degree sequences of complex networks

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in complex networks. We consider how to explicitly characterise important physical concepts such as similarity, heterogeneity and organization in these sequences, as well as updating the notion of hierarchical complexity to reflect previously unnoticed organizational principles. We also point out that neighbourhood degree sequences are related to a powerful subtree kernel for unlabeled graph classification. We study these newly defined sequence properties in a comprehensive array of graph models and over 200 real-world networks. We find that these indices are neither highly correlated with each other nor with classical network indices. Importantly, the sequences of a wide variety of real world networks are found to have greater similarity and organisation than is expected for networks of their given degree distributions. Notably, while biological, social and technological networks all showed consistently large neighbourhood similarity and organisation, hierarchical complexity was not a consistent feature of real world networks. Neighbourhood degree sequences are an interesting tool for describing unique and important characteristics of complex networks.

Graph drawing using tabu search coupled with path relinking

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function’s value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset.

Stability lies in flowers: Plant diversification mediating shifts in arthropod food webs

Arthropod community composition in agricultural landscapes is dependent on habitat characteristics, such as plant composition, landscape homogeneity and the presence of key resources, which are usually absent in monocultures. Manipulating agroecosystems through the insertion of in-field floral resources is a useful technique to reduce the deleterious effects of habitat simplification. Food web analysis can clarify how the community reacts to the presence of floral resources which favour ecosystem services such as biological control of pest species. Here, we reported quantitative and qualitative alterations in arthropod food web complexity due to the presence of floral resources from the Mexican marigold (Tagetes erecta L.) in a field scale lettuce community network. The presence of marigold flowers in the field successfully increased richness, body size, and the numerical and biomass abundance of natural enemies in the lettuce arthropod community, which affected the number of links, vulnerability, generality, omnivory rate and food chain length in the community, which are key factors for the stability of relationships between species. Our results reinforce the notion that diversification through insertion of floral resources may assist in preventing pest outbreaks in agroecosystems. This community approach to arthropod interactions in agricultural landscapes can be used in the future to predict the effect of different management practices in the food web to contribute with a more sustainable management of arthropod pest species.

Using arborescences to estimate hierarchicalness in directed complex networks

Complex networks are a useful tool for the understanding of complex systems. One of the emerging properties of such systems is their tendency to form hierarchies: networks can be organized in levels, with nodes in each level exerting control on the ones beneath them. In this paper, we focus on the problem of estimating how hierarchical a directed network is. We propose a structural argument: a network has a strong top-down organization if we need to delete only few edges to reduce it to a perfect hierarchy—an arborescence. In an arborescence, all edges point away from the root and there are no horizontal connections, both characteristics we desire in our idealization of what a perfect hierarchy requires. We test our arborescence score in synthetic and real-world directed networks against the current state of the art in hierarchy detection: agony, flow hierarchy and global reaching centrality. These tests highlight that our arborescence score is intuitive and we can visualize it; it is able to better distinguish between networks with and without a hierarchical structure; it agrees the most with the literature about the hierarchy of well-studied complex systems; and it is not just a score, but it provides an overall scheme of the underlying hierarchy of any directed complex network.

Link prediction in complex networks via matrix perturbation and decomposition

Link prediction in complex networks aims at predicting the missing links from available datasets which are always incomplete and subject to interfering noises. To obtain high prediction accuracy one should try to complete the missing information and at the same time eliminate the interfering noise from the datasets. Given that the global topological information of the networks can be exploited by the adjacent matrix, the missing information can be completed by generalizing the observed structure according to some consistency rule, and the noise can be eliminated by some proper decomposition techniques. Recently, two related works have been done that focused on each of the individual aspect and obtained satisfactory performances. Motivated by their complementary nature, here we proposed a new link prediction method that combines them together. Moreover, by extracting the symmetric part of the adjacent matrix, we also generalized the original perturbation method and extended our new method to weighted directed networks. Experimental studies on real networks from disparate fields indicate that the prediction accuracy of our method was considerably improved compared with either of the individual method as well as some other typical local indices.

Anthropogenic effects are associated with a lower persistence of marine food webs

Marine coastal ecosystems are among the most exposed to global environmental change, with reported effects on species biomass, species richness and length of trophic chains. By combining a biologically informed food-web model with information on anthropogenic influences in 701 sites across the Caribbean region, we show that fishing effort, human density and thermal stress anomaly are associated with a decrease in local food-web persistence. The conservation status of the site, in turn, is associated with an increase in food-web persistence. Some of these associations are explained through effects on food-web structure and total community biomass. Our results unveil a hidden footprint of human activities. Even when food webs may seem healthy in terms of the presence and abundance of their constituent species, they may be losing the capacity to withstand further environmental degradation.

Human activity is affecting the diversity and abundance of marine organisms. Here, Gilarranz et al. show that the persistence of marine food webs is reduced by the effects of fishing pressure, human density, and thermal stress.

Matching-centrality decomposition and the forecasting of new links in networks

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and centrality components provides a comprehensive and unifying quantification of their architecture. The matching term quantifies the assortative structure in which node makes links with which other node, whereas the centrality term quantifies the number of links that nodes make. We show, for a diverse set of networks, that this decomposition can provide a tight fit to observed networks. Then we provide three applications. First, we show that the model allows very accurate prediction of missing links in partially known networks. Second, when node characteristics are known, we show how the matching-centrality decomposition can be related to this external information. Consequently, it offers us a simple and versatile tool to explore how node characteristics explain network architecture. Finally, we demonstrate the efficiency and flexibility of the model to forecast the links that a novel node would create if it were to join an existing network.

Interactions between tick and transmitted pathogens evolved to minimise competition through nested and coherent networks

Natural foci of ticks, pathogens, and vertebrate reservoirs display complex relationships that are key to the circulation of pathogens and infection dynamics through the landscape. However, knowledge of the interaction networks involved in transmission of tick-borne pathogens are limited because empirical studies are commonly incomplete or performed at small spatial scales. Here, we applied the methodology of ecological networks to quantify >14,000 interactions among ticks, vertebrates, and pathogens in the western Palearctic. These natural networks are highly structured, modular, coherent, and nested to some degree. We found that the large number of vertebrates in the network contributes to its robustness and persistence. Its structure reduces interspecific competition and allows ample but modular circulation of transmitted pathogens among vertebrates. Accounting for domesticated hosts collapses the network’s modular structure, linking groups of hosts that were previously unconnected and increasing the circulation of pathogens. This framework indicates that ticks and vertebrates interact along the shared environmental gradient, while pathogens are linked to groups of phylogenetically close reservoirs.

Rich-cores in networks

A core comprises of a group of central and densely connected nodes which governs the overall behaviour of a network. It is recognised as one of the key meso-scale structures in complex networks. Profiling this meso-scale structure currently relies on a limited number of methods which are often complex and parameter dependent or require a null model. As a result, scalability issues are likely to arise when dealing with very large networks together with the need for subjective adjustment of parameters. The notion of a rich-club describes nodes which are essentially the hub of a network, as they play a dominating role in structural and functional properties. The definition of a rich-club naturally emphasises high degree nodes and divides a network into two subgroups. Here, we develop a method to characterise a rich-core in networks by theoretically coupling the underlying principle of a rich-club with the escape time of a random walker. The method is fast, scalable to large networks and completely parameter free. In particular, we show that the evolution of the core in World Trade and C. elegans networks correspond to responses to historical events and key stages in their physical development, respectively.

Structurally robust control of complex networks

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called controllers. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on complex networks including scale-free topologies. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations, and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard nonrobust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in Caenorhabditis elegans, and suggests a new direction to pursue in studies of complex networks in which control theory has a role.

Accurate similarity index based on the contributions of paths and end nodes for link prediction

Link prediction whose intent is to discover the likelihood of the existence of a link between two disconnected nodes is an important task in complex network analysis. To perform this task, a similarity-based algorithm that employs the similarities of nodes to find links is a very popular solution. However, when calculating the similarity between two nodes, most of the similarity-based algorithms only focus on the contributions of paths connecting these two nodes but ignore the influences of these two nodes themselves. Therefore, their results are not accurate enough. In this paper, a novel similarity index, called Scop, is proposed for link prediction. By directly defining the contributions of paths to their end nodes and the contributions of end nodes themselves, Scop not only distinguishes the contributions of different paths but also integrates the contributions of end nodes. Hence, Scop can obtain better performance on accuracy. Experiments on 10 networks compared with six baselines indicate that Scop is remarkably better than others.

Assessing the robustness of networks of spatial genetic variation

Habitat transformation is one of the leading drivers of biodiversity loss. The ecological effects of this transformation have mainly been addressed at the demographic level, for example, finding extinction thresholds. However, interpopulation genetic variability and the subsequent potential for adaptation can be eroded before effects are noticed on species abundances. To what degree this is the case has been difficult to evaluate, partly because of the lack of both spatially extended genetic data and an appropriate framework to map and analyse such data. Here, we extend recent work on the analysis of networks of spatial genetic variation to address the robustness of these networks in the face of perturbations. We illustrate the potential of this framework using the case study of an amphibian metapopulation. Our results show that while the disappearance of some spatial sites barely changes the modular structure of the genetic network, other sites have a much stronger effect. Interestingly, these consequences can not be anticipated using topological, static measures. Mapping these networks of spatial genetic variation will allow identifying significant evolutionary units and how they vanish, merge and reorganise following perturbations.

Probabilistic patterns of interaction: the effects of link-strength variability on food web structure

Patterns of species interactions affect the dynamics of food webs. An important component of species interactions that is rarely considered with respect to food webs is the strengths of interactions, which may affect both structure and dynamics. In natural systems, these strengths are variable, and can be quantified as probability distributions. We examined how variation in strengths of interactions can be described hierarchically, and how this variation impacts the structure of species interactions in predator-prey networks, both of which are important components of ecological food webs. The stable isotope ratios of predator and prey species may be particularly useful for quantifying this variability, and we show how these data can be used to build probabilistic predator-prey networks. Moreover, the distribution of variation in strengths among interactions can be estimated from a limited number of observations. This distribution informs network structure, especially the key role of dietary specialization, which may be useful for predicting structural properties in systems that are difficult to observe. Finally, using three mammalian predator-prey networks (two African and one Canadian) quantified from stable isotope data, we show that exclusion of link-strength variability results in biased estimates of nestedness and modularity within food webs, whereas the inclusion of body size constraints only marginally increases the predictive accuracy of the isotope-based network. We find that modularity is the consequence of strong link-strengths in both African systems, while nestedness is not significantly present in any of the three predator-prey networks.

Stability as a natural selection mechanism on interacting networks

Biological networks of interacting agents exhibit similar topological properties for a wide range of scales, from cellular to ecological levels, suggesting the existence of a common evolutionary origin. A general evolutionary mechanism based on global stability has been proposed recently  [J I Perotti, et al., Phys. Rev. Lett. 103, 108701 (2009)]. This mechanism was incorporated into a  model of a growing network of interacting agents in which each new agent's membership in the network is determined by the agent's effect on the network's global stability. In this work, we analyze different quantities that characterize the topology of the emerging networks, such as global connectivity, clustering and average nearest neighbors degree, showing that they reproduce scaling behaviors frequently observed in several biological systems. The influence of the stability selection  mechanism on the dynamics associated to the resulting network, as well as  the interplay  between some topological and functional features are also analyzed.Received: 17 July 2010; Accepted: 27 September 2010; Edited by: D. H. Zanette; Reviewed by: V. M. Eguiluz, Inst. Fisica Interdisciplinar y Sist. Complejos, Palma de Mallorca, Spain; DOI: 10.4279/PIP.020005

The assembly and disassembly of ecological networks

Global change has created a severe biodiversity crisis. Species are driven extinct at an increasing rate, and this has the potential to cause further coextinction cascades. The rate and shape of these coextinction cascades depend very much on the structure of the networks of interactions across species. Understanding network structure and how it relates to network disassembly, therefore, is a priority for system-level conservation biology. This process of network collapse may indeed be related to the process of network build-up, although very little is known about both processes and even less about their relationship. Here we review recent work that provides some preliminary answers to these questions. First, we focus on network assembly by emphasizing temporal processes at the species level, as well as the structural building blocks of complex ecological networks. Second, we focus on network disassembly as a consequence of species extinctions or habitat loss. We conclude by emphasizing some general rules of thumb that can help in building a comprehensive framework to understand the responses of ecological networks to global change.

Food web models: a plea for groups

The concept of a group is ubiquitous in biology. It underlies classifications in evolution and ecology, including those used to describe phylogenetic levels, the habitat and functional roles of organisms in ecosystems. Surprisingly, this concept is not explicitly included in simple models for the structure of food webs, the ecological networks formed by consumer-resource interactions. We present here the simplest possible model based on groups, and show that it performs substantially better than current models at predicting the structure of large food webs. Our group-based model can be applied to different types of biological and non-biological networks, and for the first time merges in the same framework two important notions in network theory: that of compartments (sets of highly interacting nodes) and that of roles (sets of nodes that have similar interaction patterns). This model provides a basis to examine the significance of groups in biological networks and to develop more accurate models for ecological network structure. It is especially relevant at a time when a new generation of empirical data is providing increasingly large food webs.

Quantitative analysis of the local structure of food webs

We analyze the local structure of model and empirical food webs through the statistics of three-node subgraphs. We study analytically and numerically the number of appearances of each subgraph for a simple model of food web topology, the so-called generalized cascade model, and compare them with 17 empirical community food webs from a variety of environments, including aquatic, estuarine, and terrestrial ecosystems. We obtain analytical expressions for the probability of appearances of each subgraph in the model, and also for randomizations of the model that preserve species' numbers of prey and number of predators; their difference allows us to quantify which subgraphs are over- or under-represented in both the model and the empirical food webs. We find agreement between the model predictions and the empirical results. These results indicate that simple models such as the generalized cascade can provide a good description not only of the global topology of food webs, as recently shown, but also of its local structure.

Ecological networks and their fragility

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.

Examining the potential effects of species aggregation on the network structure of food webs

One of the key measures that have been used to describe the topological properties of complex networks is the "degree distribution", which is a measure that describes the frequency distribution of number of links per node. Food webs are complex ecological networks that describe the trophic relationships among species in a community, and the topological properties of empirical food webs, including degree distributions, have been examined previously. Previously, the "niche model" has been shown to accurately predict degree distributions of empirical food webs, however, the niche model-generated food webs were referenced against empirical food webs that had their species grouped together based on their taxonomic and/or trophic relationships (aggregated food webs). Here, we explore the effects of species aggregation on the ability of the niche model to predict the total- (sum of prey and predator links per node), in- (number of predator links per node), and out- (number of prey links per node) degree distributions of empirical food webs by examining two food webs that can be aggregated at different levels of resolution. The results showed that (1) the cumulative total- and out-degree distributions were consistent with the niche model predictions when the species were aggregated, (2) when the species were disaggregated (i.e., higher resolution), there were mixed conclusions with regards to the niche model's ability to predict total- and out-degree distributions, (3) the model's ability to predict the in-degree distributions of the two food webs was generally inadequate. Although it has been argued that universal functional form based on the niche model could describe the degree distribution patterns of empirical food webs, we believe there are some limitations to the model's ability to accurately predict the structural properties of food webs.

Species loss and secondary extinctions in simple and complex model communities

1. The loss of a species from an ecological community can trigger a cascade of secondary extinctions. Here we investigate how the complexity (connectance) of model communities affects their response to species loss. Using dynamic analysis based on a global criterion of persistence (permanence) and topological analysis we investigate the extent of secondary extinctions following the loss of different kinds of species. 2. We show that complex communities are, on average, more resistant to species loss than simple communities: the number of secondary extinctions decreases with increasing connectance. However, complex communities are more vulnerable to loss of top predators than simple communities. 3. The loss of highly connected species (species with many links to other species) and species at low trophic levels triggers, on average, the largest number of secondary extinctions. The effect of the connectivity of a species is strongest in webs with low connectance. 4. Most secondary extinctions are due to direct bottom-up effects: consumers go extinct when their resources are lost. Secondary extinctions due to trophic cascades and disruption of predator-mediated coexistence also occur. Secondary extinctions due to disruption of predator-mediated coexistence are more common in complex communities than in simple communities, while bottom-up and top-down extinction cascades are more common in simple communities. 5. Topological analysis of the response of communities to species loss always predicts a lower number of secondary extinctions than dynamic analysis, especially in food webs with high connectance.

Using community viability analysis to identify fragile systems and keystone species

Owing to interdependences among species in ecological communities, the loss of one species can trigger a cascade of secondary extinctions with potentially dramatic effects on the functioning and stability of the community. It is, therefore, important to assess the risk and likely extent of secondary extinctions. Community viability analysis is a new technique that can be used to accomplish this goal. The analysis can also be used to identify fragile community structures and keystone species and, hence, to provide guidelines for conservation priorities. Here, we describe the principles underlying community viability analysis and review its contributions to our understanding of the response of ecological communities to species loss.

Random initial condition in small Barabasi-Albert networks and deviations from the scale-free behavior

Barabasi-Albert networks are constructed by adding nodes via preferential attachment to an initial core of nodes. We study the topology of small scale-free networks as a function of the size and average connectivity of their initial random core. We show that these two parameters may strongly affect the tail of the degree distribution, by consistently leading to broad-scale or single-scale networks. In particular, we argue that the size of the initial network core and its density of connections may be the main responsible for the exponential truncation of the power-law behavior observed in some small scale-free networks.