Ranking species in mutualistic networks

On the structure of species-function participation in multilayer ecological networks

Understanding how biotic interactions shape ecosystems and impact their functioning, resilience and biodiversity has been a sustained research priority in ecology. Yet, traditional assessments of ecological complexity typically focus on species-species interactions that mediate a particular function (e.g., pollination), overlooking both the synergistic effect that multiple functions might develop as well as the resulting species-function participation patterns that emerge in ecosystems that harbor multiple ecological functions. Here we propose a mathematical framework that integrates various types of biotic interactions observed between different species. Its application to recently collected data of an islet ecosystem-reporting 1537 interactions between 691 plants, animals and fungi across six different functions (pollination, herbivory, seed dispersal, decomposition, nutrient uptake, and fungal pathogenicity)-unveils a non-random, nested structure in the way plant species participate across different functions. The framework further allows us to identify a ranking of species and functions, where woody shrubs and fungal decomposition emerge as keystone actors whose removal have a larger-than-random effect on secondary extinctions. The dual insight-from species and functional perspectives-offered by the framework opens the door to a richer quantification of ecosystem complexity and to better calibrate the influence of multifunctionality on ecosystem functioning and biodiversity.

Mapping job fitness and skill coherence into wages: an economic complexity analysis

Leveraging the discrete skill and knowledge worker requirements of each occupation provided by O*NET, our empirical approach employs network-based tools from the Economic Complexity framework to characterize the US occupational network. This approach provides insights into the interplay between wages and the complexity or relatedness of the skill sets within each occupation, complementing conventional human capital frameworks. Our empirical strategy is threefold. First, we construct the Job and Skill Progression Networks, where nodes represent jobs (skills) and a link between two jobs (skills) indicates statistically significant co-occurrence of skills required to carry out those two jobs, that can be useful tools to identify job-switching paths and skill complementarities Second, by harnessing the Fitness and Complexity algorithm, we define a data-driven skill-based complexity measure of jobs that positively maps, but with interesting deviations, into wages and in the bottom-up and broad abstract/manual and routine/non-routine job characterisations, however providing a continuous and endogenous metric to assess the degree of complexity of each occupational skill-set. Third, building on relatedness and corporate coherence metrics, we introduce a measure of each job's skill coherence, that negatively maps into wages. Our findings may inform policymakers and employers on designing more effective labour market policies and training schemes, that, rather than fostering hyper-specialization, should favor the acquisition of complex and "uncoherent" skill sets, enabling workers to more easily move throughout the job and skill progression networks and make informed career choices decisions while unlocking higher wage opportunities.

The structure and robustness of ecological networks with two interaction types

Until recently, most ecological network analyses investigating the effects of species' declines and extinctions have focused on a single type of interaction (e.g. feeding). In nature, however, diverse interactions co-occur, each of them forming a layer of a 'multilayer' network. Data including information on multiple interaction types has recently started to emerge, giving us the opportunity to have a first glance at possible commonalities in the structure of these networks. We studied the structural features of 44 tripartite ecological networks from the literature, each composed of two layers of interactions (e.g. herbivory and pollination), and investigated their robustness to species losses. Considering two interactions simultaneously, we found that the robustness of the whole community is a combination of the robustness of the two ecological networks composing it. The way in which the layers of interactions are connected to each other affects the interdependence of their robustness. In many networks, this interdependence is low, suggesting that restoration efforts would not automatically propagate through the whole community. Our results highlight the importance of considering multiple interactions simultaneously to better gauge the robustness of ecological communities to species loss and to more reliably identify key species that are important for the persistence of ecological communities.

Evading tipping points in socio-mutualistic networks via structure mediated optimal strategy

The threat of large-scale pollinator decline is increasing globally under stress from multiple anthropogenic pressures. Traditional approaches have focused on managing endangered species at an individual level, in which the effect of complex interactions such as mutualism and competition are amiss. Here, we develop a coupled socio-mutualistic network model that captures the change in pollinator dynamics with human conservation opinion in a deteriorating environment. We show that the application of social norm (or conservation) at the pollinator nodes is fit to prevent sudden community collapse in representative networks of varied topology. Whilst primitive strategies have focused on regulating abundance as a mitigation strategy, the role of network structure has been largely overlooked. Here, we develop a novel network structure-mediated conservation strategy to find the optimal set of nodes on which norm implementation successfully prevents community collapse. We find that networks of intermediate nestedness require conservation at a minimum number of nodes to prevent a community collapse. We claim the robustness of the optimal conservation strategy (OCS) after validation on several simulated and empirical networks of varied complexity against a broad range of system parameters. Dynamical analysis of the reduced model shows that incorporating social norms allows the pollinator abundance to grow that would have otherwise crossed a tipping point and undergo extinction. Together, this novel means OCS provides a potential plan of action for conserving plant-pollinator networks bridging the gap between research in mutualistic networks and conservation ecology.

Quantifying the complexity and similarity of chess openings using online chess community data

Chess is a centuries-old game that continues to be widely played worldwide. Opening Theory is one of the pillars of chess and requires years of study to be mastered. In this paper, we use the games played in an online chess platform to exploit the "wisdom of the crowd" and answer questions traditionally tackled only by chess experts. We first define a relatedness network of chess openings that quantifies how similar two openings are to play. Using this network, we identify communities of nodes corresponding to the most common opening choices and their mutual relationships. Furthermore, we demonstrate how the relatedness network can be used to forecast future openings players will start to play, with back-tested predictions outperforming a random predictor. We then apply the Economic Fitness and Complexity algorithm to measure the difficulty of openings and players' skill levels. Our study not only provides a new perspective on chess analysis but also opens the possibility of suggesting personalized opening recommendations using complex network theory.

Rising temperature drives tipping points in mutualistic networks

The effect of climate warming on species' physiological parameters, including growth rate, mortality rate and handling time, is well established from empirical data. However, with an alarming rise in global temperature more than ever, predicting the interactive influence of these changes on mutualistic communities remains uncertain. Using 139 real plant-pollinator networks sampled across the globe and a modelling approach, we study the impact of species' individual thermal responses on mutualistic communities. We show that at low mutualistic strength plant-pollinator networks are at potential risk of rapid transitions at higher temperatures. Evidently, generalist species play a critical role in guiding tipping points in mutualistic networks. Further, we derive stability criteria for the networks in a range of temperatures using a two-dimensional reduced model. We identify network structures that can ascertain the delay of a community collapse. Until the end of this century, on account of increasing climate warming many real mutualistic networks are likely to be under the threat of sudden collapse, and we frame strategies to mitigate this. Together, our results indicate that knowing individual species' thermal responses and network structure can improve predictions for communities facing rapid transitions.

Predicting cascading extinctions and efficient restoration strategies in plant-pollinator networks via generalized positive feedback loops

The extinction of a species in a plant-pollinator mutualistic community can cause cascading effects and lead to major biodiversity loss. The ecologically important task of predicting the severity of the cascading effects is made challenging by the complex network of interactions among the species. In this work, we analyze an ensemble of models of communities of plant and pollinator species. These models describe the mutualistic inter-species interactions by Boolean threshold functions. We show that identifying generalized positive feedback loops can help pinpoint the species whose extinction leads to catastrophic and substantial damage to the whole community. We compare these results with the damage percentage caused by the loss of species identified as important by previously studied structural measures and show that positive feedback loops and the information gained from them can identify certain crucial species that the other measures fail to find. We also suggest mitigation measures for two specific purposes: (1) prevent the damage to the community by protecting a subset of the species, and (2) restore the community after the damage by restoring a subset of species. Our analyses indicate that the generalized positive feedback loops predict the most efficient strategies to achieve these purposes. The correct identification of species in each category has important implications for conservation efforts and developing community management strategies.

The criticality of tourism development, economic complexity, and country security on ecological footprint

What kinds of countries are likely to be prosperous and have a sustainable environment at the same time? How might countries reorient their policy setting to be more capable of suppressing environmental degradation? To explore these questions, this research examines data from 99 countries for 2006-2017, takes the six major forms of ecological footprint (EF) as indicators of environmental quality, and probes the environmental Kuznets curve (EKC) hypothesis via quantile regression approach. We find that tourism development leads to greater environmental degradation, with tourism development particularly corresponding to more usage of carbon absorption land and cropland. The lower the country security is, the better is the environmental quality. Economic complexity also worsens environmental quality. However, country security weakens the negative influence of tourism development and economic complexity on environmental quality, specifying that better country security stalls the negative impact of tourism and economic complexity on environmental quality. Results mostly support the tourism- and country security-induced EKC hypotheses in fishing footprint, whereas economic complexity-induced EKC is generally validated in cropland footprint. Finally, we present that tourism arrivals, economic complexity, and country security have varying impacts across diverse ecological footprint quantiles.

Asymmetric Relatedness from Partial Correlation

Relatedness is a key concept in economic complexity, since the assessment of the similarity between industrial sectors enables policymakers to design optimal development strategies. However, among the different ways to quantify relatedness, a measure that takes explicitly into account the time correlation structure of exports is still lacking. In this paper, we introduce an asymmetric definition of relatedness by using statistically significant partial correlations between the exports of economic sectors and we apply it to a recently introduced database that integrates the export of physical goods with the export of services. Our asymmetric relatedness is obtained by generalising a recently introduced correlation-filtering algorithm, the partial correlation planar graph, in order to allow its application on multi-sample and multi-variate datasets, and in particular, bipartite temporal networks. The result is a network of economic activities whose links represent the respective influence in terms of temporal correlations; we also compute the statistical confidence of the edges in the network via an adapted bootstrapping procedure. We find that the underlying influence structure of the system leads to the formation of intuitively-related clusters of economic sectors in the network, and to a relatively strong assortative mixing of sectors according to their complexity. Moreover, hub nodes tend to form more robust connections than those in the periphery.

Herbaceous perennial ornamental plants can support complex pollinator communities

Human-designed landscapes can host diverse pollinator communities, and the availability of floral resources is central to supporting insect biodiversity in highly modified environments. However, some urban landscapes have relatively few pollinator-attractive plant species and management in urban environments rarely considers the function of these plants in generating and supporting a stable ecological community. Evaluations of 25 cultivars within five commercially popular herbaceous perennial ornamental plant genera (Agastache, Echinacea, Nepeta, Rudbeckia, and Salvia) revealed variation in the total and proportional abundance of visitors attracted. These varieties supported multiple pollinator functional groups, however bees were the primary visitors to in this system. Cultivars were assessed according to their function within a plant–pollinator network. Comparisons of artificial networks created with the six most attractive and six least attractive cultivars demonstrated that a planting scheme using the most attractive cultivars would attract nearly four times as many bee species, including several specialists and rare species. Plant diversity in the landscape was correlated with abundance and diversity of pollinator visitors, demonstrating that community context shapes a plant’s relative attractiveness to pollinators. We conclude that herbaceous perennial cultivars can support an abundance and diversity of pollinator visitors, however, planting schemes should take into consideration the effects of cultivar, landscape plant diversity, floral phenology, floral area, and contribution to a stable ecological community.

Kindergarten Children’s Perception about the Ecological Roles of Living Organisms

Young children will inherit the biosphere; therefore, it is crucial that they recognize the importance of all living organisms based on their intrinsic value and ecosystem function, not only on their “cuteness”. However, children’s knowledge about the interdependence among organisms has been little investigated. We interviewed 56 kindergarten children (5–6 years old) in Norway. The aim of the study was to investigate their perception of the importance for nature of six organisms, representing different trophic levels of food webs (producers, consumers, decomposers) and providing different ecosystem services (production, decomposition, and pollination). There was no difference in ranking between sexes or between ordinary and farm-based kindergartens. Bumblebees and earthworms were perceived as the most important organisms, followed by squirrel, trees, and wolf. None of the children recognized the ecological role of mushrooms. Our results show that, although upon completing kindergarten many children had gained an early understanding of the role of different organisms in nature, they missed the importance of plants and fungi. Kindergarten children’s “fungi blindness” might reflect a neglect of the public for this extremely important, diverse, and dominating taxon. We should therefore put more emphasis in raising awareness about the interdependence among trophic levels in food webs.

Measuring nestedness: A comparative study of the performance of different metrics

Nestedness is a property of interaction networks widely observed in natural mutualistic communities, among other systems. A perfectly nested network is characterized by the peculiarity that the interactions of any node form a subset of the interactions of all nodes with higher degree. Despite a widespread interest on this pattern, no general consensus exists on how to measure it. Instead, several nestedness metrics, based on different but not necessarily independent properties of the networks, coexist in the literature, blurring the comparison between ecosystems. In this work, we present a detailed critical study of the behavior of six nestedness metrics and the variants of two of them. In order to evaluate their performance, we compare the obtained values of the nestedness of a large set of real networks among them and against a maximum-entropy and maximum-likelihood null model. We also analyze the dependencies of each metrics on different network parameters, as size, fill, and eccentricity. Our results point out, first, that the metrics do not rank networks universally in terms of their degree of nestedness. Furthermore, several metrics show significant dependencies on the network properties considered. The study of these dependencies allows us to understand some of the observed systematic shifts against the null model. Altogether, this paper intends to provide readers with a critical guide on how to measure nestedness patterns, by explaining the functioning of several metrics and disclosing their qualities and flaws. Besides, we also aim to extend the application of null models based on maximum entropy to the scarcely explored area of ecological networks. Finally, we provide a fully documented repository that allows constructing the null model and calculating the studied nestedness indexes. In addition, it provides the probability matrices to build the null model for a large dataset of more than 200 bipartite networks.

Economic complexity of prefectures in Japan

Every nation prioritizes the inclusive economic growth and development of all regions. However, we observe that economic activities are clustered in space, which results in a disparity in per-capita income among different regions. A complexity-based method was proposed by Hidalgo and Hausmann [PNAS 106, 10570-10575 (2009)] to explain the large gaps in per-capita income across countries. Although there have been extensive studies on countries’ economic complexity using international export data, studies on economic complexity at the regional level are relatively less studied. Here, we study the industrial sector complexity of prefectures in Japan based on the basic information of more than one million firms. We aggregate the data as a bipartite network of prefectures and industrial sectors. We decompose the bipartite network as a prefecture-prefecture network and sector-sector network, which reveals the relationships among them. Similarities among the prefectures and among the sectors are measured using a metric. From these similarity matrices, we cluster the prefectures and sectors using the minimal spanning tree technique. The computed economic complexity index from the structure of the bipartite network shows a high correlation with macroeconomic indicators, such as per-capita gross prefectural product and prefectural income per person. We argue that this index reflects the present economic performance and hidden potential of the prefectures for future growth.

Minimal fatal shocks in multistable complex networks

Multistability is a common phenomenon which naturally occurs in complex networks. Often one of the coexisting stable states can be identified as being the desired one for a particular application. We present here a global approach to identify the minimal perturbation which will instantaneously kick the system out of the basin of attraction of its desired state and hence induce a critical or fatal transition we call shock-tipping. The corresponding Minimal Fatal Shock is a vector whose length can be used as a global stability measure and whose direction in state space allows us to draw conclusions on weaknesses of the network corresponding to critical network motifs. We demonstrate this approach in plant-pollinator networks and the power grid of Great Britain. In both system classes, tree-like substructures appear to be the most vulnerable with respect to the minimal shock perturbation.

Reconciling contrasting views on economic complexity

Summarising the complexity of a country's economy in a single number is the holy grail for scholars engaging in data-based economics. In a field where the Gross Domestic Product remains the preferred indicator for many, economic complexity measures, aiming at uncovering the productive knowledge of countries, have been stirring the pot in the past few years. The commonly used methodologies to measure economic complexity produce contrasting results, undermining their acceptance and applications. Here we show that these methodologies - apparently conflicting on fundamental aspects - can be reconciled by adopting a neat mathematical perspective based on linear-algebra tools within a bipartite-networks framework. The obtained results shed new light on the potential of economic complexity to trace and forecast countries' innovation potential and to interpret the temporal dynamics of economic growth, possibly paving the way to a micro-foundation of the field.

Network Analysis of Murine Cortical Dynamics Implicates Untuned Neurons in Visual Stimulus Coding

Unbiased and dense sampling of large populations of layer 2/3 pyramidal neurons in mouse primary visual cortex (V1) reveals two functional sub-populations: neurons tuned and untuned to drifting gratings. Whether functional interactions between these two groups contribute to the representation of visual stimuli is unclear. To examine these interactions, we summarize the population partial pairwise correlation structure as a directed and weighted graph. We find that tuned and untuned neurons have distinct topological properties, with untuned neurons occupying central positions in functional networks (FNs). Implementation of a decoder that utilizes the topology of these FNs yields accurate decoding of visual stimuli. We further show that decoding performance degrades comparably following manipulations of either tuned or untuned neurons. Our results demonstrate that untuned neurons are an integral component of V1 FNs and suggest that network interactions contain information about the stimulus that is accessible to downstream elements.

K-core robustness in ecological and financial networks

In many real-world networks, the ability to withstand targeted or global attacks; extinctions; or shocks is vital to the survival of the network itself, and of dependent structures such as economies (for financial networks) or even the planet (for ecosystems). Previous attempts to characterise robustness include nestedness of mutualistic networks or exploration of degree distribution. In this work we present a new approach for characterising the stability and robustness of networks with all-positive interactions by studying the distribution of the k-shell of the underlying network. We find that high occupancy of nodes in the inner and outer k-shells and low occupancy in the middle shells of financial and ecological networks (yielding a "U-shape" in a histogram of k-shell occupancy) provide resilience against both local targeted and global attacks. Investigation of this highly-populated core gives insights into the nature of a network (such as sharp transitions in the core composition of the stock market from a mix of industries to domination by one or two in the mid-1990s) and allow predictions of future network stability, e.g., by monitoring populations of "core" species in an ecosystem or noting when stocks in the core-dominant sector begin to move in lock-step, presaging a dramatic move in the market. Moreover, this "U-shape" recalls core-periphery structure, seen in a wide range of networks including opinion and internet networks, suggesting that the "U-shaped" occupancy histogram and its implications for network health may indeed be universal.

The nested structural organization of the worldwide trade multi-layer network

Nestedness has traditionally been used to detect assembly patterns in meta-communities and networks of interacting species. Attempts have also been made to uncover nested structures in international trade, typically represented as bipartite networks in which connections can be established between countries (exporters or importers) and industries. A bipartite representation of trade, however, inevitably neglects transactions between industries. To fully capture the organization of the global value chain, we draw on the World Input-Output Database and construct a multi-layer network in which the nodes are the countries, the layers are the industries, and links can be established from sellers to buyers within and across industries. We define the buyers' and sellers' participation matrices in which the rows are the countries and the columns are all possible pairs of industries, and then compute nestedness based on buyers' and sellers' involvement in transactions between and within industries. Drawing on appropriate null models that preserve the countries' or layers' degree distributions in the original multi-layer network, we uncover variations of country- and transaction-based nestedness over time, and identify the countries and industries that most contributed to nestedness. We discuss the implications of our findings for the study of the international production network and other real-world systems.

Complexity of Products: The Effect of Data Regularisation

Among several developments, the field of Economic Complexity (EC) has notably seen the introduction of two new techniques. One is the Bootstrapped Selective Predictability Scheme (SPSb), which can provide quantitative forecasts of the Gross Domestic Product of countries. The other, Hidden Markov Model (HMM) regularisation, denoises the datasets typically employed in the literature. We contribute to EC along three different directions. First, we prove the convergence of the SPSb algorithm to a well-known statistical learning technique known as Nadaraya-Watson Kernel regression. The latter has significantly lower time complexity, produces deterministic results, and it is interchangeable with SPSb for the purpose of making predictions. Second, we study the effects of HMM regularization on the Product Complexity and logPRODY metrics, for which a model of time evolution has been recently proposed. We find confirmation for the original interpretation of the logPRODY model as describing the change in the global market structure of products with new insights allowing a new interpretation of the Complexity measure, for which we propose a modification. Third, we explore new effects of regularisation on the data. We find that it reduces noise, and observe for the first time that it increases nestedness in the export network adjacency matrix.

The Middle-Income Trap and the Coping Strategies From Network-Based Perspectives

When a developing country reaches a relatively average income level, it often stops growing further and its income does not improve. This is known as the middle-income trap. How to overcome this trap is a longstanding problem for developing countries, and has been studied in various research fields. In this work, we use the Fitness-Complexity method (FCM) to analyze the common characteristics of the countries that successfully get through the middle-income trap, and show the origin of the middle-income trap based on the international trade network. In the analysis, a novel method is proposed to characterize the interdependency between products. The results show that some middle-complexity products depend much on each other, which indicates that developing countries should focus on them simultaneously, implying high difficulty to escape the middle-income trap. To tackle the middle-income trap, developing countries should learn experiences from developed countries that share similar development history. we then design an effective method to evaluate the similarity between countries and recommend developed countries to a certain developing country. The effectiveness of our method is validated in the international trade network.

A New and Stable Estimation Method of Country Economic Fitness and Product Complexity

We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new metric is parameter free. This new map almost reproduces the results of the original homogeneous metrics already defined in literature and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm involved.

Nestedness Maximization in Complex Networks through the Fitness-Complexity Algorithm

Nestedness refers to the structural property of complex networks that the neighborhood of a given node is a subset of the neighborhoods of better-connected nodes. Following the seminal work by Patterson and Atmar (1986), ecologists have been long interested in revealing the configuration of maximal nestedness of spatial and interaction matrices of ecological communities. In ecology, the BINMATNEST genetic algorithm can be considered as the state-of-the-art approach for this task. On the other hand, the fitness-complexity ranking algorithm has been recently introduced in the economic complexity literature with the original goal to rank countries and products in World Trade export networks. Here, by bringing together quantitative methods from ecology and economic complexity, we show that the fitness-complexity algorithm is highly effective in the nestedness maximization task. More specifically, it generates matrices that are more nested than the optimal ones by BINMATNEST for 61.27% of the analyzed mutualistic networks. Our findings on ecological and World Trade data suggest that beyond its applications in economic complexity, the fitness-complexity algorithm has the potential to become a standard tool in nestedness analysis.

Technology networks: the autocatalytic origins of innovation

We analyse the autocatalytic structure of technological networks and evaluate its significance for the dynamics of innovation patenting. To this aim, we define a directed network of technological fields based on the International Patents Classification, in which a source node is connected to a receiver node via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random. We show that the evolution of the technology network is compatible with the presence of a growing autocatalytic structure, i.e. a portion of the network in which technological fields mutually benefit from being connected to one another. We further show that technological fields in the core of the autocatalytic set display greater fitness, i.e. they tend to appear in a greater number of patents, thus suggesting the presence of positive spillovers as well as positive reinforcement. Finally, we observe that core shifts take place whereby different groups of technology fields alternate within the autocatalytic structure; this points to the importance of recombinant innovation taking place between close as well as distant fields of the hierarchical classification of technological fields.

Revealing in-block nestedness: Detection and benchmarking

As new instances of nested organization-beyond ecological networks-are discovered, scholars are debating the coexistence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being solved, mainly for two reasons. First, nestedness and modularity appear to emerge from two contradictory dynamics, cooperation and competition. Second, existing methods to assess the presence of nestedness and modularity are flawed when it comes to the evaluation of concurrently nested and modular structures. In this work, we tackle the latter problem, presenting the concept of in-block nestedness, a structural property determining to what extent a network is composed of blocks whose internal connectivity exhibits nestedness. We then put forward a set of optimization methods that allow us to identify such organization successfully, in synthetic and in a large number of real networks. These findings challenge our understanding of the topology of ecological and social systems, calling for new models to explain how such patterns emerge.

Ranking of critical species to preserve the functionality of mutualistic networks using the k-core decomposition

Background

Network analysis has become a relevant approach to analyze cascading species extinctions resulting from perturbations on mutualistic interactions as a result of environmental change. In this context, it is essential to be able to point out key species, whose stability would prevent cascading extinctions, and the consequent loss of ecosystem function. In this study, we aim to explain how the k-core decomposition sheds light on the understanding the robustness of bipartite mutualistic networks.

Methods

We defined three k-magnitudes based on the k-core decomposition: k-radius, k-degree, and k-risk. The first one, k-radius, quantifies the distance from a node to the innermost shell of the partner guild, while k-degree provides a measure of centrality in the k-shell based decomposition. k-risk is a way to measure the vulnerability of a network to the loss of a particular species. Using these magnitudes we analyzed 89 mutualistic networks involving plant pollinators or seed dispersers. Two static extinction procedures were implemented in which k-degree and k-risk were compared against other commonly used ranking indexes, as for example MusRank, explained in detail in Material and Methods.

Results

When extinctions take place in both guilds, k-risk is the best ranking index if the goal is to identify the key species to preserve the giant component. When species are removed only in the primary class and cascading extinctions are measured in the secondary class, the most effective ranking index to identify the key species to preserve the giant component is k-degree. However, MusRank index was more effective when the goal is to identify the key species to preserve the greatest species richness in the second class.

Discussion

The k-core decomposition offers a new topological view of the structure of mutualistic networks. The new k-radius, k-degree and k-risk magnitudes take advantage of its properties and provide new insight into the structure of mutualistic networks. The k-risk and k-degree ranking indexes are especially effective approaches to identify key species to preserve when conservation practitioners focus on the preservation of ecosystem functionality over species richness.

The complex dynamics of products and its asymptotic properties

We analyse global export data within the Economic Complexity framework. We couple the new economic dimension Complexity, which captures how sophisticated products are, with an index called logPRODY, a measure of the income of the respective exporters. Products' aggregate motion is treated as a 2-dimensional dynamical system in the Complexity-logPRODY plane. We find that this motion can be explained by a quantitative model involving the competition on the markets, that can be mapped as a scalar field on the Complexity-logPRODY plane and acts in a way akin to a potential. This explains the movement of products towards areas of the plane in which the competition is higher. We analyse market composition in more detail, finding that for most products it tends, over time, to a characteristic configuration, which depends on the Complexity of the products. This market configuration, which we called asymptotic, is characterized by higher levels of competition.

Emergence of consensus as a modular-to-nested transition in communication dynamics

Online social networks have transformed the way in which humans communicate and interact, leading to a new information ecosystem where people send and receive information through multiple channels, including traditional communication media. Despite many attempts to characterize the structure and dynamics of these techno-social systems, little is known about fundamental aspects such as how collective attention arises and what determines the information life-cycle. Current approaches to these problems either focus on human temporal dynamics or on semiotic dynamics. In addition, as recently shown, information ecosystems are highly competitive, with humans and memes striving for scarce resources -visibility and attention, respectively. Inspired by similar problems in ecology, here we develop a methodology that allows to cast all the previous aspects into a compact framework and to characterize, using microblogging data, information-driven systems as mutualistic networks. Our results show that collective attention around a topic is reached when the user-meme network self-adapts from a modular to a nested structure, which ultimately allows minimizing competition and attaining consensus. Beyond a sociological interpretation, we explore such resemblance to natural mutualistic communities via well-known dynamics of ecological systems.

Does a Species' Extinction-Proneness Predict Its Contribution to Nestedness? A Test Using a Sunbird-Tree Visitation Network

Animal pollinators and the plants they pollinate depend on networks of mutualistic partnerships and more broadly on the stability of such networks. Based mainly on insect-plant visitation networks, theory predicts that species that are most prone to extinction contribute the most to nestedness, however empirical tests are rare. We used a sunbird-tree visitation network within which were both extinction prone vs non extinction prone sunbird species to test the idea. We predicted that the extinction prone species would contribute the most to nestedness. Using local abundance as a proxy for extinction risk we considered that locally rare sunbird species, by virtue of their small population size and associated demographic stochasticity to be more at risk of extinction than the common species. Our network was not strongly nested and all sunbird species made similar contributions to nestedness, so that in our empirical test, extinction proneness did not predict contribution to nestedness. The consequences of this finding remain unclear. It may be that network theory based on plant-insect mutualisms is not widely applicable and does not work for tree- sunbird mutualistic networks. Alternatively it may be that our network was too small to provide results with any statistical power. Without doubt our study highlights the problems faced when testing network theory in the field; a plethora of ecological considerations can variously impact on results.

A Data Driven Network Approach to Rank Countries Production Diversity and Food Specialization

The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science to disentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use country specific food production data to study binary and weighted topological properties of the bipartite country-food production matrix. This country-food production matrix can be: 1) transformed into overlap matrices which embed information regarding shared production of products among countries, and or shared countries for individual products, 2) identify subsets of countries which produce similar commodities or subsets of commodities shared by a given country allowing for visualization of correlations in large networks, and 3) used to rank country fitness (the ability to produce a diverse array of products weighted on the type of food commodities) and food specialization (quantified on the number of countries producing a specific food product weighted on their fitness). Our results show that, on average, countries with high fitness produce both low and high specializion food commodities, whereas nations with low fitness tend to produce a small basket of diverse food products, typically comprised of low specializion food commodities.

System crash as dynamics of complex networks

Complex systems, from animal herds to human nations, sometimes crash drastically. Although the growth and evolution of systems have been extensively studied, our understanding of how systems crash is still limited. It remains rather puzzling why some systems, appearing to be doomed to fail, manage to survive for a long time whereas some other systems, which seem to be too big or too strong to fail, crash rapidly. In this contribution, we propose a network-based system dynamics model, where individual actions based on the local information accessible in their respective system structures may lead to the "peculiar" dynamics of system crash mentioned above. Extensive simulations are carried out on synthetic and real-life networks, which further reveal the interesting system evolution leading to the final crash. Applications and possible extensions of the proposed model are discussed.

Intervality and coherence in complex networks

Food webs-networks of predators and prey-have long been known to exhibit "intervality": species can generally be ordered along a single axis in such a way that the prey of any given predator tend to lie on unbroken compact intervals. Although the meaning of this axis-usually identified with a "niche" dimension-has remained a mystery, it is assumed to lie at the basis of the highly non-trivial structure of food webs. With this in mind, most trophic network modelling has for decades been based on assigning species a niche value by hand. However, we argue here that intervality should not be considered the cause but rather a consequence of food-web structure. First, analysing a set of 46 empirical food webs, we find that they also exhibit predator intervality: the predators of any given species are as likely to be contiguous as the prey are, but in a different ordering. Furthermore, this property is not exclusive of trophic networks: several networks of genes, neurons, metabolites, cellular machines, airports, and words are found to be approximately as interval as food webs. We go on to show that a simple model of food-web assembly which does not make use of a niche axis can nevertheless generate significant intervality. Therefore, the niche dimension (in the sense used for food-web modelling) could in fact be the consequence of other, more fundamental structural traits. We conclude that a new approach to food-web modelling is required for a deeper understanding of ecosystem assembly, structure, and function, and propose that certain topological features thought to be specific of food webs are in fact common to many complex networks.

Moderation is best: effects of grazing intensity on plant--flower visitor networks in Mediterranean communities

The structure of pollination networks is an important indicator of ecosystem stability and functioning. Livestock grazing is a frequent land use practice that directly affects the abundance and diversity of flowers and pollinators and, therefore, may indirectly affect the structure of pollination networks. We studied how grazing intensity affected the structure of plant-flower visitor networks along a wide range of grazing intensities by sheep and goats, using data from 11 Mediterranean plant-flower visitor communities from Lesvos Island, Greece. We hypothesized that intermediate grazing might result in higher diversity as predicted by the Intermediate Disturbance Hypothesis, which could in turn confer more stability to the networks. Indeed, we found that networks at intermediate grazing intensities were larger, more generalized, more modular, and contained more diverse and even interactions. Despite general responses at the network level, the number of interactions and selectiveness of particular flower visitor and plant taxa in the networks responded differently to grazing intensity, presumably as a consequence of variation in the abundance of different taxa with grazing. Our results highlight the benefit of maintaining moderate levels of livestock grazing by sheep and goats to preserve the complexity and biodiversity of the rich Mediterranean communities, which have a long history of grazing by these domestic animals.

Ranking nodes in growing networks: When PageRank fails

PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of science, the relation between the algorithm's efficacy and properties of the network on which it acts has not yet been fully understood. We study here PageRank's performance on a network model supported by real data, and show that realistic temporal effects make PageRank fail in individuating the most valuable nodes for a broad range of model parameters. Results on real data are in qualitative agreement with our model-based findings. This failure of PageRank reveals that the static approach to information filtering is inappropriate for a broad class of growing systems, and suggest that time-dependent algorithms that are based on the temporal linking patterns of these systems are needed to better rank the nodes.