Ecological interactions typically vary across both space and time. Here, the authors outline a framework for incorporating multiple layers of complexity into ecological networks, and discuss their potential applications and future challenges.
Network science is now a mature research field, whose growth was catalysed by the introduction of the ‘small world’ network model in 1998. Networks give mathematical descriptions of systems containing containing many interacting components, including power grids, neuronal networks and ecosystems. This collection brings together selected research, comments and review articles on how networks are structured (Layers & structure); how networks can describe healthy and disordered systems (Brain & disorders); how dynamics unfold on networks (Dynamics & spread); and community structures and resilience in networks (Community & resilience).
LAYERS & STRUCTURE
A dynamic dependency framework describes general interdependent and competitive interactions between nodes in multilayer networks and is used to study spreading phenomena.
Network neuroscience tackles the challenge of discovering the principles underlying complex brain function and cognition from an explicitly integrative perspective. Here, the authors discuss emerging trends in network neuroscience, charting a path towards a better understanding of the brain that bridges computation, theory and experiment across spatial scales and species.
Multilayer networks reveal the spatial structure of seed-dispersal interactions across the Great Rift landscapes
Species interaction networks have been usually delimited by perceived habitat borders. Here, seed-dispersal is analyzed as a regional multilayer network of interconnected habitats, highlighting the key role of versatile dispersers for the functional cohesion of the whole Gorongosa landscape.
Mapping higher-order relations between brain structure and function with embedded vector representations of connectomes
The function of a brain region is determined by the network it is embedded in. Here the authors implement the word2vec algorithm for connectomes generating a vector embedding of the connectivity structure for each node allowing inference about functional relationships between brain regions.
Aspects concerning the structure and behaviours of individual networks have been studied intensely in the past decade, but the exploration of interdependent systems in the context of complex networks has started only recently. This article reviews a general framework for modelling the percolation properties of interacting networks and the first results drawn from its study.
Complex networks are not obviously renormalizable, as different length scales coexist. Embedding networks in a geometrical space allows the definition of a renormalization group that can be used to construct smaller-scale replicas of large networks.
A technique allows optimal inference of the structure of a network when the available observed data are rich but noisy, incomplete or otherwise unreliable.
Waniek and colleagues show that individuals and communities can disguise themselves from detection online by standard social network analysis tools through simple changes to their social network connections.
Aral and Dhillon specify a class of empirically motivated influence maximization models that incorporate more realistic features of real-world social networks and predict substantially greater influence propagation compared with traditional models.
An application of network science reveals the institutional and corporate structure of the climate change counter-movement in the United States, while computational text analysis shows its influence in the news media and within political circles.
Mathematical modelling suggests that nestedness and other features of mutualistic webs are spandrels resulting from the creation of diversity through speciation-divergence dynamics.
The role of adaptive foraging in the threat of invasive pollinators to plant-pollinator systems is difficult to characterise. Here, Valdavinos et al. use network modelling to show the importance of foraging efficiency, diet overlap, plant species visitation, and degree of specialism in native pollinators.
How biotic interactions change across spatial scales is not well characterized. Here, the authors outline a theoretical framework to explore the spatial scaling of multitrophic communities, and present testable predictions on network-area relationships (NARs).
The structure of ecological networks can vary dramatically, yet there may be common features across networks from different ecosystem types. Here, Bramon Mora et al. use network alignment to demonstrate that there is a common backbone of interactions underlying empirical food webs.
Andreas Pavlogiannis et al. present an approach for constructing strong amplifiers of natural selection using evolutionary graph theory. They also identify features of population structures that are necessary for amplification and suggest their algorithm could be used to construct amplifiers in vitro.
Understanding ecological interactions in microbial communities is limited by lack of informative longitudinal abundance data necessary for reliable inference. Here, Xiao et al. develop a method to infer the interactions between microbes based on their abundances in steady-state samples.
The ProximID approach generates single-cell expression profiles and a network of enriched physical cellular interactions within a tissue.
The activity of cortical neurons is extremely noisy. This study builds a mathematical theory linking the spatial scales of cortical wiring to how noise is generated and distributed over a population of neurons. Predictions from the theory are validated using population recordings in primate visual area V1.
In order to guide action based on past experience, animals have evolved high-order parallel-fibre systems, such as the cerebellum in mammals and the mushroom body in the brains of certain insects. These circuits are specialized in forming large numbers of associative memories, but their full understanding has been impaired by incomplete neuro-anatomical data. Albert Cardona and colleagues provide, for the first time, a full wiring diagram at synapse resolution of such an associative system: the Drosophila larval mushroom body. The work reveals multiple novel and surprising neuronal circuits, such as both random and stereotyped inputs from projection neurons to Kenyon cells. These findings will instruct future experiments and modelling in neuroscience, psychology and robotics.
BRAIN & DISORDERS
Micro-connectomics involves determining the principles of how neuronal networks are organized at the cellular level. In this Review, Schröter, Paulsen and Bullmore examine studies that have provided insight into the network organization of relatively small, as well as more complex, nervous systems.
Control theory is widely used to explore how complex biological, social or technological networks can achieve desired outcomes from specific inputs, but experimental proof of its core principles is still scarce. Now, Albert-László Barabási and colleagues apply network control theory to the neuronal connectome of the roundworm Caenorhabditis elegans to predict the involvement of individual neurons in locomotion. They successfully predict all neuronal groups previously identified as well as one new class, and reveal counterintuitive roles for individual neurons in known classes, which they validate through laser ablation and behaviour tracking experiments. The results are also robust to small perturbations of the reference connectome and suggest that the same analytical framework may be applied to larger and less-well-characterized nervous systems.
To unravel structural regularities in neocortical networks, Gal et al. analyzed a biologically constrained model of a neocortical microcircuit. Using extended graph theory, they found multiple cell-type-specific wiring features, including small-word and rich-club topologies that might contribute to the large repertoire of computations performed by the neocortex.
Parkinson et al. combine social network analysis and multi-voxel pattern analysis of functional magnetic resonance imaging data to show that the brain spontaneously encodes social distance, the centrality of the individuals encountered, and the extent to which they serve to broker connections between members.
This study shows that every individual has a unique pattern of functional connections between brain regions. This functional connectivity profile acts as a ‘fingerprint’ that can accurately identify the individual from a large group. Furthermore, an individual's connectivity profile can predict his or her level of fluid intelligence.
This protocol describes how to develop linear models to predict individual behavior from brain connectivity data with proper cross-validation, and how to use an online tool to visualize the most predictive features of the models.
The energy needed to control a network is related to the links between driver and non-driver nodes, a linear control theory suggests. Applying the theory to connectome data reveals that diverse dynamics in brain networks incur small energetic cost.
Dynamic network models are useful tools for studying complex disease progression. Here, the authors define and review the concepts of pleiotropy, robustness and rewiring, and highlight the importance of considering them jointly and in relation to disease co-occurrences in an individual.
The application of network science to several common neurological disorders challenges the idea that these disorders are either 'local' or 'global'. In this Review, Kees Stam proposes a model of hub overload and failure as a possible final common pathway in diverse neurological disorders.
Pathological perturbations of the brain can be described and modelled using network science. In this Review, Fornito, Zalesky and Breakspear discuss adaptive and maladaptive neural responses to such insults and consider how connectomics can be used to map, track and predict disease progression.
Co-morbidity and symptom overlap make it difficult to associate psychiatric disorders with unique neural signatures. Here, the authors use a data-driven approach to show that the symptom dimensions of mood, psychosis, fear and externalizing behavior exhibit unique patterns of functional dysconnectivity.
Although attentional abilities vary widely and have profound everyday effects, a standardized measure of these abilities is lacking. This study introduces a new fMRI measure based on patterns of whole-brain connectivity, which predicts adults' attention performance and children's ADHD symptoms from data acquired while individuals are resting in the scanner.
Spatiotemporal profile of postsynaptic interactomes integrates components of complex brain disorders
Using large-scale analysis of protein interactions and bioinformatics, Li et al. describe the organization of the core-scaffold machinery of the postsynaptic density and its assembly in protein-interaction networks. The authors show how mutations associated with complex brain disorders are distributed along spatiotemporal protein complexes and modulate their protein interactions.
A molecular network of the aging human brain provides insights into the pathology and cognitive decline of Alzheimer’s disease
The authors constructed and validated a molecular network of the aging human cortex from RNA sequencing data from 478 individuals and identified genes that affect cognitive decline or neuropathology in Alzheimer’s disease.
DYNAMICS & SPREAD
Predicting the collapse of a dynamical system by monitoring the structure of its network of interaction takes the form of stability conditions formulated in terms of a topological invariant of the network, the k-core.
Cognitive activity requires the collective behavior of cortical, thalamic and spinal neurons across large-scale systems of the CNS. This paper provides an illustrated introduction to dynamic models of large-scale brain activity, from the tenets of the underlying theory to challenges, controversies and recent breakthroughs.
In the final pages of The Origin of Species, Charles Darwin presented the image of a tangled bank to evoke the constant interplay of plants and animals in an ecosystem. As each individual struggles to survive and reproduce, its efforts affect the whole ecosystem. It is a beautiful image, but much remains to be learned about the details of such effects. The selective pressures that shape intimate mutualisms between a plant and a specialist pollinator, for example, or the general behaviour of ecological networks, are well known, but less is understood about how selective pressures at various levels ripple through networks. Here, the authors integrate coevolutionary dynamics and network structure to show that selection in mutualisms is shaped not only by the mutualistic partners but by all sorts of indirect effects rippling across the tangled bank.
Collective action towards a common goal, even if everyone's interests are aligned, faces a 'coordination' problem: an individual's attempts to reach a personal, locally optimized solution may not be optimal for the group as a whole. Now Nicholas Christakis and colleagues have introduced autonomous software ('bots') in small networks of humans engaged in solving a standard colour coordination game in which the collective goal is for every node to have a colour different from all of its neighbour nodes, so as to study the potential benefits of introducing noise in the decision making. They find that noisy bots work best when displaying moderate (10%) randomness and placed centrally in the network. Such bots not only improve human–bot but also human–human interactions at distant nodes, thus helping humans to help themselves.
Network propagation is based on the principle that genes underlying similar phenotypes are more likely to interact with each other. It is proving to be a powerful approach for extracting biological information from molecular networks that is relevant to human disease.
The brain comprises complex structural and functional networks, but much remains to be determined regarding how these networks support the communication processes that underlie neuronal computation. In this Review, Avena-Koenigsberger, Misic and Sporns discuss the network basis of communication dynamics in the brain.
The authors used graph signal processing to examine whether fMRI signals correspond to underlying anatomical networks. They found that alignment between functional signals and anatomical structure was associated with greater cognitive flexibility.
Coordination of neural activity between distant brain areas is necessary for cognition. Here, the authors report using MEG that various brain networks show dynamic phase coupling through specific frequency bands in the alpha and delta/theta range transiently during the resting state.
Reshaping network theory to describe the multilayered structures of the real world has formed a focus in complex networks research in recent years. Progress in our understanding of dynamical processes is but one of the fruits of this labour.
Analysing high-resolution mobility traces from almost 40,000 individuals reveals that people typically revisit a set of 25 familiar locations day-to-day, but that this set evolves over time and is proportional to the size of their social sphere.
A network experiment in a major environmental NGO finds that the diffusion of innovation is four times more likely when information regarding novel practices is targeted to staff members who participate in a greater number, and a more diverse set, of projects.
The common policy of replacing infected individuals with healthy substitutes can have the effect of accelerating disease transmission. A dynamic network model suggests that standard modelling approaches underplay the effect of network structure.
An optimal computationally efficient solution to the problem of finding the minimum taxi fleet size using a vehicle-sharing network is presented.
Complex ecological networks are likely to be disrupted as species shift in response to environmental change. A simulation model shows that the level of dispersal determines whether species associations within networks are maintained.
Understanding global epidemics spread is crucial for preparedness and response. Here the authors introduce an analytical framework to study epidemic spread on air transport networks, and demonstrate its power to estimate key epidemic parameters by application to the recent influenza pandemic and Ebola outbreak.
Mass drug administration depends on the distributors’ contact with community members. Using data of deworming treatment distribution from Ugandan villages, the authors show that community medicine distributors with tightly-knit friendship connections achieve the greatest reach and speed of coverage.
Brain function relies on flexible communication between cortical regions. It has been proposed that changing patterns of oscillatory coherence underlie information routing. However, oscillations in vivo are very irregular. This study shows that short-lived and stochastic oscillatory bursts coordinate across areas to selectively modulate interareal communication.
Resting-state functional connectivity has helped reveal the brain's network organization, yet its relevance to cognitive task activations has been unclear. The authors found that estimating activity flow over resting-state networks allows prediction of held-out activations, suggesting activity flow as a linking mechanism between resting-state networks and cognitive task activations.
Taking into account the spatial distribution of population and its mobility, a reaction–diffusion model of an epidemic process reveals several different critical regimes, in which human mobility may even be detrimental to the spread of the disease.
COMMUNITY & RESILIENCE
The recent proliferation of omics data has required a toolbox of integrative systems biology bioinformatics approaches to elucidate functional relationships between molecules. Here the authors explain the principles behind these approaches and discuss their applications.
Current understanding of eco-evolutionary feedbacks rests primarily on simple systems at small spatial scales. Here, the authors outline a framework for examining spatiotemporal dynamics in species-rich networks at the metacommunity scale.
Analysing a model of randomly interacting species, the authors show that stable, biodiverse communities can be achieved in which network structure has little influence.
Modularity in food webs can be caused by spatial and temporal mismatches in interactions. Here, Jacopo Grilli, Tim Rogers and Stefano Allesina show that modularity, contrary to expectations, does not generally help stabilizing ecological communities.
By developing wireless sensors to track social interactions among hunter-gatherers in the Republic of the Congo and the Philippines, Migliano et al. find that a few strong friendship ties connecting unrelated families lead to more efficient social networks.
Altenburger and Ugander identify ‘monophily’ or the overdispersion of attribute preferences in a social network and show that it can be used to predict otherwise hidden attribute information about an individual.
Empirical analysis of climate change debates in the US Congress shows that policymakers are most likely to seek out experts confirming their existing views. That information then gets disseminated among like-minded individuals in ‘echo chambers’.
Human activities often have damaging effects on biodiversity and ecosystem functions, but whether the targeted manipulation of ecological communities can successfully mitigate and reverse these impacts is the subject of much debate. Here, Christopher Kaiser-Bunbury et al. assess the effect of one form of restoration—the removal of all alien plant species—on the structure and function of plant–pollinator networks in mountain-top communities in the Seychelles. Vegetation restoration leads to a marked increase in the number of pollinator species and pollinator visits to flowers. There is also an increase in the diversity of pollinator interactions and, importantly, the pollination of fruit crops and native plants. The findings suggest that the degradation of ecosystem functions, in this case pollination, is at least partly reversible.
The stability of ecological networks depends on both inter- and intraspecific interactions. Here, the authors show that intraspecific self-regulation is a necessary feature for the stabilization of empirical and theoretical networks.
A central question in theoretical ecology is how diverse species can coexist in communities, and how that coexistence depends on network properties. Here, Grilliet al. quantify the extent of feasible coexistence of empirical networks, showing that it is smaller for trophic than mutualism networks.
Sustainability depends on the resilience of natural, social and engineered systems. This theoretical study quantifies resilience to repeated disturbances, synthesizing understanding of how the sizes of shocks, or ‘kicks’, and recovery, or ‘flows’, contribute to maintaining systems in desirable states.
Ecological interaction networks may fall on a continuum between mutualism and antagonism. Here, the authors show that community robustness increases when both the beneficial and detrimental effects of parrots feeding on plants is taken into account.
Ecological theory suggests that ecosystem stability—the ability of an ecosystem to persist through perturbations—is influenced by changes in the interactions between different species. Masayuki Ushio and colleagues use a 12-year observational dataset of species interactions in a marine fish community in Maizuru Bay, Japan, to examine the link between fluctuations in interspecific interactions and community stability. They find that short-term changes in the interaction network influence the overall community dynamics, with weak interactions and higher species diversity promoting community stability.
The evolution of cooperation depends on social structure, which may evolve in response. Here, Akçay models coevolution between cooperation and social network formation strategies, showing that coevolutionary feedbacks lead cooperation to collapse unless constrained by costs of social connections.
In an analysis of 15,000 Facebook networks, Hobbs and Burke find that online social networks are resilient to the death of an individual, showing an increase in interactions between friends following a loss, which remains stable for years after.
Gollo et al. introduce random ‘mutations’ to the human connectome to study the trade-off between complexity vs. parsimony. The cortical hubs that are most fragile to these perturbations show the strongest loss of gray matter volume in schizophrenia.
The spread of instabilities in financial systems, similarly to ecosystems, is influenced by topological features of the underlying network structures. Here the authors show, independently of specific financial models, that market integration and diversification can drive the system towards instability.
Although networks of interacting genes and metabolic reactions are interdependent, they have largely been treated as separate systems. Here the authors apply a statistical framework for interdependent networks to E. coli, and show that it is sensitive to gene and protein perturbations but robust against metabolic changes.
Drought conditions can alter the composition of soil microbial communities, but the effects of drought on network properties have not been tested. Here, de Vries and colleagues show that co-occurrence networks are destabilised under drought for bacteria but not fungi.