Collection |

Networks

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

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.

Perspective | | Nature Ecology & Evolution

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.

Review Article | | Nature Neuroscience

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.

Article | Open Access | | Nature Communications

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.

Article | Open Access | | Nature Communications

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.

Progress Article | | Nature Physics

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.

Article | Open Access | | Nature Physics

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.

Article | Open Access | | Nature Communications

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).

Perspective | | Nature Ecology & Evolution

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.

Article | Open Access | | Communications Biology

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.

Article | Open Access | | Nature Communications

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.

Article | | Nature Neuroscience

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.

Article | | Nature

BRAIN & DISORDERS

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.

Letter | | Nature

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.

Article | | Nature Neuroscience

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.

Letter | | Nature Human Behaviour

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.

Article | | Nature Neuroscience

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.

Review Article | | Nature Reviews Genetics

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.

Review Article | | Nature Reviews Neuroscience

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.

Review Article | | Nature Reviews Neuroscience

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.

Article | Open Access | | Nature Communications

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.

Article | | Nature Neuroscience

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.

Resource | | Nature Neuroscience

DYNAMICS & SPREAD

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.

Review Article | | Nature Neuroscience

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.

Letter | | Nature

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.

Letter | | Nature

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.

Review Article | | Nature Reviews Neuroscience

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.

Progress Article | | Nature Physics

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.

Letter | | Nature Human Behaviour

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.

Letter | | Nature Physics

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.

Article | Open Access | | Nature Communications

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.

Article | Open Access | | Nature Communications

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.

Article | | Nature Neuroscience

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.

Article | | Nature Neuroscience

COMMUNITY & RESILIENCE

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.

Article | Open Access | | Nature Communications

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.

Letter | | Nature

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.

Article | Open Access | | Nature Communications

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.

Article | | Nature Sustainability

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.

Letter | | Nature

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.

Article | Open Access | | Nature Communications

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.

Article | Open Access | | Nature Communications

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.

Article | Open Access | | Nature Communications