Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.     

Network modeling of dynamic brain interactions predicts emergence of neural information that supports human cognitive behavior

How cognitive task behavior is generated by brain network interactions is a central question in neuroscience. Answering this question calls for the development of novel analysis tools that can firstly capture neural signatures of task information with high spatial and temporal precision (the “where and when”) and then allow for empirical testing of alternative network models of brain function that link information to behavior (the “how”). We outline a novel network modeling approach suited to this purpose that is applied to noninvasive functional neuroimaging data in humans. We first dynamically decoded the spatiotemporal signatures of task information in the human brain by combining MRI-individualized source electroencephalography (EEG) with multivariate pattern analysis (MVPA). A newly developed network modeling approach—dynamic activity flow modeling—then simulated the flow of task-evoked activity over more causally interpretable (relative to standard functional connectivity [FC] approaches) resting-state functional connections (dynamic, lagged, direct, and directional). We demonstrate the utility of this modeling approach by applying it to elucidate network processes underlying sensory–motor information flow in the brain, revealing accurate predictions of empirical response information dynamics underlying behavior. Extending the model toward simulating network lesions suggested a role for the cognitive control networks (CCNs) as primary drivers of response information flow, transitioning from early dorsal attention network-dominated sensory-to-response transformation to later collaborative CCN engagement during response selection. These results demonstrate the utility of the dynamic activity flow modeling approach in identifying the generative network processes underlying neurocognitive phenomena.

How is cognitive task behavior generated by brain network interactions? This study describes a novel network modeling approach and applies it to source electroencephalography data. The model accurately predicts future information dynamics underlying behavior and (via simulated lesioning) suggests a role for cognitive control networks as key drivers of response information flow.     

The DIOS framework for optimizing infectious disease surveillance: Numerical methods for simulation and multi-objective optimization of surveillance network architectures

Infectious disease surveillance systems provide vital data for guiding disease prevention and control policies, yet the formalization of methods to optimize surveillance networks has largely been overlooked. Decisions surrounding surveillance design parameters—such as the number and placement of surveillance sites, target populations, and case definitions—are often determined by expert opinion or deference to operational considerations, without formal analysis of the influence of design parameters on surveillance objectives. Here we propose a simulation framework to guide evidence-based surveillance network design to better achieve specific surveillance goals with limited resources. We define evidence-based surveillance design as an optimization problem, acknowledging the many operational constraints under which surveillance systems operate, the many dimensions of surveillance system design, the multiple and competing goals of surveillance, and the complex and dynamic nature of disease systems. We describe an analytical framework—the Disease Surveillance Informatics Optimization and Simulation (DIOS) framework—for the identification of optimal surveillance designs through mathematical representations of disease and surveillance processes, definition of objective functions, and numerical optimization. We then apply the framework to the problem of selecting candidate sites to expand an existing surveillance network under alternative objectives of: (1) improving spatial prediction of disease prevalence at unmonitored sites; or (2) estimating the observed effect of a risk factor on disease. Results of this demonstration illustrate how optimal designs are sensitive to both surveillance goals and the underlying spatial pattern of the target disease. The findings affirm the value of designing surveillance systems through quantitative and adaptive analysis of network characteristics and performance. The framework can be applied to the design of surveillance systems tailored to setting-specific disease transmission dynamics and surveillance needs, and can yield improved understanding of tradeoffs between network architectures.     

The importance of bottlenecks in protein networks: correlation with gene essentiality and expression dynamics

It has been a long-standing goal in systems biology to find relations between the topological properties and functional features of protein networks. However, most of the focus in network studies has been on highly connected proteins (“hubs”). As a complementary notion, it is possible to define bottlenecks as proteins with a high betweenness centrality (i.e., network nodes that have many “shortest paths” going through them, analogous to major bridges and tunnels on a highway map). Bottlenecks are, in fact, key connector proteins with surprising functional and dynamic properties. In particular, they are more likely to be essential proteins. In fact, in regulatory and other directed networks, betweenness (i.e., “bottleneck-ness”) is a much more significant indicator of essentiality than degree (i.e., “hub-ness”). Furthermore, bottlenecks correspond to the dynamic components of the interaction network—they are significantly less well coexpressed with their neighbors than nonbottlenecks, implying that expression dynamics is wired into the network topology.     

Conditional Heteroskedasticity Forecasts Regime Shift in a Whole-Ecosystem Experiment

Regime shifts in stochastic ecosystem models are often preceded by early warning signals such as increased variance and increased autocorrelation in time series. There is considerable theoretical support for early warning signals, but there is a critical lack of field observations to test the efficacy of early warning signals at spatial and temporal scales relevant for ecosystem management. Conditional heteroskedasticity is persistent periods of high and low variance that may be a powerful leading indicator of regime shift. We evaluated conditional heteroskedasticity as an early warning indicator by applying moving window conditional heteroskedasticity tests to time series of chlorophyll-a and fish catches derived from a whole-lake experiment designed to create a regime shift. There was significant conditional heteroskedasticity at least a year prior to the regime shift in the manipulated lake but there was no significant conditional heteroskedasticity in an adjacent reference lake. Conditional heteroskedasticity was an effective leading indicator of regime shift for the ecosystem manipulation.     

Heteroskedasticity as a leading indicator of desertification in spatially explicit data

Regime shifts are abrupt transitions between alternate ecosystem states including desertification in arid regions due to drought or overgrazing. Regime shifts may be preceded by statistical anomalies such as increased autocorrelation, indicating declining resilience and warning of an impending shift. Tests for conditional heteroskedasticity, a type of clustered variance, have proven powerful leading indicators for regime shifts in time series data, but an analogous indicator for spatial data has not been evaluated. A spatial analog for conditional heteroskedasticity might be especially useful in arid environments where spatial interactions are critical in structuring ecosystem pattern and process. We tested the efficacy of a test for spatial heteroskedasticity as a leading indicator of regime shifts with simulated data from spatially extended vegetation models with regular and scale‐free patterning. These models simulate shifts from extensive vegetative cover to bare, desert‐like conditions. The magnitude of spatial heteroskedasticity increased consistently as the modeled systems approached a regime shift from vegetated to desert state. Relative spatial autocorrelation, spatial heteroskedasticity increased earlier and more consistently. We conclude that tests for spatial heteroskedasticity can contribute to the growing toolbox of early warning indicators for regime shifts analyzed with spatially explicit data.     

Resilience indicators: prospects and limitations for early warnings of regime shifts

In the vicinity of tipping points—or more precisely bifurcation points—ecosystems recover slowly from small perturbations. Such slowness may be interpreted as a sign of low resilience in the sense that the ecosystem could easily be tipped through a critical transition into a contrasting state. Indicators of this phenomenon of ‘critical slowing down (CSD)’ include a rise in temporal correlation and variance. Such indicators of CSD can provide an early warning signal of a nearby tipping point. Or, they may offer a possibility to rank reefs, lakes or other ecosystems according to their resilience. The fact that CSD may happen across a wide range of complex ecosystems close to tipping points implies a powerful generality. However, indicators of CSD are not manifested in all cases where regime shifts occur. This is because not all regime shifts are associated with tipping points. Here, we review the exploding literature about this issue to provide guidance on what to expect and what not to expect when it comes to the CSD-based early warning signals for critical transitions.     

Wounded cells drive rapid epidermal repair in the early Drosophila embryo

Epithelial tissues are protective barriers that display a remarkable ability to repair wounds. Wound repair is often associated with an accumulation of actin and nonmuscle myosin II around the wound, forming a purse string. The role of actomyosin networks in generating mechanical force during wound repair is not well understood. Here we investigate the mechanisms of force generation during wound repair in the epidermis of early and late Drosophila embryos. We find that wound closure is faster in early embryos, where, in addition to a purse string around the wound, actomyosin networks at the medial cortex of the wounded cells contribute to rapid wound repair. Laser ablation demonstrates that both medial and purse-string actomyosin networks generate contractile force. Quantitative analysis of protein localization dynamics during wound closure indicates that the rapid contraction of medial actomyosin structures during wound repair in early embryos involves disassembly of the actomyosin network. By contrast, actomyosin purse strings in late embryos contract more slowly in a mechanism that involves network condensation. We propose that the combined action of two force-generating structures—a medial actomyosin network and an actomyosin purse string—contributes to the increased efficiency of wound repair in the early embryo.     

The frustrated brain: from dynamics on motifs to communities and networks

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.     

Precursors of state transitions in stochastic systems with delay

Ecosystem dynamics may exhibit alternative stable states induced by positive feedbacks between the state of the system and environmental drivers. Bistable systems are prone to abrupt shifts from one state to another in response to even small and gradual changes in external drivers. These transitions are often catastrophic and difficult to predict by analyzing the mean state of the system. Indicators of the imminent occurrence of phase transitions can serve as important tools to warn ecosystem managers about an imminent transition before the bifurcation point is actually reached. Thus, leading indicators of phase transitions can be used either to prepare for or to prevent the occurrence of a shift to the other state. In recent years, theories of leading indicators of ecosystem shift have been developed and applied to a variety of ecological models and geophysical time series. It is unclear, however, how some of these indicators would perform in the case of systems with a delay. Here, we develop a theoretical framework for the investigation of precursors of state shift in the presence of drivers acting with a delay. We discuss how the effectiveness of leading indicators of state shift based on rising variance may be affected by the presence of delays. We apply this framework to an ecological model of desertification in arid grasslands.     

The Evolutionary Origins of Hierarchy

Hierarchical organization—the recursive composition of sub-modules—is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force–the cost of connections–promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.     

DebtRank: A Microscopic Foundation for Shock Propagation

The DebtRank algorithm has been increasingly investigated as a method to estimate the impact of shocks in financial networks, as it overcomes the limitations of the traditional default-cascade approaches. Here we formulate a dynamical “microscopic” theory of instability for financial networks by iterating balance sheet identities of individual banks and by assuming a simple rule for the transfer of shocks from borrowers to lenders. By doing so, we generalise the DebtRank formulation, both providing an interpretation of the effective dynamics in terms of basic accounting principles and preventing the underestimation of losses on certain network topologies. Depending on the structure of the interbank leverage matrix the dynamics is either stable, in which case the asymptotic state can be computed analytically, or unstable, meaning that at least one bank will default. We apply this framework to a dataset of the top listed European banks in the period 2008–2013. We find that network effects can generate an amplification of exogenous shocks of a factor ranging between three (in normal periods) and six (during the crisis) when we stress the system with a 0.5% shock on external (i.e. non-interbank) assets for all banks.     

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.     

Critical slowing down as an indicator of transitions in two-species models

Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems.     

Modulating RhoA effectors induces transitions to oscillatory and more wavelike RhoA dynamics in Caenorhabditis elegans zygotes

Pulsatile RhoA dynamics underlie a wide range of cell and tissue behaviors. The circuits that produce these dynamics in different cells share common architectures based on fast positive and delayed negative feedback through F-actin, but they can produce very different spatiotemporal patterns of RhoA activity. However, the underlying causes of this variation remain poorly understood. Here we asked how this variation could arise through modulation of actin network dynamics downstream of active RhoA in early Caenorhabditis elegans embryos. We find that perturbing two RhoA effectors—formin and anillin—induce transitions from nonrecurrent focal pulses to either large noisy oscillatory pulses (formin depletion) or noisy oscillatory waves (anillin depletion). In both cases these transitions could be explained by changes in local F-actin levels and depletion dynamics, leading to changes in spatial and temporal patterns of RhoA inhibition. However, the underlying mechanisms for F-actin depletion are distinct, with different dependencies on myosin II activity. Thus, modulating actomyosin network dynamics could shape the spatiotemporal dynamics of RhoA activity for different physiological or morphogenetic functions.     

Motor-related signals support localization invariance for stable visual perception

Our ability to perceive a stable visual world in the presence of continuous movements of the body, head, and eyes has puzzled researchers in the neuroscience field for a long time. We reformulated this problem in the context of hierarchical convolutional neural networks (CNNs)—whose architectures have been inspired by the hierarchical signal processing of the mammalian visual system—and examined perceptual stability as an optimization process that identifies image-defining features for accurate image classification in the presence of movements. Movement signals, multiplexed with visual inputs along overlapping convolutional layers, aided classification invariance of shifted images by making the classification faster to learn and more robust relative to input noise. Classification invariance was reflected in activity manifolds associated with image categories emerging in late CNN layers and with network units acquiring movement-associated activity modulations as observed experimentally during saccadic eye movements. Our findings provide a computational framework that unifies a multitude of biological observations on perceptual stability under optimality principles for image classification in artificial neural networks.     

Consequences of plant invasions on compartmentalization and species’ roles in plant–pollinator networks

Compartmentalization—the organization of ecological interaction networks into subsets of species that do not interact with other subsets (true compartments) or interact more frequently among themselves than with other species (modules)—has been identified as a key property for the functioning, stability and evolution of ecological communities. Invasions by entomophilous invasive plants may profoundly alter the way interaction networks are compartmentalized. We analysed a comprehensive dataset of 40 paired plant–pollinator networks (invaded versus uninvaded) to test this hypothesis. We show that invasive plants have higher generalization levels with respect to their pollinators than natives. The consequences for network topology are that—rather than displacing native species from the network—plant invaders attracting pollinators into invaded modules tend to play new important topological roles (i.e. network hubs, module hubs and connectors) and cause role shifts in native species, creating larger modules that are more connected among each other. While the number of true compartments was lower in invaded compared with uninvaded networks, the effect of invasion on modularity was contingent on the study system. Interestingly, the generalization level of the invasive plants partially explains this pattern, with more generalized invaders contributing to a lower modularity. Our findings indicate that the altered interaction structure of invaded networks makes them more robust against simulated random secondary species extinctions, but more vulnerable when the typically highly connected invasive plants go extinct first. The consequences and pathways by which biological invasions alter the interaction structure of plant–pollinator communities highlighted in this study may have important dynamical and functional implications, for example, by influencing multi-species reciprocal selection regimes and coevolutionary processes.     

Ecological networks: delving into the architecture of biodiversity

In recent years, the analysis of interaction networks has grown popular as a framework to explore ecological processes and the relationships between community structure and its functioning. The field has rapidly grown from its infancy to a vibrant youth, as reflected in the variety and quality of the discussions held at the first international symposium on Ecological Networks in Coimbra—Portugal (23–25 October 2013). The meeting gathered 170 scientists from 22 countries, who presented data from a broad geographical range, and covering all stages of network analyses, from sampling strategies to effective ways of communicating results, presenting new analytical tools, incorporation of temporal and spatial dynamics, new applications and visualization tools.¹ During the meeting it became evident that while many of the caveats diagnosed in early network studies are successfully being tackled, new challenges arise, attesting to the health of the discipline.     

Disease Surveillance on Complex Social Networks

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors—sampling the most connected, random, and friends of random individuals—in three complex social networks—a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals—early and accurate detection of epidemic emergence and peak, and general situational awareness—we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R₀). For diseases with a low R₀, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R₀ is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.