Rescuing ecosystems from extinction cascades through compensatory perturbations

Impact of human intervention and predator-prey dynamics on ecosystem virus transmission

Humans and predators occupy dominant positions in ecosystems and are generally believed to play a decisive role in maintaining ecosystem stability, particularly in the context of virus transmission. However, this may not always be the case. By establishing some ecosystem virus transmission models that cover both human perspectives and predators, we have drawn the following conclusions: (1) Controlling vaccination activities from the human perspective can potentially lower the transmission rate and improve herd immunity, thereby indirectly protecting unvaccinated risk groups. (2) In the ecosystem, the human perspective does not always determine the spread of viruses. Once the ecological balance between predators and prey is disrupted, there may be scenarios where predator populations die out, prey populations overpopulate, or both predators and prey go extinct. In such cases, the spread of the virus has little impact, and the system cannot restore itself to a new equilibrium state. In this case, even if humans intervene, it is difficult to change the fate of species extinction. (3) In situations where predator and prey populations maintain a stable state, human attitudes and actions are particularly critical. Human intervention can directly affect the transmission rate of the virus and the recovery rate of hosts, thereby rapidly reducing the infection rate and mitigating the harm caused by the virus. If humans do not intervene, predators may remain infected for a long time, thereby posing a serious threat to the ecosystem.

Calibrated Ecosystem Models Cannot Predict the Consequences of Conservation Management Decisions

Ecosystem models are often used to predict the consequences of management interventions in applied ecology and conservation. These models are often high-dimensional and nonlinear, yet limited data are available to calibrate or validate them. Consequently, their utility as decision-support tools is unclear. In this paper, we calibrate ecosystem models to time series data from 110 different experimental microcosm ecosystems, each containing three to five interacting species. Then, we assess their ability to predict the consequences of management interventions. Our results show that for each time series dataset, multiple divergent parameter sets offer equivalent, good fits. However, these models have poor predictive accuracy when forecasting future dynamics or when predicting how the ecosystem will respond to management intervention. Closer inspection reveals that the models fail because calibration cannot determine the nature of the interspecific interactions. Our findings question whether ecosystem models can support applied ecological decision-making when calibrated against real-world datasets.

Global network control from local information

In the classical control of network systems, the control actions on a node are determined as a function of the states of all nodes in the network. Motivated by applications where the global state cannot be reconstructed in real time due to limitations in the collection, communication, and processing of data, here we introduce a control approach in which the control actions can be computed as a function of the states of the nodes within a limited state information neighborhood. The trade-off between the control performance and the size of this neighborhood is primarily determined by the condition number of the controllability Gramian. Our theoretical results are supported by simulations on regular and random networks and are further illustrated by an application to the control of power-grid synchronization. We demonstrate that for well-conditioned Gramians, there is no significant loss of control performance as the size of the state information neighborhood is reduced, allowing efficient control of large networks using only local information.

Control of cascading failures using protective measures

Cascading failures, triggered by a local perturbation, can be catastrophic and cause irreparable damages in a wide area. Hence, blocking the devastating cascades is an important issue in real world networks. One of the ways to control the cascade is to use protective me‌asures, so that the agents decide to be protected against failure. Here, we consider a coevolution of the linear threshold mo‌del for the spread of cascading failures and a decision-making game based on the perceived risk of failure. Protected agents are less vulnerable to failure and in return the size of the cascade affects the agent's decision to get insured. We find at what range of protection efficiency and cost of failure, the global cascades stop. Also we observe that in some range of protection efficiency, a bistable region emerges for the size of cascade and the prevalence of protected agents. Moreover, we show how savings or the ability of agents to repair can prevent cascades from occurring.

Efficient keystone species identification strategy based on tabu search

As species extinction accelerates globally and biodiversity declines dramatically, identifying keystone species becomes an effective way to conserve biodiversity. In traditional approaches, it is considered that the extinction of species with high centrality poses the greatest threat to secondary extinction. However, the indirect effect, which is equally important as the local and direct effects, is not included. Here, we propose an optimized disintegration strategy model for quantitative food webs and introduced tabu search, a metaheuristic optimization algorithm, to identify keystone species. Topological simulations are used to record secondary extinctions during species removal and secondary extinction areas, as well as to evaluate food web robustness. The effectiveness of the proposed strategy is also validated by comparing it with traditional methods. Results of our experiments demonstrate that our strategy can optimize the effect of food web disintegration and identify the species whose extinction is most destructive to the food web through global search. The algorithm provides an innovative and efficient way for further development of keystone species identification in the ecosystem.

Forecasting the evolution of fast-changing transportation networks using machine learning

Transportation networks play a critical role in human mobility and the exchange of goods, but they are also the primary vehicles for the worldwide spread of infections, and account for a significant fraction of CO₂ emissions. We investigate the edge removal dynamics of two mature but fast-changing transportation networks: the Brazilian domestic bus transportation network and the U.S. domestic air transportation network. We use machine learning approaches to predict edge removal on a monthly time scale and find that models trained on data for a given month predict edge removals for the same month with high accuracy. For the air transportation network, we also find that models trained for a given month are still accurate for other months even in the presence of external shocks. We take advantage of this approach to forecast the impact of a hypothetical dramatic reduction in the scale of the U.S. air transportation network as a result of policies to reduce CO₂ emissions. Our forecasting approach could be helpful in building scenarios for planning future infrastructure.

Transportation networks undergo permanent changes influenced by a variety of human-induced and natural factors. The authors propose here a machine learning framework for prediction of connections removal that could be useful in building scenarios for transportation infrastructure needs.

Prevalence and scalable control of localized networks

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer's disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

Percolation in networks with local homeostatic plasticity

Percolation is a process that impairs network connectedness by deactivating links or nodes. This process features a phase transition that resembles paradigmatic critical transitions in epidemic spreading, biological networks, traffic and transportation systems. Some biological systems, such as networks of neural cells, actively respond to percolation-like damage, which enables these structures to maintain their function after degradation and aging. Here we study percolation in networks that actively respond to link damage by adopting a mechanism resembling synaptic scaling in neurons. We explain critical transitions in such active networks and show that these structures are more resilient to damage as they are able to maintain a stronger connectedness and ability to spread information. Moreover, we uncover the role of local rescaling strategies in biological networks and indicate a possibility of designing smart infrastructures with improved robustness to perturbations.

Non-target impacts of fungicide disturbance on phyllosphere yeasts in conventional and no-till management

Fungicides reduce fungal pathogen populations and are essential to food security. Understanding the impacts of fungicides on crop microbiomes is vital to minimizing unintended consequences while maintaining their use for plant protection. However, fungicide disturbance of plant microbiomes has received limited attention, and has not been examined in different agricultural management systems. We used amplicon sequencing of fungi and prokaryotes in maize and soybean microbiomes before and after foliar fungicide application in leaves and roots from plots under long-term no-till and conventional tillage management. We examined fungicide disturbance and resilience, which revealed consistent non-target effects and greater resiliency under no-till management. Fungicides lowered pathogen abundance in maize and soybean and decreased the abundance of Tremellomycetes yeasts, especially Bulleribasidiaceae, including core microbiome members. Fungicide application reduced network complexity in the soybean phyllosphere, which revealed altered co-occurrence patterns between yeast species of Bulleribasidiaceae, and Sphingomonas and Hymenobacter in fungicide treated plots. Results indicate that foliar fungicides lower pathogen and non-target fungal abundance and may impact prokaryotes indirectly. Treatment effects were confined to the phyllosphere and did not impact belowground microbial communities. Overall, these results demonstrate the resilience of no-till management to fungicide disturbance, a potential novel ecosystem service provided by no-till agriculture.

An Expanded Framework for Community Viability Analysis

Community viability analysis (CVA) has been put forth as an analogue for population viability analysis (PVA), an accepted conservation tool for evaluating species-specific threat and management scenarios. The original proposal recommended that CVAs examine resistance-based questions. PVAs, however, are broadly applicable to multiple types of viability questions, suggesting that the original CVA definition may be too narrow. In the present article, we advance an expanded framework in which CVA includes any analysis assessing the status, threats, or management options of an ecological community. We discuss viability questions that can be investigated with CVA. We group those inquiries into categories of resistance, resilience, and persistence, and provide case studies for each. Finally, we broadly present the steps in a CVA.

Network isolators inhibit failure spreading in complex networks

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.

Greedy control of cascading failures in interdependent networks

Complex systems are challenging to control because the system responds to the controller in a nonlinear fashion, often incorporating feedback mechanisms. Interdependence of systems poses additional difficulties, as cross-system connections enable malicious activity to spread between layers, increasing systemic risk. In this paper we explore the conditions for an optimal control of cascading failures in a system of interdependent networks. Specifically, we study the Bak-Tang-Wiesenfeld sandpile model incorporating a control mechanism, which affects the frequency of cascades occurring in individual layers. This modification allows us to explore sandpile-like dynamics near the critical state, with supercritical region corresponding to infrequent large cascades and subcritical zone being characterized by frequent small avalanches. Topological coupling between networks introduces dependence of control settings adopted in respective layers, causing the control strategy of a given layer to be influenced by choices made in other connected networks. We find that the optimal control strategy for a layer operating in a supercritical regime is to be coupled to a layer operating in a subcritical zone, since such condition corresponds to reduced probability of inflicted avalanches. However this condition describes a parasitic relation, in which only one layer benefits. Second optimal configuration is a mutualistic one, where both layers adopt the same control strategy. Our results provide valuable insights into dynamics of cascading failures and and its control in interdependent complex systems.

Using social network analysis of mixed-species groups in African savannah herbivores to assess how community structure responds to environmental change

The dynamics of wildlife populations often depend heavily on interspecific interactions and understanding the underlying principles can be an important step in designing conservation strategies. Behavioural ecological studies can here provide useful insights into the structure and function of communities and their likely response to environmental changes. In this study of the Masai Mara herbivore community, we use a social network approach to investigate social affinities between species and how these change over the year in response to seasonal changes in ecological conditions. We find that even though social networks were correlated across different ecological conditions, for half the species dyads in the community, the strength of social affinities responded to changes in rainfall and/or the presence of migratory wildebeest. Several species consequentially adopted more or less central positions in the network depending on the ecological conditions. The findings point out interspecific social links that are likely to be attenuated or strengthened as a consequence of human-induced environmental changes and therefore call for particular attention from conservation managers. The eco-evolutionary ramifications of the perturbations of social affinities still require further study.

This article is part of the theme issue ‘Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation’.

Cascading failures in scale-free interdependent networks

Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as well as intra- and interlayer degree correlations. We find that three properties, scale-free degree distribution, internal network assortativity, and cross-network hub-to-hub connections, are all necessary components to significantly reduce the size of large cascades in the Bak-Tang-Wiesenfeld sandpile model. We demonstrate that correlations present in the structure of the multilayer network influence the dynamical cascading process and can prevent failures from spreading across connected layers. These findings highlight the importance of internal and cross-network topology in optimizing robustness of interconnected systems.

Antagonistic Phenomena in Network Dynamics

Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a wealth of phenomena that not only cannot be anticipated from merely examining their parts, as per the textbook definition of complexity, but also challenge intuition even when considered in the context of what is now known in network science. Here we review the recent literature on two major classes of such phenomena that have far-reaching implications: (i) antagonistic responses to changes of states or parameters and (ii) coexistence of seemingly incongruous behaviors or properties-both deriving from the collective and inherently decentralized nature of the dynamics. They include effects as diverse as negative compressibility in engineered materials, rescue interactions in biological networks, negative resistance in fluid networks, and the Braess paradox occurring across transport and supply networks. They also include remote synchronization, chimera states and the converse of symmetry breaking in brain, power-grid and oscillator networks as well as remote control in biological and bio-inspired systems. By offering a unified view of these various scenarios, we suggest that they are representative of a yet broader class of unprecedented network phenomena that ought to be revealed and explained by future research.

Cascading Failures as Continuous Phase-Space Transitions

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in a closed form using a global Hamiltonian-like function. From this function, we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that, in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.

Small vulnerable sets determine large network cascades in power grids

The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causes of cascading failures relevant for grid design and operation and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.

Optimal deployment of resources for maximizing impact in spreading processes

The effective use of limited resources for controlling spreading processes on networks is of prime significance in diverse contexts, ranging from the identification of "influential spreaders" for maximizing information dissemination and targeted interventions in regulatory networks, to the development of mitigation policies for infectious diseases and financial contagion in economic systems. Solutions for these optimization tasks that are based purely on topological arguments are not fully satisfactory; in realistic settings, the problem is often characterized by heterogeneous interactions and requires interventions in a dynamic fashion over a finite time window via a restricted set of controllable nodes. The optimal distribution of available resources hence results from an interplay between network topology and spreading dynamics. We show how these problems can be addressed as particular instances of a universal analytical framework based on a scalable dynamic message-passing approach and demonstrate the efficacy of the method on a variety of real-world examples.

Conditions for Eltonian Pyramids in Lotka-Volterra Food Chains

In ecological communities consumers (excluding parasites and parasitoids) are in general larger and less numerous than their resource. This results in a well-known observation known as 'Eltonian pyramids' or the 'pyramid of numbers', and metabolic arguments suggest that this pattern is independent of the number of trophic levels in a system. At the same time, Lotka-Volterra (LV) consumer-resource models are a frequently used tool to study many questions in community ecology, but their capacity to produce Eltonian pyramids has not been formally analysed. Here, I address this knowledge gap by investigating if and when LV food chain models give rise to Eltonian pyramids. I show that Eltonian pyramids are difficult to reproduce without density-dependent mortality in the consumers, unless biologically plausible relationships between mortality rate and interaction strength are taken into account.

Enhancing structural robustness of scale-free networks by information disturbance

Many real-world systems can be described by scale-free networks with power-law degree distributions. Scale-free networks show a “robust yet fragile” feature due to their heterogeneous degree distributions. We propose to enhance the structural robustness of scale-free networks against intentional attacks by changing the displayed network structure information rather than modifying the network structure itself. We first introduce a simple mathematical model for attack information and investigate the impact of attack information on the structural robustness of scale-free networks. Both analytical and numerical results show that decreasing slightly the attack information perfection by information disturbance can dramatically enhance the structural robustness of scale-free networks. Then we propose an optimization model of disturbance strategies in which the cost constraint is considered. We analyze the optimal disturbance strategies and show an interesting but counterintuitive finding that disturbing “poor nodes” with low degrees preferentially is more effective than disturbing “rich nodes” with high degrees preferentially. We demonstrate the efficiency of our method by comparison with edge addition method and validate the feasibility of our method in two real-world critical infrastructure networks.

Vulnerability and Cosusceptibility Determine the Size of Network Cascades

In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Here, we develop a statistical framework that can predict cascade size distributions by incorporating two ingredients only: the vulnerability of individual components and the cosusceptibility of groups of components (i.e., their tendency to fail together). Using cascades in power grids as a representative example, we show that correlations between component failures define structured and often surprisingly large groups of cosusceptible components. Aside from their implications for blackout studies, these results provide insights and a new modeling framework for understanding cascades in financial systems, food webs, and complex networks in general.

Trade-offs between robustness and small-world effect in complex networks

Robustness and small-world effect are two crucial structural features of complex networks and have attracted increasing attention. However, little is known about the relation between them. Here we demonstrate that, there is a conflicting relation between robustness and small-world effect for a given degree sequence. We suggest that the robustness-oriented optimization will weaken the small-world effect and vice versa. Then, we propose a multi-objective trade-off optimization model and develop a heuristic algorithm to obtain the optimal trade-off topology for robustness and small-world effect. We show that the optimal network topology exhibits a pronounced core-periphery structure and investigate the structural properties of the optimized networks in detail.

On controlling networks of limit-cycle oscillators

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.

Effect of correlations on controllability transition in network control

The network control problem has recently attracted an increasing amount of attention, owing to concerns including the avoidance of cascading failures of power-grids and the management of ecological networks. It has been proven that numerical control can be achieved if the number of control inputs exceeds a certain transition point. In the present study, we investigate the effect of degree correlation on the numerical controllability in networks whose topological structures are reconstructed from both real and modeling systems, and we find that the transition point of the number of control inputs depends strongly on the degree correlation in both undirected and directed networks with moderately sparse links. More interestingly, the effect of the degree correlation on the transition point cannot be observed in dense networks for numerical controllability, which contrasts with the corresponding result for structural controllability. In particular, for directed random networks and scale-free networks, the influence of the degree correlation is determined by the types of correlations. Our approach provides an understanding of control problems in complex sparse networks.

Regularity underlies erratic population abundances in marine ecosystems

The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a well-defined double-exponential (Laplace) distribution. This striking regularity allows us to devise a stochastic model despite seemingly irregular variations in population abundances. The model identifies the effect of reduced growth at low population density as a key factor missed in current approaches of population variability analysis and without which extinction risks are severely underestimated. The model also allows us to separate the effect of demographic stochasticity and show that single-species growth rates are dominantly determined by stochasticity common to all species. This dominance-and the implications it has for interspecies correlations, including co-extinctions-emphasizes the need for ecosystem-level management approaches to reduce the extinction risk of the individual species themselves.

Using food-web theory to conserve ecosystems

Food-web theory can be a powerful guide to the management of complex ecosystems. However, we show that indices of species importance common in food-web and network theory can be a poor guide to ecosystem management, resulting in significantly more extinctions than necessary. We use Bayesian Networks and Constrained Combinatorial Optimization to find optimal management strategies for a wide range of real and hypothetical food webs. This Artificial Intelligence approach provides the ability to test the performance of any index for prioritizing species management in a network. While no single network theory index provides an appropriate guide to management for all food webs, a modified version of the Google PageRank algorithm reliably minimizes the chance and severity of negative outcomes. Our analysis shows that by prioritizing ecosystem management based on the network-wide impact of species protection rather than species loss, we can substantially improve conservation outcomes.

The influence of species conservation on food webs is less well understood than the effects of species loss. Here, the authors test several indices against optimal food web management and find no current metrics are reliably effective at identifying species conservation priorities.

Past, present and future of host-parasite co-extinctions

Human induced ecosystem alterations and climate change are expected to drive several species to extinction. In this context, the attention of public opinion, and hence conservationists' efforts, are often targeted towards species having emotional, recreational and/or economical value. This tendency may result in a high number of extinctions happening unnoticed. Among these, many could involve parasites. Several studies have highlighted various reasons why we should care about this, that go far beyond the fact that parasites are amazingly diverse. A growing corpus of evidence suggests that parasites contribute much to ecosystems both in terms of biomass and services, and the seemingly paradoxical idea that a healthy ecosystem is one rich in parasites is becoming key to the whole concept of parasite conservation. Although various articles have covered different aspects of host-parasite co-extinctions, I feel that some important conceptual issues still need to be formally addressed. In this review, I will attempt at clarifying some of them, with the aim of providing researchers with a unifying conceptual framework that could help them designing future studies. In doing this, I will try to draw a more clear distinction between the (co-)evolutionary and the ecological dimensions of co-extinction studies, since the ongoing processes that are putting parasites at risk now operate at a scale that is extremely different from the one that has shaped host-parasite networks throughout million years of co-evolution. Moreover, I will emphasize how the complexity of direct and indirect effects of parasites on ecosystems makes it much challenging to identify the mechanisms possibly leading to co-extinction events, and to predict how such events will affect ecosystems in the long run.

Networkcontrology

An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control. Here, I discuss recent advances on mathematical and computational approaches to control high-dimensional nonlinear network dynamics under general constraints on the admissible interventions. I also discuss the potential of network control to address pressing scientific problems in various disciplines.

Control of coupled oscillator networks with application to microgrid technologies

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.

Control of Stochastic and Induced Switching in Biophysical Networks

Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. Here we present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. We apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model. This framework offers a systems approach to identifying the key factors for rationally manipulating biophysical dynamics, and should also find use in controlling other classes of noisy complex networks.

Controllability and observability of Boolean networks arising from biology

Boolean networks are currently receiving considerable attention as a computational scheme for system level analysis and modeling of biological systems. Studying control-related problems in Boolean networks may reveal new insights into the intrinsic control in complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper considers controllability and observability of Boolean biological networks. We propose a new approach, which draws from the rich theory of symbolic computation, to solve the problems. Consequently, simple necessary and sufficient conditions for reachability, controllability, and observability are obtained, and algorithmic tests for controllability and observability which are based on the Gröbner basis method are presented. As practical applications, we apply the proposed approach to several different biological systems, namely, the mammalian cell-cycle network, the T-cell activation network, the large granular lymphocyte survival signaling network, and the Drosophila segment polarity network, gaining novel insights into the control and/or monitoring of the specific biological systems.

Controlling systems that drift through a tipping point

Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory will then go to another attractor of the system. We consider the case where there are more than one of these possible final attractors, and we ask whether we can control the outcome (i.e., the attractor that ultimately captures the trajectory) using only small controlling perturbations. Specifically, we consider the problem of controlling a noisy system whose parameter slowly drifts through a saddle-node bifurcation taking place on a fractal boundary between the basins of multiple attractors. We show that, when the noise level is low, a small perturbation of size comparable to the noise amplitude applied at a single point in time can ensure that the system will evolve toward a target attracting state with high probability. For a range of noise levels, we find that the minimum size of perturbation required for control is much smaller within a time period that starts some time after the bifurcation, providing a "window of opportunity" for driving the system toward a desirable state. We refer to this procedure as tipping point control.

Coexistence of phases and the observability of random graphs

In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolationlike emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth-L percolation--where the state of nodes up to a distance L of monitored nodes is known--can be mapped onto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L. We then demonstrate a nontrivial coexistence of an observable and of a nonobservable extensive component. This coexistence suggests that monitoring a macroscopic portion of a graph does not prevent a macroscopic event to occur unbeknown to the observer. We also show that real complex systems behave quite differently with regard to observability depending on whether they are geographically constrained or not.

Realistic control of network dynamics

The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behaviour or fail. Here we show that it is possible to exploit the same principle to control network behaviour. Our approach accounts for the nonlinear dynamics inherent to real systems, and allows bringing the system to a desired target state even when this state is not directly accessible due to constraints that limit the allowed interventions. Applications show that this framework permits reprogramming a network to a desired task, as well as rescuing networks from the brink of failure-which we illustrate through the mitigation of cascading failures in a power-grid network and the identification of potential drug targets in a signalling network of human cancer.

Parasites affect food web structure primarily through increased diversity and complexity

Parasites primarily affect food web structure through changes to diversity and complexity. However, compared to free-living species, their life-history traits lead to more complex feeding niches and altered motifs.

Comparative research on food web structure has revealed generalities in trophic organization, produced simple models, and allowed assessment of robustness to species loss. These studies have mostly focused on free-living species. Recent research has suggested that inclusion of parasites alters structure. We assess whether such changes in network structure result from unique roles and traits of parasites or from changes to diversity and complexity. We analyzed seven highly resolved food webs that include metazoan parasite data. Our analyses show that adding parasites usually increases link density and connectance (simple measures of complexity), particularly when including concomitant links (links from predators to parasites of their prey). However, we clarify prior claims that parasites “dominate” food web links. Although parasites can be involved in a majority of links, in most cases classic predation links outnumber classic parasitism links. Regarding network structure, observed changes in degree distributions, 14 commonly studied metrics, and link probabilities are consistent with scale-dependent changes in structure associated with changes in diversity and complexity. Parasite and free-living species thus have similar effects on these aspects of structure. However, two changes point to unique roles of parasites. First, adding parasites and concomitant links strongly alters the frequency of most motifs of interactions among three taxa, reflecting parasites' roles as resources for predators of their hosts, driven by trophic intimacy with their hosts. Second, compared to free-living consumers, many parasites' feeding niches appear broader and less contiguous, which may reflect complex life cycles and small body sizes. This study provides new insights about generic versus unique impacts of parasites on food web structure, extends the generality of food web theory, gives a more rigorous framework for assessing the impact of any species on trophic organization, identifies limitations of current food web models, and provides direction for future structural and dynamical models.

Food webs are networks of feeding interactions among species. Although parasites comprise a large proportion of species diversity, they have generally been underrepresented in food web data and analyses. Previous analyses of the few datasets that contain parasites have indicated that their inclusion alters network structure. However, it is unclear whether those alterations were a result of unique roles that parasites play, or resulted from the changes in diversity and complexity that would happen when any type of species is added to a food web. In this study, we analyzed many aspects of the network structure of seven highly resolved coastal estuary or marine food webs with parasites. In most cases, we found that including parasites in the analysis results in generic changes to food web structure that would be expected with increased diversity and complexity. However, in terms of specific patterns of links in the food web (“motifs”) and the breadth and contiguity of feeding niches, parasites do appear to alter structure in ways that result from unique traits—in particular, their close physical intimacy with their hosts, their complex life cycles, and their small body sizes. Thus, this study disentangles unique from generic effects of parasites on food web organization, providing better understanding of similarities and differences between parasites and free-living species in their roles as consumers and resources.

Controllability transition and nonlocality in network control

A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely underexplored. Here we show that (i) numerical control fails in practice even for linear systems if the controllability Gramian is ill conditioned, which occurs frequently even when existing controllability criteria are satisfied unambiguously, (ii) the control trajectories are generally nonlocal in the phase space, and their lengths are strongly anti-correlated with the numerical success rate and number of control inputs, and (iii) numerical success rate increases abruptly from zero to nearly one as the number of control inputs is increased, a transformation we term numerical controllability transition. This reveals a trade-off between nonlocality of the control trajectory in the phase space and nonlocality of the control inputs in the network itself. The failure of numerical control cannot be overcome in general by merely increasing numerical precision--successful control requires instead increasing the number of control inputs beyond the numerical controllability transition.

Robustness of empirical food webs with varying consumer's sensitivities to loss of resources

Food web responses to species loss have been mostly studied in binary food webs, thus without accounting for the amount of energy transferred in consumer-resource interactions. We introduce an energetic criterion, called extinction threshold, for which a species goes secondarily extinct when a certain fraction of its incoming energy is lost. We study the robustness to random node loss of 10 food webs based on empirically-derived weightings. We use different extinction scenarios (random removal and from most- to least-connected species), and we simulate 10(5) replicates for each extinction threshold to account for stochasticity of extinction dynamics. We quantified robustness on the basis of how many additional species (i.e. secondary extinctions) were lost after the direct removal of species (i.e. primary extinctions). For all food webs, the expected robustness linearly decreases with extinction threshold, although a large variance in robustness is observed. The sensitivity of robustness to variations in extinction threshold increases with food web species richness and quantitative unweighted link density, while we observed a nonlinear relationship when the predictor is food web connectance and no relationship with the proportion of autotrophs.

Engineering ecosystems and synthetic ecologies

Microbial ecosystems play an important role in nature. Engineering these systems for industrial, medical, or biotechnological purposes are important pursuits for synthetic biologists and biological engineers moving forward. Here we provide a review of recent progress in engineering natural and synthetic microbial ecosystems. We highlight important forward engineering design principles, theoretical and quantitative models, new experimental and manipulation tools, and possible applications of microbial ecosystem engineering. We argue that simply engineering individual microbes will lead to fragile homogenous populations that are difficult to sustain, especially in highly heterogeneous and unpredictable environments. Instead, engineered microbial ecosystems are likely to be more robust and able to achieve complex tasks at the spatial and temporal resolution needed for truly programmable biology.

Food webs: reconciling the structure and function of biodiversity

The global biodiversity crisis concerns not only unprecedented loss of species within communities, but also related consequences for ecosystem function. Community ecology focuses on patterns of species richness and community composition, whereas ecosystem ecology focuses on fluxes of energy and materials. Food webs provide a quantitative framework to combine these approaches and unify the study of biodiversity and ecosystem function. We summarise the progression of food-web ecology and the challenges in using the food-web approach. We identify five areas of research where these advances can continue, and be applied to global challenges. Finally, we describe what data are needed in the next generation of food-web studies to reconcile the structure and function of biodiversity.

Some clouds have a silver lining: paradoxes of anthropogenic perturbations from study cases on long-lived social birds

In recent centuries and above all over the last few decades, human activities have generated perturbations (from mild to very severe or catastrophes) that, when added to those of natural origin, constitute a global threat to biodiversity. Predicting the effects of anthropogenic perturbations on species and communities is a great scientific challenge given the complexity of ecosystems and the need for detailed population data from both before and after the perturbations. Here we present three cases of well-documented anthropogenic severe perturbations (different forms of habitat loss and deterioration influencing fertility and survival) that have affected three species of birds (a raptor, a scavenger and a waterbird) for which we possess long-term population time series. We tested whether the perturbations caused serious population decline or whether the study species were resilient, that is, its population dynamics were relatively unaffected. Two of the species did decline, although to a relatively small extent with no shift to a state of lower population numbers. Subsequently, these populations recovered rapidly and numbers reached similar levels to before the perturbations. Strikingly, in the third species a strong breakpoint took place towards greater population sizes, probably due to the colonization of new areas by recruits that were queuing at the destroyed habitat. Even though it is difficult to draw patterns of resilience from only three cases, the study species were all long-lived, social species with excellent dispersal and colonization abilities, capable of skipping reproduction and undergoing a phase of significant long-term population increase. The search for such patterns is crucial for optimizing the limited resources allocated to conservation and for predicting the future impact of planned anthropogenic activities on ecosystems.