Stability of ecosystems under oscillatory driving with frequency modulation.

Consumer-resource cycles are widespread in ecosystems, and seasonal forcing is known to influence them profoundly. Typically, seasonal forcing perturbs an ecosystem with time-varying frequency; however, previous studies have explored the dynamics of such systems under oscillatory forcing with constant frequency. Studies of the effect of time-varying frequency on ecosystem stability are lacking. Here we investigate isolated and network models of a cyclic consumer-resource ecosystem with oscillatory driving subjected to frequency modulation. We show that frequency modulation can induce stability in the system in the form of stable synchronized solutions, depending on intrinsic model parameters and extrinsic modulation strength. The stability of synchronous solutions is determined by calculating the maximal Lyapunov exponent, which determines that the fraction of stable synchronous solution increases with an increase in the modulation strength. We also uncover intermittent synchronization when synchronous dynamics are intermingled with episodes of asynchronous dynamics. Using the phase-reduction method for the network model, we reduce the system into a phase equation that clearly distinguishes synchronous, intermittently synchronous, and asynchronous solutions. While investigating the role of network topology, we find that variation in rewiring probability has a negligible effect on the stability of synchronous solutions. This study deepens our understanding of ecosystems under seasonal perturbations.

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

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

Rising temperature drives tipping points in mutualistic networks.

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

Identifying critical transitions in complex diseases.

Mortality and the burden of diseases worldwide continue to reach substantial numbers with societal development and urbanization. In the face of decline in human health, early detection of complex diseases is indispensable, albeit challenging. In this review, we document the research carried out thus far on the appearance of complex diseases marked by a critical transition or a sudden shift from a healthy state to a disease state. The theory of resilience and critical slowing down can provide practical tools to forecast the onset of various fatal and perpetuating diseases. However, critical transitions in diseases across diverse temporal and spatial scales may not always be preceded by critical slowing down. In this backdrop, an in-depth study of the underlying molecular mechanisms provides dynamic network biomarkers that can forecast potential critical transitions. We have put together the theory of complex diseases and resilience, and have discussed the need for advanced research in developing early warning signals in the field of medicine and health care. We conclude the review with a few open questions and prospects for research in this emerging field.

Effects of time-varying habitat connectivity on metacommunity persistence.

Network structure or connectivity patterns are critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure, though most real network structures change in time, forming time-varying networks. This raises the question, in metacommunities, how does the pattern of synchrony vary with temporal evolution in the network structure. The synchronous dynamics among species are known to reduce metacommunity persistence. Here we consider a time-varying metacommunity small-world network consisting of a chaotic three-species food chain oscillator in each patch or node. The rate of change in the network connectivity is determined by the natural frequency or its subharmonics of the constituent oscillator to allow sufficient time for the evolution of species in between successive rewirings. We find that over a range of coupling strengths and rewiring periods, even higher rewiring probabilities drive a network from asynchrony towards synchrony. Moreover, in networks with a small rewiring period, an increase in average degree (more connected networks) pushes the asynchronous dynamics to synchrony. On the other hand, in networks with a low average degree, a higher rewiring period drives the synchronous dynamics to asynchrony resulting in increased species persistence. Our results also follow the calculation of synchronization time and are robust across other ecosystem models. Overall, our study opens the possibility of developing temporal connectivity strategies to increase species persistence in ecological networks.

Network resilience of FitzHugh-Nagumo neurons in the presence of nonequilibrium dynamics.

Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the face of perturbations. Most of the research on network resilience has focused on the transition from one equilibrium state to an alternative equilibrium state. Although the presence of nonequilibrium dynamics in some nodes may advance or delay sudden transitions in networks and give early warning signals of an impending collapse, it has not been studied much in the context of network resilience. Here we bridge this gap by studying a neuronal network model with diverse topologies, in which nonequilibrium dynamics may appear in the network even before the transition to a resting state from an active state in response to environmental stress deteriorating their external conditions. We find that the percentage of uncoupled nodes exhibiting nonequilibrium dynamics plays a vital role in determining the network's transition type. We show that a higher proportion of nodes with nonequilibrium dynamics can delay the tipping and increase networks' resilience against environmental stress, irrespective of their topology. Further, predictability of an upcoming transition weakens, as the network topology moves from regular to disordered.

Long-range dispersal promotes species persistence in climate extremes.

Anthropogenic global warming in this century can act as a leading factor for large scale species extinctions in the near future. Species, in order to survive, need to develop dispersal strategies depending upon their environmental niche. Based on empirical evidence only a few previous studies have addressed how dispersal can evolve with changing temperature. However, for the analytical tractability, there is a need to develop an explicit model to ask how the temperature-dependent dispersal alters ecological dynamics. We investigate the persistence of species in a spatial ecological model, where dispersal is considered as a function of temperature. Spatial persistence is of major concern and dispersal is reasonably an important factor for extinction risk in the context of promoting synchrony. Our study yields how the temperature influences species decision of dispersal, resulting in either short-range or long-range dispersal. We examine synchronous or asynchronous behavior of species under their thermal dependence of dispersal. Moreover, we also analyze the transients to study the collective behavior of species away from their final or asymptotic dynamics. One of the key findings is at the most unfavorable environmental conditions long-range dispersal works out as the driving force for the persistence of species.