Universal resilience patterns in complex networks

Common bean under different water availability reveals classifiable stimuli-specific signatures in plant electrome

Plant electrophysiology has unveiled the involvement of electrical signals in the physiology and behavior of plants. Spontaneously generated bioelectric activity can be altered in response to changes in environmental conditions, suggesting that a plant's electrome may possess a distinct signature associated with various stimuli. Analyzing electrical signals, particularly the electrome, in conjunction with Machine Learning (ML) techniques has emerged as a promising approach to classify characteristic electrical signals corresponding to each stimulus. This study aimed to characterize the electrome of common bean (Phaseolus vulgaris L.) cv. BRS-Expedito, subjected to different water availabilities, seeking patterns linked to these stimuli. For this purpose, bean plants in the vegetative stage were subjected to the following treatments: (I) distilled water; (II) half-strength Hoagland's nutrient solution; (III) -2 MPa PEG solution; and (IV) -2 MPa NaCl solution. Electrical signals were recorded within a Faraday's cage using the MP36 electronic system for data acquisition. Concurrently, plant water status was assessed by monitoring leaf turgor variation. Leaf temperature was additionally measured. Various analyses were conducted on the electrical time series data, including arithmetic average of voltage variation, skewness, kurtosis, Probability Density Function (PDF), autocorrelation, Power Spectral Density (PSD), Approximate Entropy (ApEn), Fast Fourier Transform (FFT), and Multiscale Approximate Entropy (ApEn(s)). Statistical analyses were performed on leaf temperature, voltage variation, skewness, kurtosis, PDF µ exponent, autocorrelation, PSD β exponent, and approximate entropy data. Machine Learning analyses were applied to identify classifiable patterns in the electrical time series. Characterization of the electrome of BRS-Expedito beans revealed stimulus-dependent profiles, even when alterations in water availability stimuli were similar in terms of quality and intensity. Additionally, it was observed that the bean electrome exhibits high levels of complexity, which are altered by different stimuli, with more intense and aversive stimuli leading to drastic reductions in complexity levels. Notably, one of the significant findings was the 100% accuracy of Small Vector Machine in detecting salt stress using electrome data. Furthermore, the study highlighted alterations in the plant electrome under low water potential before observable leaf turgor changes. This work demonstrates the potential use of the electrome as a physiological indicator of the water status in bean plants.

Expanding China's protected areas network to enhance resilience of climate connectivity

Expanding the network of connected and resilient protected areas (PAs) for climate change adaptation can help species track suitable climate conditions and safeguard biodiversity. This is often overlooked when expanding PAs and quantifying their benefits, resulting in an underestimate of the benefits of expanding PAs. We expanded PAs through terrestrial mammalian species distribution hotspots, Key Biodiversity Areas (KBAs), and wilderness areas. Then, we constructed climate connectivity networks using a resistance-based approach and further quantified the network resilience to propose resilient climate response strategies in China. The results showed that existing PAs suffered from location biases with important biodiversity areas. The existing PAs represented about half of the KBAs and wilderness areas, yet only 12.08% of terrestrial mammalian species distribution hotspots were located within existing PAs. Compared with the existing PA network, the network efficiency and resilience of the expanded PAs' climate connectivity increased to 1.80 times and 1.78 times, respectively. With 56% of the nodes remaining, the network efficiency of the expanded PAs was equivalent to that of the existing PAs with all nodes. The network resilience of preferentially protecting and restoring low human footprint patches was approximately 1.5-2 times that of the random scenario. These findings highlighted that confronted with the unoptimistic situation of global warming, nature conservation based on existing PAs was no longer optimal. It was critical to construct a connected and resilient conservation network relying on both important biodiversity areas and low human footprint patches.

On the role of diffusion dynamics on community-aware centrality measures

Theoretical and empirical studies on diffusion models have revealed their versatile applicability across different fields, spanning from sociology and finance to biology and ecology. The presence of a community structure within real-world networks has a substantial impact on how diffusion processes unfold. Key nodes located both within and between these communities play a crucial role in initiating diffusion, and community-aware centrality measures effectively identify these nodes. While numerous diffusion models have been proposed in literature, very few studies investigate the relationship between the diffusive ability of key nodes selected by community-aware centrality measures, the distinct dynamical conditions of various models, and the diverse network topologies. By conducting a comparative evaluation across four diffusion models, utilizing both synthetic and real-world networks, along with employing two different community detection techniques, our study aims to gain deeper insights into the effectiveness and applicability of the community-aware centrality measures. Results suggest that the diffusive power of the selected nodes is affected by three main factors: the strength of the network's community structure, the internal dynamics of each diffusion model, and the budget availability. Specifically, within the category of simple contagion models, such as SI, SIR, and IC, we observe similar diffusion patterns when the network's community structure strength and budget remain constant. In contrast, the LT model, which falls under the category of complex contagion dynamics, exhibits divergent behavior under the same conditions.

Quantifying the Resilience of Coal Energy Supply in China Toward Carbon Neutrality

Facing the challenge of achieving the goal of carbon neutrality, China is decoupling the currently close dependence of its economy on coal use. The energy supply and demand decarbonization has substantial influence on the resilience of the coal supply. However, a general understanding of the precise impact of energy decarbonization on the resilience of the coal energy supply is still lacking. Here, from the perspective of network science, we propose a theoretical framework to explore the resilience of the coal market of China. We show that the processes of increasing the connectivity and the competition between the coal enterprises, which are widely believed to improve the resilience of the coal market, can undermine the sustainability of the coal supply. Moreover, our results reveal that the policy of closing small-sized coal mines may not only reduce the safety accidents in the coal production but also improve the resilience of the coal market network. Using our model, we also suggest a few practical policies for minimizing the systemic risk of the coal energy supply.

Network properties determine neural network performance

Machine learning influences numerous aspects of modern society, empowers new technologies, from Alphago to ChatGPT, and increasingly materializes in consumer products such as smartphones and self-driving cars. Despite the vital role and broad applications of artificial neural networks, we lack systematic approaches, such as network science, to understand their underlying mechanism. The difficulty is rooted in many possible model configurations, each with different hyper-parameters and weighted architectures determined by noisy data. We bridge the gap by developing a mathematical framework that maps the neural network's performance to the network characters of the line graph governed by the edge dynamics of stochastic gradient descent differential equations. This framework enables us to derive a neural capacitance metric to universally capture a model's generalization capability on a downstream task and predict model performance using only early training results. The numerical results on 17 pre-trained ImageNet models across five benchmark datasets and one NAS benchmark indicate that our neural capacitance metric is a powerful indicator for model selection based only on early training results and is more efficient than state-of-the-art methods.

Healthcare system resilience and adaptability to pandemic disruptions in the United States

Understanding healthcare system resilience has become paramount, particularly in the wake of the COVID-19 pandemic, which imposed unprecedented burdens on healthcare services and severely impacted public health. Resilience is defined as the system's ability to absorb, recover from and adapt to disruptions; however, despite extensive studies on this subject, we still lack empirical evidence and mathematical tools to quantify its adaptability (the ability of the system to adjust to and learn from disruptions). By analyzing millions of patients' electronic medical records across US states, we find that the COVID-19 pandemic caused two successive waves of disruptions within the healthcare systems, enabling natural experiment analysis of the adaptive capacity of each system to adapt to past disruptions. We generalized the quantification framework and found that the US healthcare systems exhibit substantial adaptability (ρ = 0.58) but only a moderate level of resilience (r = 0.70). When considering system responses across racial groups, Black and Hispanic groups were more severely impacted by pandemic disruptions than white and Asian groups. Physician abundance was the key characteristic for determining healthcare system resilience. Our results offer vital guidance in designing resilient and sustainable healthcare systems to prepare for future waves of disruptions akin to COVID-19 pandemics.

Control of ecological networks: Abundance control or ecological regulation?

Complex ecosystems often exhibit a tipping point around which a small perturbation can lead to the loss of the basic functionality of ecosystems. It is challenging to develop a control strategy to bring ecosystems to the desired stable states. Typically, two methods are employed to restore the functionality of ecosystems: abundance control and ecological regulation. Abundance control involves directly managing species abundance through methods such as trapping, shooting, or poisoning. On the other hand, ecological regulation is a strategy for ecosystems to self-regulate through environment improvement. To enhance the effectiveness of ecosystem recovery, we propose adaptive regulation by combining the two control strategies from mathematical and network science perspectives. Criteria for controlling ecosystems to reach equilibrium with or without noise perturbation are established. The time and energy costs of restoring an ecosystem to equilibrium often determine the choice of control strategy, thus, we estimate the control costs. Furthermore, we observe that the regulation parameter in adaptive regulation affects both time and energy costs, with a trade-off existing between them. By optimizing the regulation parameter based on a performance index with fixed weights for time and energy costs, we can minimize the total cost. Moreover, we discuss the impact of the complexity of ecological networks on control costs, where the more complex the networks, the higher the costs. We provide corresponding theoretical analyses for random networks, predator-prey networks, and mixture networks.

Resilience of human-nature interaction network to pandemic conditions

Cultural ecosystem services (CES) contribute to maintaining and improving human well-being. Understanding the network of interactions involved in co-producing CES is essential for maximizing well-being. In this study, we used social media data to estimate a CES network and assess human-nature interactions underpinning CES co-production. We employed a replicable bottom-up approach, using 682,000 Reddit posts to define a comprehensive repertoire of nature features and human activities, and then sampled the co-occurrence of these features and activities reported in 41.7 million tweets from 2018 to 2022. We expected to observe large changes in the CES network topology in relation to mobility restrictions during the COVID-19 pandemic, but instead the CES network was resilient. However, there was an impulse on the link between self care activities and urban greenspace. This demonstrates that urban greenspaces facilitated local CES production and, thus, provided resilience for maintaining well-being during the pandemic. This study emphasizes the importance of promoting access to nature features that provide CES within local communities.

Precision psychiatry: predicting predictability

Precision psychiatry is an emerging field that aims to provide individualized approaches to mental health care. An important strategy to achieve this precision is to reduce uncertainty about prognosis and treatment response. Multivariate analysis and machine learning are used to create outcome prediction models based on clinical data such as demographics, symptom assessments, genetic information, and brain imaging. While much emphasis has been placed on technical innovation, the complex and varied nature of mental health presents significant challenges to the successful implementation of these models. From this perspective, I review ten challenges in the field of precision psychiatry, including the need for studies on real-world populations and realistic clinical outcome definitions, and consideration of treatment-related factors such as placebo effects and non-adherence to prescriptions. Fairness, prospective validation in comparison to current practice and implementation studies of prediction models are other key issues that are currently understudied. A shift is proposed from retrospective studies based on linear and static concepts of disease towards prospective research that considers the importance of contextual factors and the dynamic and complex nature of mental health.

Duality between predictability and reconstructability in complex systems

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. We provide analytical calculations of the uncertainty coefficients for many different systems, including continuous deterministic systems, and describe a numerical procedure when exact calculations are intractable. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process. Finally, we provide evidence that predictability-reconstruction dualities may exist in dynamical processes on real networks close to criticality.

Is resilience a unifying concept for the biological sciences?

There is increasing interest in applying resilience concepts at different scales of biological organization to address major interdisciplinary challenges from cancer to climate change. It is unclear, however, whether resilience can be a unifying concept consistently applied across the breadth of the biological sciences, or whether there is limited capacity for integration. In this review, we draw on literature from molecular biology to community ecology to ascertain commonalities and shortcomings in how resilience is measured and interpreted. Resilience is studied at all levels of biological organization, although the term is often not used. There is a suite of resilience mechanisms conserved across biological scales, and there are tradeoffs that affect resilience. Resilience is conceptually useful to help diverse researchers think about how biological systems respond to perturbations, but we need a richer lexicon to describe the diversity of perturbations, and we lack widely applicable metrics of resilience.

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individually, their collective behavior remains poorly understood. In this work, we combine experiments, theory, and numerical simulations to understand the main mechanisms underlying the collective behavior of soft flow networks with elements that exhibit negative differential resistance. Strikingly, our theoretical analysis and experiments reveal that a minimal network of nonlinear resistors, which we have termed a 'fluidic memristor', displays history-dependent resistance. This new class of element can be understood as a collection of hysteresis loops that allows this fluidic system to store information, and it can be directly used as a tunable resistor in fluidic setups. Our results provide insights that can inform other applications of fluid flow networks in soft materials science, biomedical settings, and soft robotics, and may also motivate new understanding of the flow networks involved in animal and plant physiology.

Assessing the effects of extreme climate risk on urban ecological resilience in China

The frequent occurrence of extreme weather events has imparted significant pressure on urban ecosystem management. Evaluating the relationship between extreme climate risk (ECR) and urban ecological resilience (UER) is a key issue in achieving the green and sustainable development objectives of cities. This study measures UER in China from 2005 to 2020 using the entropy weight method-TOPSIS method, investigates the relationship between ECR and UER using the dynamic GMM model, and further explores the influencing mechanism. The results suggest that ECR has an inhibiting influence on UER. Additionally, the moderating mechanism investigation demonstrates that environmental regulation can mitigate the threat of ECR to UER to a certain extent, and with the regulation effect based on the government's environmental concern being better than that of the market pollution fee payment. The group test outcomes demonstrate that the discrepancies in regions and marketization lead to certain differences in the relationship between ECR and UER. Additional investigation indicates that ECR has an asymmetric relationship with UER at distinct quantiles. Our findings reflect the subtle associations between ECR and UER as a whole, and will help relevant organizations in formulating more precise and scientific policies to enhance urban ecological resilience.

Robustness of coupled networks with multiple support from functional components at different scales

Robustness is an essential component of modern network science. Here, we investigate the robustness of coupled networks where the functionality of a node depends not only on its connectivity, here measured by the size of its connected component in its own network, but also the support provided by at least M links from another network. We here develop a theoretical framework and investigate analytically and numerically the cascading failure process when the system is under attack, deriving expressions for the proportion of functional nodes in the stable state, and the critical threshold when the system collapses. Significantly, our results show an abrupt phase transition and we derive the minimum inner and inter-connectivity density necessary for the system to remain active. We also observe that the system necessitates an increased density of links inside and across networks to prevent collapse, especially when conditions on the coupling between the networks are more stringent. Finally, we discuss the importance of our results in real-world settings and their potential use to aid decision-makers design more resilient infrastructure systems.

A taxonomy of multiple stable states in complex ecological communities

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

Predicting multiple observations in complex systems through low-dimensional embeddings

Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equations to compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

Integrating FRAM and BN for enhanced resilience evaluation in construction emergency response: A scaffold collapse case study

The construction system's complexity can generate substantial uncertainties during emergencies. Resilience, as a new perspective on emergency response, can significantly mitigate these challenges. This paper introduces an innovative model to assess the resilience of construction emergency response processes utilizing a scaffold collapse scenario as a demonstrative case study. Grounded in resilience engineering, our model integrates the merits of the Functional Resonance Analysis Method (FRAM) with the probabilistic strengths of Bayesian Networks (BNs). The process commences with FRAM, mapping out the emergency response in qualitative terms by identifying functions, variabilities, and couplings. This culminates in a topological network which serves as a foundational structure for the directed Complex Network (CN) and the BN model. Thereafter, the Delphi method and the modified K-shell (MKS) decomposition algorithm guide the computation of prior probabilities for root nodes and the conditional probability table within the BN model. Subsequently, the BN model is subjected to a simulation using the AgenaRisk software, executing both forward and backward propagation as well as sensitivity analyses. Our findings pinpoint "Intersectoral Coordination and Linkage" as the most crucial function, with rapidity being the most sensitive aspect influencing resilience during a scaffold collapse emergency response process.

Anticipating regime shifts by mixing early warning signals from different nodes

Real systems showing regime shifts, such as ecosystems, are often composed of many dynamical elements interacting on a network. Various early warning signals have been proposed for anticipating regime shifts from observed data. However, it is unclear how one should combine early warning signals from different nodes for better performance. Based on theory of stochastic differential equations, we propose a method to optimize the node set from which to construct an early warning signal. The proposed method takes into account that uncertainty as well as the magnitude of the signal affects its predictive performance, that a large magnitude or small uncertainty of the signal in one situation does not imply the signal's high performance, and that combining early warning signals from different nodes is often but not always beneficial. The method performs well particularly when different nodes are subjected to different amounts of dynamical noise and stress.

Learning interpretable collective variables for spreading processes on networks

Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.

Coexistence mechanism of ecological specialists and generalists based on a network dimension reduction method

As an ecological strategy for species coexistence, some species adapt to a wide range of habitats, while others specialize in particular environments. Such 'generalists' and 'specialists' achieve normal ecological balance through a complex network of interactions between species. However, the role of these interactions in maintaining the coexistence of generalist and specialist species has not been elucidated within a general theoretical framework. Here, we analyze the ecological mechanism for the coexistence of specialist and generalist species in a class of mutualistic and competitive interaction ecosystems based on the network dimension reduction method. We find that ecological specialists and generalists can be identified based on the number of their respective interactions. We also find, using real-world empirical network simulations, that the removal of ecological generalists can lead to the collapse of local ecosystems, which is rarely observed with the loss of ecological specialists.

Facilitation and competition deconstructed: a mechanistic modelling approach to the stress gradient hypothesis applied to drylands

Facilitative interactions among species are key in plant communities. While experimental tests support the Stress Gradient Hypothesis (SGH) as an association between facilitation and stress, whether the shape of net effects along stress gradients can be predicted is controversial, with no available mathematical modelling approaches. We proposed a novel test, using a modification of the R* model to study how negative and positive partial effects of plant interactions in drylands combine along two common stress gradients. We modelled different interactions: competition for water and light, amelioration of soil infiltration and/or grazing protection, obtaining that intensity and importance of facilitation did not generally increase along stress gradients, being dependent on the interaction type. While along the water stress gradient net interactions became more positive, reaching a maximum and then waning again, various outcomes were observed along the grazing gradient. Shape variety was mainly driven by the various shapes of the partial positive effects. Under resource stress, additive interaction effects can be expected, whereas when including grazing, the effects were non-additive. In the context of the SGH, deconstructing the effect of positive and negative interaction in a pairwise mechanistic models of drylands does not show a unique shape along stress gradients.

Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle-particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system's variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network's resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid-liquid phase boundary using a single volume fraction of particles well beyond this phase boundary.

Mechanistic description of spontaneous loss of memory persistent activity based on neuronal synaptic strength

Persistent neural activity associated with working memory (WM) lasts for a limited time duration. Current theories suggest that its termination is actively obtained via inhibitory currents, and there is currently no theory regarding the possibility of a passive memory-loss mechanism that terminates memory persistent activity. Here, we develop an analytical-framework, based on synaptic strength, and show via simulations and fitting to wet-lab experiments, that passive memory-loss might be a result of an ionic-current long-term plateau, i.e., very slow reduction of memory followed by abrupt loss. We describe analytically the plateau, when the memory state is just below criticality. These results, including the plateau, are supported by experiments performed on rats. Moreover, we show that even just above criticality, forgetfulness can occur due to neuronal noise with ionic-current fluctuations, yielding a plateau, representing memory with very slow decay, and eventually a fast memory decay. Our results could have implications for developing new medications, targeted against memory impairments, through modifying neuronal noise.

DomiRank Centrality reveals structural fragility of complex networks via node dominance

Determining the key elements of interconnected infrastructure and complex systems is paramount to ensure system functionality and integrity. This work quantifies the dominance of the networks' nodes in their respective neighborhoods, introducing a centrality metric, DomiRank, that integrates local and global topological information via a tunable parameter. We present an analytical formula and an efficient parallelizable algorithm for DomiRank centrality, making it applicable to massive networks. From the networks' structure and function perspective, nodes with high values of DomiRank highlight fragile neighborhoods whose integrity and functionality are highly dependent on those dominant nodes. Underscoring this relation between dominance and fragility, we show that DomiRank systematically outperforms other centrality metrics in generating targeted attacks that effectively compromise network structure and disrupt its functionality for synthetic and real-world topologies. Moreover, we show that DomiRank-based attacks inflict more enduring damage in the network, hindering its ability to rebound and, thus, impairing system resilience. DomiRank centrality capitalizes on the competition mechanism embedded in its definition to expose the fragility of networks, paving the way to design strategies to mitigate vulnerability and enhance the resilience of critical infrastructures.

Resilience of transportation infrastructure networks to road failures

Anthropogenic climate change drives extreme weather events, leading to significant consequences for both society and the environment. This includes damage to road infrastructure, causing disruptions in transportation, obstructing access to emergency services, and hindering humanitarian organizations after natural disasters. In this study, we develop a novel method for analyzing the impacts of natural hazards on transportation networks rooted in the gravity model of travel, offering a fresh perspective to assess the repercussions of natural hazards on transportation network stability. Applying this approach to the Ahr valley flood of 2021, we discovered that the destruction of bridges and roads caused major bottlenecks, affecting areas considerably distant from the flood's epicenter. Furthermore, the flood-induced damage to the infrastructure also increased the response time of emergency vehicles, severely impeding the accessibility of emergency services. Our findings highlight the need for targeted road repair and reinforcement, with a focus on maintaining traffic flow for emergency responses. This research provides a new perspective that can aid in prioritizing transportation network resilience measures to reduce the economic and social costs of future extreme weather events.

Targeted rainfall enhancement as an objective of forestation

Forestation efforts are accelerating across the globe in the fight against global climate change, in order to restore biodiversity, and to improve local livelihoods. Yet, so far the non-local effects of forestation on rainfall have largely remained a blind spot. Here we build upon emerging work to propose that targeted rainfall enhancement may also be considered in the prioritization of forestation. We show that the tools to achieve this are rapidly becoming available, but we also identify drawbacks and discuss which further developments are still needed to realize robust assessments of the rainfall effects of forestation in the face of climate change. Forestation programs may then mitigate not only global climate change itself but also its adverse effects in the form of drying.

Diversity-induced trivialization and resilience of neural dynamics

Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.

Landscape quantifies the intermediate state and transition dynamics in ecological networks

Understanding the ecological mechanisms associated with the collapse and restoration is especially critical in promoting harmonious coexistence between humans and nature. So far, it remains challenging to elucidate the mechanisms of stochastic dynamical transitions for ecological systems. Using an example of plant-pollinator network, we quantified the energy landscape of ecological system. The landscape displays multiple attractors characterizing the high, low and intermediate abundance stable states. Interestingly, we detected the intermediate states under pollinator decline, and demonstrated the indispensable role of the intermediate state in state transitions. From the landscape, we define the barrier height (BH) as a global quantity to evaluate the transition feasibility. We propose that the BH can serve as a new early-warning signal (EWS) for upcoming catastrophic breakdown, which provides an earlier and more accurate warning signal than traditional metrics based on time series. Our results promote developing better management strategies to achieve environmental sustainability.

Systematic loss in biotic heterogeneity but not biodiversity across multiple trophic levels in Erhai lake, China

Anthropogenic disturbances and climate change have significantly altered the biotic composition across many ecosystems, leading to changes in biodiversity and even ecological collapse. An ecosystem comprises multiple trophic levels, and the issue how these disturbances affect their assembly processes remains unclear. Ecological stability of assemblages was maintained by their structure, and thus, revealing structure changes across trophic levels could improve our understanding of how ecosystems response to disturbances as a whole. In this study, we combined methods from palaeolimnology, ecology and network analysis, and observed the changes of biodiversity and network structure of two trophic levels (algae - diatoms and zoobenthos - chironomids) in Erhai lake, Southwest China over the last century. Results showed nutrient enrichment induced shifts in diatom and chironomid assemblages at ∼2001 CE, suggesting that the shift in Erhai lake may have occurred at multiple trophic levels. We found biodiversity exhibit different trends across trophic levels as it decreased in diatoms but increased in chironomids. However, network skewness declined in both trophic levels, indicating the common loss of biotic heterogeneity. The consistent decline of skewness among trophic levels long before the compositional shift is a potential parameter to warn of the shifts in lake ecosystems.

Rate-induced tipping in complex high-dimensional ecological networks

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Network-based restoration strategies maximize ecosystem recovery

Redressing global patterns of biodiversity loss requires quantitative frameworks that can predict ecosystem collapse and inform restoration strategies. By applying a network-based dynamical approach to synthetic and real-world mutualistic ecosystems, we show that biodiversity recovery following collapse is maximized when extirpated species are reintroduced based solely on their total number of connections in the original interaction network. More complex network-based strategies that prioritize the reintroduction of species that improve 'higher order' topological features such as compartmentalization do not provide meaningful performance improvements. These results suggest that it is possible to design nearly optimal restoration strategies that maximize biodiversity recovery for data-poor ecosystems in order to ensure the delivery of critical natural services that fuel economic development, food security, and human health around the globe.

Biodiversity and Constrained Information Dynamics in Ecosystems: A Framework for Living Systems

The increase in ecosystem biodiversity can be perceived as one of the universal processes converting energy into information across a wide range of living systems. This study delves into the dynamics of living systems, highlighting the distinction between ex post adaptation, typically associated with natural selection, and its proactive counterpart, ex ante adaptability. Through coalescence experiments using synthetic ecosystems, we (i) quantified ecosystem stability, (ii) identified correlations between some biodiversity indexes and the stability, (iii) proposed a mechanism for increasing biodiversity through moderate inter-ecosystem interactions, and (iv) inferred that the information carrier of ecosystems is species composition, or merged genomic information. Additionally, it was suggested that (v) changes in ecosystems are constrained to a low-dimensional state space, with three distinct alteration trajectories-fluctuations, rapid environmental responses, and long-term changes-converging into this state space in common. These findings suggest that daily fluctuations may predict broader ecosystem changes. Our experimental insights, coupled with an exploration of living systems' information dynamics from an ecosystem perspective, enhance our predictive capabilities for natural ecosystem behavior, providing a universal framework for understanding a broad spectrum of living systems.

Exploring the landscape of dismantling strategies based on the community structure of networks

Network dismantling is a relevant research area in network science, gathering attention both from a theoretical and an operational point of view. Here, we propose a general framework for dismantling that prioritizes the removal of nodes that bridge together different network communities. The strategies we detect are not unique, as they depend on the specific realization of the community detection algorithm considered. However, when applying the methodology to some synthetic benchmark and real-world networks we find that the dismantling performances are strongly robust, and do not depend on the specific algorithm. Thus, the stochasticity inherently present in many community detection algorithms allows to identify several strategies that have comparable effectiveness but require the removal of distinct subsets of nodes. This feature is highly relevant in operational contexts in which the removal of nodes is costly and allows to identify the least expensive strategy that still holds high effectiveness.

Resilience of hybrid herbivore-plant-pollinator networks

The concept of network resilience has gained increasing attention in the last few decades owing to its great potential in strengthening and maintaining complex systems. From network-based approaches, researchers have explored resilience of real ecological systems comprising diverse types of interactions, such as mutualism, antagonist, and predation, or mixtures of them. In this paper, we propose a dimension-reduction method for analyzing the resilience of hybrid herbivore-plant-pollinator networks. We qualitatively evaluate the contribution of species toward maintaining resilience of networked systems, as well as the distinct roles played by different categories of species. Our findings demonstrate that the strong contributors to network resilience within each category are more vulnerable to extinction. Notably, among the three types of species in consideration, plants exhibit a higher likelihood of extinction, compared to pollinators and herbivores.

Efficient simulations of epidemic models with tensor networks: Application to the one-dimensional susceptible-infected-susceptible model

The contact process is an emblematic model of a nonequilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible model, and it is widely used to describe contagious spreading. In this work, we demonstrate how accurate and efficient representations of the full probability distribution over all configurations of the contact process on a one-dimensional chain can be obtained by means of matrix product states (MPSs). We modify and adapt MPS methods from many-body quantum systems to study the classical distributions of the driven contact process at late times. We give accurate and efficient results for the distribution of large gaps, and illustrate the advantage of our methods over Monte Carlo simulations. Furthermore, we study the large deviation statistics of the dynamical activity, defined as the total number of configuration changes along a trajectory, and investigate quantum-inspired entropic measures, based on the second Rényi entropy.

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

Latent sub-structural resilience mechanisms in temporal human mobility networks during urban flooding

In studying resilience in temporal human networks, relying solely on global network measures would be inadequate; latent sub-structural network mechanisms need to be examined to determine the extent of impact and recovery of these networks during perturbations, such as urban flooding. In this study, we utilize high-resolution aggregated location-based data to construct temporal human mobility networks in Houston in the context of the 2017 Hurricane Harvey. We examine motif distribution, motif persistence, temporal stability, and motif attributes to reveal latent sub-structural mechanisms related to the resilience of human mobility networks during disaster-induced perturbations. The results show that urban flood impacts persist in human mobility networks at the sub-structure level for several weeks. The impact extent and recovery duration are heterogeneous across different network types. Also, while perturbation impacts persist at the sub-structure level, global topological network properties indicate that the network has recovered. The findings highlight the importance of examining the microstructures and their dynamic processes and attributes in understanding the resilience of temporal human mobility networks (and other temporal networks). The findings can also provide disaster managers, public officials, and transportation planners with insights to better evaluate impacts and monitor recovery in affected communities.

Spatial and temporal changes in the assembly mechanism and co-occurrence network of the chromophytic phytoplankton communities in coastal ecosystems under anthropogenic influences

As a typical semiclosed coastal sea area in China, the ecological environment of Bohai Bay has been significantly disturbed by human activities. As primary producers, the chromophytic phytoplankton are the basis of ecosystems, especially in coastal ecosystems, and changes in the chromophytic phytoplankton community can affect the stability of the entire ecosystem. In this study, we investigated the effects of the human activity-induced spatial and temporal environmental heterogeneity on the community composition, diversity, assembly mechanisms, and co-occurrence networks of chromophytic phytoplankton in Bohai Bay during the wet season and the dry season. The results showed that in both seasons, there was obvious environmental heterogeneity between the nearshore area and the offshore area, and the nearshore areas were more affected by human disturbance. Although higher diversity was supported by the abundance of nutrients in nearshore areas, co-occurrence network analysis revealed that the chromophytic phytoplankton were less closely connected to each other in nearshore areas than in offshore areas due to chemical oxygen demand (COD), eutrophication index (EI), and dissolved inorganic nitrogen (DIN). The nearshore network was less stable than the offshore co-occurrence network in both seasons, which was related to the concentration of dissolved oxygen and COD. Both stochastic and deterministic processes dominated the assembly of the chromophytic phytoplankton communities, with different importance rankings of stochastic and deterministic processes in the nearshore and offshore areas. Drift dominated the assembly of the communities in nearshore areas, while variable selection dominated the assembly of the communities in offshore areas. DIN, EI, and COD, rather than geographic distance, were the main environmental factors affecting the phylogenetic turnover of the chromophytic phytoplankton. Our study showed that environmental heterogeneity caused by human disturbance had a greater impact on the chromophytic phytoplankton communities in Bohai Bay than natural factors such as temperature and salinity.

A perturbation-based approach to identifying potentially superfluous network constituents

Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.

Integrating ecosystem services and complex network theory to construct and optimize ecological security patterns: a case study of Guangdong-Hong Kong-Macao Greater Bay Area, China

The urban agglomerations' rapid expansion and population growth have led to the fragmentation of landscape patterns and the degradation of ecosystems, seriously threatening regional ecological security. Ecological security pattern (ESP) is a spatial planning approach to effectively balance the development of urbanization and ecological protection. However, previous studies have ignored the difference in the importance of ecosystem services and the spatial compactness of ecological sources. The quantitative management objectives for maintaining the resilience of ESP are also rarely discussed. In this study, taking the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) as an example, ecological sources were identified by simulating multiple ES weight assignment scenarios through GeoSOS area optimization. Ecological corridors and strategic points were extracted by Linkage Mapper. The robustness analysis based on complex network theory was performed to quantify the management objectives of ESPs. The results showed that ESPs include 26,130.61 km² ecological sources (accounting for 46.6% of the area of GBA), 557 ecological corridors, and 112 ecological strategic points. In more detail, ecological sources are mainly distributed in the western and eastern mountainous areas, and ecological corridors primarily link peripheral edge areas of GBA in a circular radial shape. Compared with the current nature reserves, the identified ecological sources are more compact in landscape pattern. According to the robustness analysis, at least 23% of the important ecological sources should be strictly restricted from development activities to maintain the ESP's ability to resist ecological risks. This study also proposed corresponding differentiated ESPs management strategies. By optimizing the existing ESPs construction method and clarifying the ESPs management strategies, this study provides a completely scientific framework for the construction and management of ESPs in urban agglomerations.

Respiratory eukaryotic virome expansion and bacteriophage deficiency characterize childhood asthma

Asthma development and exacerbation is linked to respiratory virus infections. There is limited information regarding the presence of viruses during non-exacerbation/infection periods. We investigated the nasopharyngeal/nasal virome during a period of asymptomatic state, in a subset of 21 healthy and 35 asthmatic preschool children from the Predicta cohort. Using metagenomics, we described the virome ecology and the cross-species interactions within the microbiome. The virome was dominated by eukaryotic viruses, while prokaryotic viruses (bacteriophages) were independently observed with low abundance. Rhinovirus B species consistently dominated the virome in asthma. Anelloviridae were the most abundant and rich family in both health and asthma. However, their richness and alpha diversity were increased in asthma, along with the co-occurrence of different Anellovirus genera. Bacteriophages were richer and more diverse in healthy individuals. Unsupervised clustering identified three virome profiles that were correlated to asthma severity and control and were independent of treatment, suggesting a link between the respiratory virome and asthma. Finally, we observed different cross-species ecological associations in the healthy versus the asthmatic virus-bacterial interactome, and an expanded interactome of eukaryotic viruses in asthma. Upper respiratory virome "dysbiosis" appears to be a novel feature of pre-school asthma during asymptomatic/non-infectious states and merits further investigation.

Stability for IT2 T-S fuzzy systems under alternate event-triggered control

In this paper, an alternate event-triggered control is proposed to achieve stability of interval type-2 Takagi-Sugeno fuzzy systems. Comparing with the existing literature, this new control strategy displays an almost complete aperiodic feature which eliminates the conservativeness caused by time-triggered property of the traditional aperiodically intermittent control. Moreover, with two events being triggered alternately in this control strategy through examining two predetermined conditions, the efficiency of control can be further improved and the resources consumption can be greatly reduced. By employing the Lyapunov function and graph theory, several stability criteria are rigorously demonstrated. In addition, Zeno behavior is excluded in our system through obtaining a positive lower bound of the time interval between two triggering points. Subsequently, the validity of the presented strategy is evidenced by single-link robot arms systems. Finally, a numerical example is given to lend insight into the feasibility of our theoretical results.

Dimension reduction of dynamics on modular and heterogeneous directed networks

Dimension reduction is a common strategy to study nonlinear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of the key dynamical features of the original system. Finding such a reduced representation for complex systems is, however, a difficult task. We address this problem for dynamics on weighted directed networks, with special emphasis on modular and heterogeneous networks. We propose a two-step dimension-reduction method that takes into account the properties of the adjacency matrix. First, units are partitioned into groups of similar connectivity profiles. Each group is associated to an observable that is a weighted average of the nodes' activities within the group. Second, we derive a set of equations that must be fulfilled for these observables to properly represent the original system's behavior, together with a method for approximately solving them. The result is a reduced adjacency matrix and an approximate system of ODEs for the observables' evolution. We show that the reduced system can be used to predict some characteristic features of the complete dynamics for different types of connectivity structures, both synthetic and derived from real data, including neuronal, ecological, and social networks. Our formalism opens a way to a systematic comparison of the effect of various structural properties on the overall network dynamics. It can thus help to identify the main structural driving forces guiding the evolution of dynamical processes on networks.

Dimension reduction in higher-order contagious phenomena

We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network's resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.

Multimodal distribution of transient time of predator extinction in a three-species food chain

The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.

Directional switches in network-organized swarming systems with delay

Coordinated directional switches can emerge between members of moving biological groups. Previous studies have shown that the self-propelled particles model can well reproduce directional switching behaviors, but it neglects the impact of social interactions. Thus, we focus on the influence of social interactions on the ordered directional switching motion of swarming systems, in which homogeneous Erdös-Rényi networks, heterogeneous scale-free networks, networks with community structures, and real-world animal social networks have been considered. The theoretical estimation of mean switching time is obtained, and the results show that the interplay between social and delayed interactions plays an important role in regulating directional switching behavior. To be specific, for homogeneous Erdös-Rényi networks, the increase in mean degree may suppress the directional switching behaviors if the delay is sufficiently small. However, when the delay is large, the large mean degree may promote the directional switching behavior. For heterogeneous scale-free networks, the increase of degree heterogeneity can reduce the mean switching time if the delay is sufficiently small, while the increasing degree heterogeneity may suppress the ordered directional switches if the delay is large. For networks with community structures, higher communities can promote directional switches for small delays, while for large delays, it may inhibit directional switching behavior. For dolphin social networks, delay can promote the directional switching behavior. Our results bring to light the role of social and delayed interactions in the ordered directional switching motion.

Computational capability of ecological dynamics

Ecological dynamics is driven by complex ecological networks. Computational capabilities of artificial networks have been exploited for machine learning purposes, yet whether an ecological network possesses a computational capability and whether/how we can use it remain unclear. Here, we developed two new computational/empirical frameworks based on reservoir computing and show that ecological dynamics can be used as a computational resource. In silico ecological reservoir computing (ERC) reconstructs ecological dynamics from empirical time series and uses simulated system responses for information processing, which can predict near future of chaotic dynamics and emulate nonlinear dynamics. The real-time ERC uses real population dynamics of a unicellular organism, Tetrahymena thermophila. The temperature of the medium is an input signal and population dynamics is used as a computational resource. Intriguingly, the real-time ecological reservoir has necessary conditions for computing (e.g. synchronized dynamics in response to the same input sequences) and can make near-future predictions of empirical time series, showing the first empirical evidence that population-level phenomenon is capable of real-time computations. Our finding that ecological dynamics possess computational capability poses new research questions for computational science and ecology: how can we efficiently use it and how is it actually used, evolved and maintained in an ecosystem?

Disentangling the impact of straw incorporation on soil microbial communities: Enhanced network complexity and ecological stochasticity

Straw incorporation is typically employed to enhance the nutrient content of soil and promote crop growth in intensive agricultural systems. Despite studies regarding the effects of straw incorporation on soil microbial communities, the underlying mechanisms of its effect on community co-occurrence interactions and assembly processes remain poorly understood. Herein, soil samples with or without straw incorporation were collected across a latitudinal gradient from north to central China. We found that straw incorporation considerably altered the structure of soil microbial community. The relative abundance of bacterial Latescibacterota and fungal Mortierellomycota were higher in straw-amended soils owing to their ability to decompose straw residues. The co-occurrence network in straw-amended soil exhibited greater complexity, including more network connectivity and keystone species, and higher average degrees and clustering coefficients compared with the control sample network. The network robustness and vulnerability indices suggested that straw incorporation increased the microbial network stability. Normalized stochastic ratios demonstrated that the stochastic process was the dominant mechanisms shaping the assembly of microbial communities in straw-amended soils. Concurrently, null model analysis revealed that straw increased the contribution of dispersal limitation to the assembly of bacterial and fungal communities. The migration rate of the microbial community, obtained from Sloan neutral community model, was relatively low in straw-amended soil at all the sample sites, potentially indicating the great importance of dispersal limitation. These findings would enhance our understanding of the ecological patterns and interactions of soil microbial communities in response to straw incorporation.