1
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Legault V, Pu Y, Weinans E, Cohen AA. Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1299162. [PMID: 38595863 PMCID: PMC11002238 DOI: 10.3389/fnetp.2024.1299162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 03/15/2024] [Indexed: 04/11/2024]
Abstract
Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.
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Affiliation(s)
- Véronique Legault
- Research Center of the Centre Hospitalier Universitaire de Sherbrooke, Sherbrooke, QC, Canada
| | - Yi Pu
- PRIMUS Research Group, Department of Family Medicine, University of Sherbrooke, Sherbrooke, QC, Canada
| | - Els Weinans
- Copernicus Institute of Sustainable Development, Environmental Science, Faculty of Geosciences, Utrecht University, Utrecht, Netherlands
| | - Alan A. Cohen
- Research Center of the Centre Hospitalier Universitaire de Sherbrooke, Sherbrooke, QC, Canada
- PRIMUS Research Group, Department of Family Medicine, University of Sherbrooke, Sherbrooke, QC, Canada
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2
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Masuda N, Aihara K, MacLaren NG. Anticipating regime shifts by mixing early warning signals from different nodes. Nat Commun 2024; 15:1086. [PMID: 38316802 PMCID: PMC10844243 DOI: 10.1038/s41467-024-45476-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 01/25/2024] [Indexed: 02/07/2024] Open
Abstract
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.
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Affiliation(s)
- Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, 14260-2900, USA.
- Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, NY, 14260-5030, USA.
| | - Kazuyuki Aihara
- International Research Center for Neurointelligence, The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Bunkyo City, Japan
| | - Neil G MacLaren
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, 14260-2900, USA
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3
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O'Brien DA, Deb S, Gal G, Thackeray SJ, Dutta PS, Matsuzaki SIS, May L, Clements CF. Early warning signals have limited applicability to empirical lake data. Nat Commun 2023; 14:7942. [PMID: 38040724 PMCID: PMC10692136 DOI: 10.1038/s41467-023-43744-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 11/17/2023] [Indexed: 12/03/2023] Open
Abstract
Research aimed at identifying indicators of persistent abrupt shifts in ecological communities, a.k.a regime shifts, has led to the development of a suite of early warning signals (EWSs). As these often perform inaccurately when applied to real-world observational data, it remains unclear whether critical transitions are the dominant mechanism of regime shifts and, if so, which EWS methods can predict them. Here, using multi-trophic planktonic data on multiple lakes from around the world, we classify both lake dynamics and the reliability of classic and second generation EWSs methods to predict whole-ecosystem change. We find few instances of critical transitions, with different trophic levels often expressing different forms of abrupt change. The ability to predict this change is highly processing dependant, with most indicators not performing better than chance, multivariate EWSs being weakly superior to univariate, and a recent machine learning model performing poorly. Our results suggest that predictive ecology should start to move away from the concept of critical transitions, developing methods suitable for predicting resilience loss not limited to the strict bounds of bifurcation theory.
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Affiliation(s)
- Duncan A O'Brien
- School of Biological Sciences, University of Bristol, Bristol, BS8 1TQ, UK.
| | - Smita Deb
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India
| | - Gideon Gal
- Kinneret Limnological Laboratory, Israel Oceanographic & Limnological Research, PO Box 447, Migdal, Israel
| | - Stephen J Thackeray
- Lake Ecosystems Group, UK Centre for Ecology & Hydrology, Bailrigg, Lancaster, UK
| | - Partha S Dutta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India
| | - Shin-Ichiro S Matsuzaki
- Biodiversity Division, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki, 305-8506, Japan
| | - Linda May
- UK Centre for Ecology & Hydrology, Bush Estate, Penicuik, Midlothian, EH26 OQB, UK
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4
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Heino MTJ, Proverbio D, Marchand G, Resnicow K, Hankonen N. Attractor landscapes: a unifying conceptual model for understanding behaviour change across scales of observation. Health Psychol Rev 2023; 17:655-672. [PMID: 36420691 PMCID: PMC10261543 DOI: 10.1080/17437199.2022.2146598] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 11/07/2022] [Indexed: 11/25/2022]
Abstract
Models and theories in behaviour change science are not in short supply, but they almost exclusively pertain to a particular facet of behaviour, such as automaticity or reasoned action, or to a single scale of observation such as individuals or communities. We present a highly generalisable conceptual model which is widely used in complex systems research from biology to physics, in an accessible form to behavioural scientists. The proposed model of attractor landscapes can be used to understand human behaviour change on different levels, from individuals to dyads, groups and societies. We use the model as a tool to present neglected ideas in contemporary behaviour change science, such as hysteresis and nonlinearity. The model of attractor landscapes can deepen understanding of well-known features of behaviour change (research), including short-livedness of intervention effects, problematicity of focusing on behavioural initiation while neglecting behavioural maintenance, continuum and stage models of behaviour change understood within a single accommodating framework, and the concept of resilience. We also demonstrate potential methods of analysis and outline avenues for future research.
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Affiliation(s)
| | | | | | - Kenneth Resnicow
- School of Public Health, University of Michigan. Rogel Cancer Center University of Michigan
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5
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Grziwotz F, Chang CW, Dakos V, van Nes EH, Schwarzländer M, Kamps O, Heßler M, Tokuda IT, Telschow A, Hsieh CH. Anticipating the occurrence and type of critical transitions. SCIENCE ADVANCES 2023; 9:eabq4558. [PMID: 36608135 PMCID: PMC9821862 DOI: 10.1126/sciadv.abq4558] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/09/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.
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Affiliation(s)
- Florian Grziwotz
- Institute for Evolution and Biodiversity, Westphalian Wilhelms-University Münster, Münster 48149, Germany
| | - Chun-Wei Chang
- Institute of Fisheries Science, Department of Life Science, National Taiwan University, Taipei 10617, Taiwan
- National Center for Theoretical Sciences, Taipei 10617, Taiwan
| | - Vasilis Dakos
- ISEM, CNRS, University of Montpellier, IRD, EPHE, Montpellier, France
| | - Egbert H. van Nes
- Department of Environmental Science, Wageningen University, Wageningen P.O. Box 47, 6700 AA, Netherlands
| | - Markus Schwarzländer
- Institute of Plant Biology and Biotechnology, University of Münster, Münster 48143, Germany
| | - Oliver Kamps
- Center for Nonlinear Science, Westphalian Wilhelms-University Münster, Münster 48149, Germany
| | - Martin Heßler
- Center for Nonlinear Science, Westphalian Wilhelms-University Münster, Münster 48149, Germany
- Institute for Theoretical Physics, Westphalian Wilhelms-University Münster, Münster 48149, Germany
| | - Isao T. Tokuda
- Department of Mechanical Engineering, Ritsumeikan University, Kusatsu 525-8577, Japan
| | - Arndt Telschow
- Institute for Evolution and Biodiversity, Westphalian Wilhelms-University Münster, Münster 48149, Germany
- Institute for Environmental Systems Science, University of Osnabrück, Osnabrück 49076, Germany
| | - Chih-hao Hsieh
- National Center for Theoretical Sciences, Taipei 10617, Taiwan
- Institute of Oceanography, National Taiwan University, Taipei 10617, Taiwan
- Institute of Ecology and Evolutionary Biology, Department of Life Science, National Taiwan University, Taipei 10617, Taiwan
- Research Center for Environmental Changes, Academia Sinica, Taipei 11529, Taiwan
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6
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Zhong J, Liu H, Chen P. The single-sample network module biomarkers (sNMB) method reveals the pre-deterioration stage of disease progression. J Mol Cell Biol 2022; 14:6693713. [PMID: 36069893 PMCID: PMC9923387 DOI: 10.1093/jmcb/mjac052] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Revised: 05/27/2022] [Accepted: 09/02/2022] [Indexed: 11/12/2022] Open
Abstract
The progression of complex diseases generally involves a pre-deterioration stage that occurs during the transition from a healthy state to disease deterioration, at which a drastic and qualitative shift occurs. The development of an effective approach is urgently needed to identify such a pre-deterioration stage or critical state just before disease deterioration, which allows the timely implementation of appropriate measures to prevent a catastrophic transition. However, identifying the pre-deterioration stage is a challenging task in clinical medicine, especially when only a single sample is available for most patients, which is responsible for the failure of most statistical methods. In this study, a novel computational method, called single-sample network module biomarkers (sNMB), is presented to predict the pre-deterioration stage or critical point using only a single sample. Specifically, the proposed single-sample index effectively quantifies the disturbance caused by a single sample against a group of given reference samples. Our method successfully detected the early warning signal of the critical transitions when applied to both a numerical simulation and four real datasets, including acute lung injury, stomach adenocarcinoma, esophageal carcinoma, and rectum adenocarcinoma. In addition, it provides signaling biomarkers for further practical application, which helps to discover prognostic indicators and reveal the underlying molecular mechanisms of disease progression.
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Affiliation(s)
- Jiayuan Zhong
- School of Mathematics and Big Data, Foshan University, Foshan 528000, China,School of Mathematics, South China University of Technology, Guangzhou 510640, China
| | - Huisheng Liu
- School of Life Sciences and Technology, Tongji University, Shanghai 200092, China
| | - Pei Chen
- Correspondence to: Pei Chen, E-mail:
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7
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Ghadami A, Epureanu BI. Data-driven prediction in dynamical systems: recent developments. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210213. [PMID: 35719077 PMCID: PMC9207538 DOI: 10.1098/rsta.2021.0213] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.
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Affiliation(s)
- Amin Ghadami
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Bogdan I. Epureanu
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA
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8
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Structure-based identification of sensor species for anticipating critical transitions. Proc Natl Acad Sci U S A 2021; 118:2104732118. [PMID: 34911755 DOI: 10.1073/pnas.2104732118] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/15/2021] [Indexed: 11/18/2022] Open
Abstract
Ecological systems can undergo sudden, catastrophic changes known as critical transitions. Anticipating these critical transitions remains challenging in systems with many species because the associated early warning signals can be weakly present or even absent in some species, depending on the system dynamics. Therefore, our limited knowledge of ecological dynamics may suggest that it is hard to identify those species in the system that display early warning signals. Here, we show that, in mutualistic ecological systems, it is possible to identify species that early anticipate critical transitions by knowing only the system structure-that is, the network topology of plant-animal interactions. Specifically, we leverage the mathematical theory of structural observability of dynamical systems to identify a minimum set of "sensor species," whose measurement guarantees that we can infer changes in the abundance of all other species. Importantly, such a minimum set of sensor species can be identified by using the system structure only. We analyzed the performance of such minimum sets of sensor species for detecting early warnings using a large dataset of empirical plant-pollinator and seed-dispersal networks. We found that species that are more likely to be sensors tend to anticipate earlier critical transitions than other species. Our results underscore how knowing the structure of multispecies systems can improve our ability to anticipate critical transitions.
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9
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Zhong J, Han C, Zhang X, Chen P, Liu R. scGET: Predicting Cell Fate Transition During Early Embryonic Development by Single-cell Graph Entropy. GENOMICS, PROTEOMICS & BIOINFORMATICS 2021; 19:461-474. [PMID: 34954425 PMCID: PMC8864248 DOI: 10.1016/j.gpb.2020.11.008] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Revised: 11/08/2020] [Accepted: 01/02/2021] [Indexed: 01/26/2023]
Abstract
During early embryonic development, cell fate commitment represents a critical transition or "tipping point" of embryonic differentiation, at which there is a drastic and qualitative shift of the cell populations. In this study, we presented a computational approach, scGET, to explore the gene-gene associations based on single-cell RNA sequencing (scRNA-seq) data for critical transition prediction. Specifically, by transforming the gene expression data to the local network entropy, the single-cell graph entropy (SGE) value quantitatively characterizes the stability and criticality of gene regulatory networks among cell populations and thus can be employed to detect the critical signal of cell fate or lineage commitment at the single-cell level. Being applied to five scRNA-seq datasets of embryonic differentiation, scGET accurately predicts all the impending cell fate transitions. After identifying the "dark genes" that are non-differentially expressed genes but sensitive to the SGE value, the underlying signaling mechanisms were revealed, suggesting that the synergy of dark genes and their downstream targets may play a key role in various cell development processes.The application in all five datasets demonstrates the effectiveness of scGET in analyzing scRNA-seq data from a network perspective and its potential to track the dynamics of cell differentiation. The source code of scGET is accessible at https://github.com/zhongjiayuna/scGET_Project.
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Affiliation(s)
- Jiayuan Zhong
- School of Mathematics, South China University of Technology, Guangzhou 510640, PR China
| | - Chongyin Han
- School of Biology and Biological Engineering, South China University of Technology, Guangzhou 510640, PR China
| | - Xuhang Zhang
- School of Computer Science and Engineering, South China University of Technology, Guangzhou 510640, PR China
| | - Pei Chen
- School of Mathematics, South China University of Technology, Guangzhou 510640, PR China.
| | - Rui Liu
- School of Mathematics, South China University of Technology, Guangzhou 510640, PR China; Pazhou Lab, Guangzhou 510330, PR China.
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10
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Weinans E, Quax R, van Nes EH, Leemput IAVD. Evaluating the performance of multivariate indicators of resilience loss. Sci Rep 2021; 11:9148. [PMID: 33911086 PMCID: PMC8080839 DOI: 10.1038/s41598-021-87839-y] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Accepted: 04/01/2021] [Indexed: 11/09/2022] Open
Abstract
Various complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These 'tipping points' are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.
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Affiliation(s)
- Els Weinans
- Department of Environmental Sciences, Wageningen University, Wageningen, The Netherlands.
| | - Rick Quax
- Computational Science, University of Amsterdam, Amsterdam, The Netherlands
| | - Egbert H van Nes
- Department of Environmental Sciences, Wageningen University, Wageningen, The Netherlands
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11
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Bhandary S, Kaur T, Banerjee T, Dutta PS. Network resilience of FitzHugh-Nagumo neurons in the presence of nonequilibrium dynamics. Phys Rev E 2021; 103:022314. [PMID: 33736003 DOI: 10.1103/physreve.103.022314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Accepted: 02/01/2021] [Indexed: 11/07/2022]
Abstract
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.
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Affiliation(s)
- Subhendu Bhandary
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
| | - Taranjot Kaur
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Partha Sharathi Dutta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
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12
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Southall E, Tildesley MJ, Dyson L. Prospects for detecting early warning signals in discrete event sequence data: Application to epidemiological incidence data. PLoS Comput Biol 2020; 16:e1007836. [PMID: 32960900 PMCID: PMC7531856 DOI: 10.1371/journal.pcbi.1007836] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Revised: 10/02/2020] [Accepted: 07/30/2020] [Indexed: 11/18/2022] Open
Abstract
Early warning signals (EWS) identify systems approaching a critical transition, where the system undergoes a sudden change in state. For example, monitoring changes in variance or autocorrelation offers a computationally inexpensive method which can be used in real-time to assess when an infectious disease transitions to elimination. EWS have a promising potential to not only be used to monitor infectious diseases, but also to inform control policies to aid disease elimination. Previously, potential EWS have been identified for prevalence data, however the prevalence of a disease is often not known directly. In this work we identify EWS for incidence data, the standard data type collected by the Centers for Disease Control and Prevention (CDC) or World Health Organization (WHO). We show, through several examples, that EWS calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data. In particular, the variance displays a decreasing trend on the approach to disease elimination, contrary to that expected from critical slowing down theory; this could lead to unreliable indicators of elimination when calculated on real-world data. We derive analytical predictions which can be generalised for many epidemiological systems, and we support our theory with simulated studies of disease incidence. Additionally, we explore EWS calculated on the rate of incidence over time, a property which can be extracted directly from incidence data. We find that although incidence might not exhibit typical critical slowing down properties before a critical transition, the rate of incidence does, presenting a promising new data type for the application of statistical indicators.
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Affiliation(s)
- Emma Southall
- EPSRC & MRC Centre for Doctoral Training in Mathematics for Real-World Systems, University of Warwick, Coventry, UK
| | - Michael J. Tildesley
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, Mathematics Institute and School of Life Sciences, University of Warwick, Coventry, UK
| | - Louise Dyson
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, Mathematics Institute and School of Life Sciences, University of Warwick, Coventry, UK
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13
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Li T, Dong Y, Liu Z. A review of social-ecological system resilience: Mechanism, assessment and management. THE SCIENCE OF THE TOTAL ENVIRONMENT 2020; 723:138113. [PMID: 32224405 DOI: 10.1016/j.scitotenv.2020.138113] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Revised: 03/20/2020] [Accepted: 03/20/2020] [Indexed: 06/10/2023]
Abstract
Social-ecological system (SES) resilience involves the large information and complex relationships of nature, society and economy. To promote multi-disciplinary integration to jointly balance current well-being and long-term sustainability, it is necessary to sort resilience studies on different perspectives into a comprehensive framework to establish interdisciplinary consensus. Based on literature analysis and review, this paper presents an analytical framework for resilience in regional management, and gives a review of SES resilience studies in terms of mechanism, assessment, and management. We outline the current state of resilience research, identify the remaining challenges, and make key recommendations for future research. Our recommendations include promoting interdisciplinary consensus, emphasising dynamic adaptation processes, synthesizing multiple systems and scales, building comprehensive databases, and using mixed methods approach. The paper offers a framework for researchers, practitioners and policy makers to have a more comprehensive understanding of resilience as a whole, and thus helps navigate more fully the challenge of adapting complex resource and environmental problems.
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Affiliation(s)
- Ting Li
- Guangdong Provincial Key Laboratory of Urbanization and Geo-simulation, School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China
| | - Yuxiang Dong
- Guangdong Provincial Key Laboratory of Urbanization and Geo-simulation, School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China; Department of Resources and Urban Planning, Xinhua College of Sun Yat-sen University, Guangzhou 510520, China.
| | - Zhenhuan Liu
- Guangdong Provincial Key Laboratory of Urbanization and Geo-simulation, School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China
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14
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Lever JJ, van de Leemput IA, Weinans E, Quax R, Dakos V, van Nes EH, Bascompte J, Scheffer M. Foreseeing the future of mutualistic communities beyond collapse. Ecol Lett 2020; 23:2-15. [PMID: 31707763 PMCID: PMC6916369 DOI: 10.1111/ele.13401] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Revised: 06/20/2019] [Accepted: 09/14/2019] [Indexed: 02/02/2023]
Abstract
Changing conditions may lead to sudden shifts in the state of ecosystems when critical thresholds are passed. Some well-studied drivers of such transitions lead to predictable outcomes such as a turbid lake or a degraded landscape. Many ecosystems are, however, complex systems of many interacting species. While detecting upcoming transitions in such systems is challenging, predicting what comes after a critical transition is terra incognita altogether. The problem is that complex ecosystems may shift to many different, alternative states. Whether an impending transition has minor, positive or catastrophic effects is thus unclear. Some systems may, however, behave more predictably than others. The dynamics of mutualistic communities can be expected to be relatively simple, because delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. Here, we address the question of whether this relative simplicity allows us to foresee a community's future state. As a case study, we use a model of a bipartite mutualistic network and show that a network's post-transition state is indicated by the way in which a system recovers from minor disturbances. Similar results obtained with a unipartite model of facilitation suggest that our results are of relevance to a wide range of mutualistic systems.
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Affiliation(s)
- J. Jelle Lever
- Department of Evolutionary Biology and Environmental StudiesUniversity of ZurichWinterthurerstrasse 190CH‐8057ZurichSwitzerland
- Department of Aquatic Ecology and Water Quality ManagementWageningen UniversityP.O. Box 47NL‐6700 AAWageningenThe Netherlands
| | - Ingrid A. van de Leemput
- Department of Aquatic Ecology and Water Quality ManagementWageningen UniversityP.O. Box 47NL‐6700 AAWageningenThe Netherlands
| | - Els Weinans
- Department of Aquatic Ecology and Water Quality ManagementWageningen UniversityP.O. Box 47NL‐6700 AAWageningenThe Netherlands
| | - Rick Quax
- Computational Science LabUniversity of AmsterdamNL‐1098 XHAmsterdamThe Netherlands
- Institute of Advanced StudiesUniversity of Amsterdam1012 GCAmsterdamThe Netherlands
| | - Vasilis Dakos
- Institut des Sciences de l'Evolution de Montpellier (ISEM)BioDICée TeamCNRSUniversité de MontpellierMontpellierFrance
| | - Egbert H. van Nes
- Department of Aquatic Ecology and Water Quality ManagementWageningen UniversityP.O. Box 47NL‐6700 AAWageningenThe Netherlands
| | - Jordi Bascompte
- Department of Evolutionary Biology and Environmental StudiesUniversity of ZurichWinterthurerstrasse 190CH‐8057ZurichSwitzerland
| | - Marten Scheffer
- Department of Aquatic Ecology and Water Quality ManagementWageningen UniversityP.O. Box 47NL‐6700 AAWageningenThe Netherlands
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Gama Dessavre A, Southall E, Tildesley MJ, Dyson L. The problem of detrending when analysing potential indicators of disease elimination. J Theor Biol 2019; 481:183-193. [PMID: 30980869 PMCID: PMC6859505 DOI: 10.1016/j.jtbi.2019.04.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2018] [Revised: 04/08/2019] [Accepted: 04/10/2019] [Indexed: 01/04/2023]
Abstract
As we strive towards the elimination of many burdensome diseases, the question of when intervention efforts may cease is increasingly important. It can be very difficult to know when prevalences are low enough that the disease will die out without further intervention, particularly for diseases that lack accurate tests. The consequences of stopping an intervention prematurely can put back elimination efforts by decades. Critical slowing down theory predicts that as a dynamical system moves through a critical transition, deviations from the steady state return increasingly slowly. We study two potential indicators of disease elimination predicted by this theory, and investigate their response using a simple stochastic model. We compare our dynamical predictions to simulations of the fluctuation variance and coefficient of variation as the system moves through the transition to elimination. These comparisons demonstrate that the primary challenge facing the analysis of early warning signs in timeseries data is that of accurately 'detrending' the signal, in order to preserve the statistical properties of the fluctuations. We show here that detrending using the mean of even just four realisations of the process can give a significant improvement when compared to using a moving window average. Taking this idea further, we consider a 'metapopulation' model of an endemic disease, in which infection spreads in various separated areas with some movement between the subpopulations. We successfully predict the behaviour of both variance and the coefficient of variation in a metapopulation by using information from the other subpopulations to detrend the system.
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Affiliation(s)
| | - Emma Southall
- Mathematics Institute, University of Warwick, Coventry, UK
| | - Michael J Tildesley
- Mathematics Institute, University of Warwick, Coventry, UK; School of Life Sciences, University of Warwick, Coventry, UK
| | - Louise Dyson
- Mathematics Institute, University of Warwick, Coventry, UK; School of Life Sciences, University of Warwick, Coventry, UK.
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