{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:35Z","timestamp":1760239655124,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Dynamical systems are known to exhibit sudden state transitions, with abrupt shifts from one stable state to another. Such transitions are widely observed, with examples ranging from abrupt extinctions of species in ecosystems to unexpected financial crises in the economy or sudden changes in medical conditions. Statistical methods known as early warning signals (EWSs) are used to predict these transitions. In most studies to date, EWSs have been tested on data generated using equation-based methods that represent a system\u2019s aggregate state and thus show limitations in considering the interactions of a system at the component level. Agent-based models offer an alternative without these limitations. This study compares the performance of EWSs when applied to data from an equation-based and from an agent-based version of the Ising model. The results provide a reason to consider agent-based modelling a promising complementary method for investigating the predictability of state changes with EWSs.<\/jats:p>","DOI":"10.3390\/systems8040054","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T08:59:34Z","timestamp":1607590774000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Comparing Equation-Based and Agent-Based Data Generation Methods for Early Warning Signal Analysis"],"prefix":"10.3390","volume":"8","author":[{"given":"Daniel","family":"Reisinger","sequence":"first","affiliation":[{"name":"Institute of Systems Sciences, Innovation and Sustainability Research, University of Graz, 8010 Graz, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7772-4061","authenticated-orcid":false,"given":"Manfred","family":"F\u00fcllsack","sequence":"additional","affiliation":[{"name":"Institute of Systems Sciences, Innovation and Sustainability Research, University of Graz, 8010 Graz, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s12080-013-0192-6","article-title":"Early warning signals: The charted and uncharted territories","volume":"6","author":"Boettiger","year":"2013","journal-title":"Theor. Ecol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Scheffer, M. (2009). Critical Transitions in Nature and Society, Princeton University Press.","DOI":"10.1515\/9781400833276"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1016\/j.physd.2011.02.012","article-title":"A mathematical framework for critical transitions: Bifurcations, fast\u2013slow systems and stochastic dynamics","volume":"240","author":"Kuehn","year":"2011","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_4","first-page":"591","article-title":"Catastrophic shifts in ecosystems","volume":"413","author":"Scheffer","year":"2001","journal-title":"Nat. Cell Biol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.tree.2003.09.002","article-title":"Catastrophic regime shifts in ecosystems: Linking theory to observation","volume":"18","author":"Scheffer","year":"2003","journal-title":"Trends Ecol. Evol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1038\/451893a","article-title":"Ecology for bankers","volume":"451","author":"May","year":"2008","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1038\/nm0303-241","article-title":"Prediction of epileptic seizures: Are nonlinear methods relevant?","volume":"9","author":"McSharry","year":"2003","journal-title":"Nat. Med."},{"key":"ref_8","first-page":"777","article-title":"Self-organized patchiness in asthma as a prelude to catastrophic shifts","volume":"434","author":"Venegas","year":"2005","journal-title":"Nat. Cell Biol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1038\/ngeo439","article-title":"Rapid oceanic and atmospheric changes during the Younger Dryas cold period","volume":"2","author":"Bakke","year":"2009","journal-title":"Nat. Geosci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.1073\/pnas.0705414105","article-title":"Tipping elements in the Earth\u2019s climate system","volume":"105","author":"Lenton","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Dakos, V., Carpenter, S.R., Brock, W.A., Ellison, A.M., Guttal, V., Ives, A.R., K\u00e9fi, S., Livina, V.N., Seekell, D.A., and Van Nes, E.H. (2012). Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0041010"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"J\u00e4ger, G., and F\u00fcllsack, M. (2019). Systematically false positives in early warning signal analysis. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0211072"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14889","DOI":"10.1073\/pnas.0701020104","article-title":"On the trend, detrending, and variability of nonlinear and nonstationary time series","volume":"104","author":"Wu","year":"2007","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","first-page":"641","article-title":"Early warning signals also precede non-catastrophic transitions","volume":"122","author":"Dakos","year":"2012","journal-title":"Oikos"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1073\/pnas.0811729106","article-title":"Turning back from the brink: Detecting an impending regime shift in time to avert it","volume":"106","author":"Biggs","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"D\u2019Souza, K., Epureanu, B.I., and Pascual, M. (2015). Forecasting Bifurcations from Large Perturbation Recoveries in Feedback Ecosystems. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0137779"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"F\u00fcllsack, M., Plakolb, S., and J\u00e4ger, G. (2020). Predicting regime shifts in social systems modelled with agent-based methods. J. Comput. Soc. Sci., 1\u201323.","DOI":"10.1007\/s42001-020-00071-y"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.3934\/jdg.2018014","article-title":"Critical transitions and Early Warning Signals in repeated Cooperation Games","volume":"5","author":"Hofer","year":"2018","journal-title":"J. Dyn. Games"},{"key":"ref_19","unstructured":"Huet, S., Edwards, M., and Deffuant, G. (2004, January 16\u201319). Taking into account the variations of social network in the mean-field approximation of the threshold behaviour diffusion model. Proceedings of the ESSA Conference Model to Model Workshop, Valladolid, Spain."},{"key":"ref_20","unstructured":"Mabrouk, N. (2010). Analyzing Individual-Based Models of Microbial Systems. [Ph.D. Thesis, Universit\u00e9 Blaise Pascal Clermont II]."},{"key":"ref_21","first-page":"4","article-title":"Comparing an individual-based model of behaviour diffusion with its mean field aggregate approximation","volume":"6","author":"Edwards","year":"2003","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF02980577","article-title":"Beitrag zur theorie des ferromagnetismus","volume":"31","author":"Ising","year":"1925","journal-title":"Zeitschrift f\u00fcr Physik"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Morales, I.O., Landa, E., Angeles, C.C., Toledo, J.C., Rivera, A.L., Temis, J.M., and Frank, A. (2015). Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0130751"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Smug, D., Sornette, D., and Ashwin, P. (2018). A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises). Int. J. Bifurc. Chaos, 28.","DOI":"10.1142\/S0218127418300100"},{"key":"ref_25","unstructured":"McCoy, B.M., and Wu, T.T. (2014). The Two-Dimensional Ising Model, Courier Corporation."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.physa.2005.06.102","article-title":"Ising-based model of opinion formation in a complex network of interpersonal interactions","volume":"361","author":"Grabowski","year":"2006","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1016\/j.procs.2010.04.262","article-title":"Statistical mechanics of rumour spreading in network communities","volume":"1","author":"Ostilli","year":"2010","journal-title":"Procedia Comput. Sci."},{"key":"ref_28","unstructured":"Roli, A. (2020, December 09). An Introduction to Complex System Science. Available online: http:\/\/www.lia.disi.unibo.it\/~aro\/download\/css-course\/css-lecture_notes.pdf."},{"key":"ref_29","unstructured":"Singh, R. (2020, December 09). IsingModel. Available online: https:\/\/rajeshrinet.github.io\/blog\/2014\/ising-model."},{"key":"ref_30","unstructured":"Stone, J.V. (2015). Information Theory: A Tutorial Introduction, Sebtel Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1902","DOI":"10.4249\/scholarpedia.1902","article-title":"Normal forms","volume":"1","author":"Murdock","year":"2006","journal-title":"Scholarpedia"},{"key":"ref_32","unstructured":"Tan, P.-N., Steinbach, M., and Kumar, V. (2014). Introduction to Data Mining, Pearson."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"M\u00fcller, M. (2007). Information Retrieval for Music and Motion. Information Retrieval for Music and Motion, Springer.","DOI":"10.1007\/978-3-540-74048-3"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"17546","DOI":"10.1073\/pnas.1406326111","article-title":"Critical slowing down as early warning for the onset of collapse in mutualistic communities","volume":"111","author":"Dakos","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1126\/science.1225244","article-title":"Anticipating Critical Transitions","volume":"338","author":"Scheffer","year":"2012","journal-title":"Science"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1093\/biomet\/33.3.239","article-title":"The treatment of ties in ranking problems","volume":"33","author":"Kendall","year":"1945","journal-title":"Biometrika"},{"key":"ref_37","unstructured":"Jones, E., Oliphant, T., and Peterson, P. (2020, December 09). SciPy: Open Source Scientific Tools for Python. Available online: http:\/\/www.scipy.org."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wen, H., Ciamarra, M.P., and Cheong, S.A. (2018). How one might miss early warning signals of critical transitions in time series data: A systematic study of two major currency pairs. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0191439"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/8\/4\/54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:43:07Z","timestamp":1760179387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/8\/4\/54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":38,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["systems8040054"],"URL":"https:\/\/doi.org\/10.3390\/systems8040054","relation":{},"ISSN":["2079-8954"],"issn-type":[{"type":"electronic","value":"2079-8954"}],"subject":[],"published":{"date-parts":[[2020,12,10]]}}}