{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T11:03:10Z","timestamp":1774177390574,"version":"3.50.1"},"reference-count":63,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Leibniz Association (project DominoES)","award":["743080 ERA"],"award-info":[{"award-number":["743080 ERA"]}]},{"name":"Leibniz Association (project DominoES)","award":["01LS2001A"],"award-info":[{"award-number":["01LS2001A"]}]},{"name":"European Research Council (ERC) under the European Union\u2019s Horizon 2020 Research and Innovation Programme","award":["743080 ERA"],"award-info":[{"award-number":["743080 ERA"]}]},{"name":"European Research Council (ERC) under the European Union\u2019s Horizon 2020 Research and Innovation Programme","award":["01LS2001A"],"award-info":[{"award-number":["01LS2001A"]}]},{"name":"German National Academic Foundation","award":["743080 ERA"],"award-info":[{"award-number":["743080 ERA"]}]},{"name":"German National Academic Foundation","award":["01LS2001A"],"award-info":[{"award-number":["01LS2001A"]}]},{"DOI":"10.13039\/501100002347","name":"German Federal Ministry for Education and Research (BMBF)","doi-asserted-by":"publisher","award":["743080 ERA"],"award-info":[{"award-number":["743080 ERA"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"German Federal Ministry for Education and Research (BMBF)","doi-asserted-by":"publisher","award":["01LS2001A"],"award-info":[{"award-number":["01LS2001A"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Regional Development Fund (ERDF), the BMBF and the Land Brandenburg","award":["743080 ERA"],"award-info":[{"award-number":["743080 ERA"]}]},{"name":"European Regional Development Fund (ERDF), the BMBF and the Land Brandenburg","award":["01LS2001A"],"award-info":[{"award-number":["01LS2001A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent years, several global events have severely disrupted economies and social structures, undermining confidence in the resilience of modern societies. Examples include the COVID-19 pandemic, which brought unprecedented health challenges and economic disruptions, and the emergence of geopolitical tensions and conflicts that have further strained international relations and economic stability. While empirical evidence on the dynamics and drivers of past societal collapse is mounting, a process-based understanding of these dynamics is still in its infancy. Here, we aim to identify and illustrate the underlying drivers of such societal instability or even collapse. The inspiration for this work is Joseph Tainter\u2019s theory of the \u201ccollapse of complex societies\u201d, which postulates that the complexity of societies increases as they solve problems, leading to diminishing returns on complexity investments and ultimately to collapse. In this work, we abstract this theory into a low-dimensional and stylized model of two classes of networked agents, hereafter referred to as \u201claborers\u201d and \u201cadministrators\u201d. We numerically model the dynamics of societal complexity, measured as the fraction of \u201cadministrators\u201d, which was assumed to affect the productivity of connected energy-producing \u201claborers\u201d. We show that collapse becomes increasingly likely as the complexity of the model society continuously increases in response to external stresses that emulate Tainter\u2019s abstract notion of problems that societies must solve. We also provide an analytical approximation of the system\u2019s dominant dynamics, which matches well with the numerical experiments, and use it to study the influence on network link density, social mobility and productivity. Our work advances the understanding of social-ecological collapse and illustrates its potentially direct link to an ever-increasing societal complexity in response to external shocks or stresses via a self-reinforcing feedback.<\/jats:p>","DOI":"10.3390\/e26020098","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T08:28:28Z","timestamp":1705998508000},"page":"98","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter\u2019s Theory of Collapse"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7245-953X","authenticated-orcid":false,"given":"Florian","family":"Schunck","sequence":"first","affiliation":[{"name":"Research Group System Ecotox, Helmholtz Centre for Environmental Research GmbH\u2014UFZ, Permoserstra\u00dfe 15, 04318 Leipzig, Germany"},{"name":"Research Group System Science, Institute of Mathematics, Osnabr\u00fcck University, Barbarastra\u00dfe 12, 49076 Osnabr\u00fcck, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9869-3789","authenticated-orcid":false,"given":"Marc","family":"Wiedermann","sequence":"additional","affiliation":[{"name":"FutureLab on Game Theory and Networks of Interacting Agents, FutureLab on Earth Resilience in the Anthropocene, Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0442-8077","authenticated-orcid":false,"given":"Jobst","family":"Heitzig","sequence":"additional","affiliation":[{"name":"FutureLab on Game Theory and Networks of Interacting Agents, FutureLab on Earth Resilience in the Anthropocene, Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5233-7703","authenticated-orcid":false,"given":"Jonathan F.","family":"Donges","sequence":"additional","affiliation":[{"name":"FutureLab on Game Theory and Networks of Interacting Agents, FutureLab on Earth Resilience in the Anthropocene, Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany"},{"name":"Stockholm Resilience Centre, Stockholm University, Albanov\u00e4gen 28, 106 91 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e2218834120","DOI":"10.1073\/pnas.2218834120","article-title":"The Vulnerability of Aging States: A Survival Analysis across Premodern Societies","volume":"120","author":"Scheffer","year":"2023","journal-title":"Proc. Natl. Acad. Sci. 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