Global Population: from Super-Malthus behavior to Doomsday Criticality

Global Population: from Super-Malthus behavior to Doomsday Criticality | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Global Population: from Super-Malthus behavior to Doomsday Criticality Aleksandra Drozd-Rzoska, Agata Sojecka This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4006620/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Apr, 2024 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: \(P\left(t\right)={P}_{0}exp{\left[\pm \left(t/\right)\right]}^{}\) , and SM-2 is the Malthus-type relation with the time-dependent growth rate \(r\left(t\right)\) or relaxation time \(\left(t\right)=1/r\left(t\right)\) : \(P\left(t\right)={P}_{0}exp\left(r\left(t\right)\times t\right)={P}_{0}exp\left[/\left(t\right)\right]\) . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~3 billion): from the compressed exponential behavior ( \(>1)\) to the stretched exponential one ( \(<1\) ). For SM-2 dependence, linear changes of \(\left(T\right)\) during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior \(P\left(t\right)={P}_{0}exp\left[b{\prime }t/\left({T}_{C}-t\right)\right]\) , where \({T}_{C}\approx 2216\) is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis. Biological sciences/Ecology Biological sciences/Evolution Earth and environmental sciences/Ecology Earth and environmental sciences/Environmental social sciences Earth and environmental sciences/Planetary science Physical sciences/Mathematics and computing Physical sciences/Physics Global population growth Super Malthus behavior distortions-sensitive analysis constrained criticality Doomsday criticality physics of complex systems Weibull distribution historical impacts Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryInformation.docx Cite Share Download PDF Status: Published Journal Publication published 29 Apr, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 09 Apr, 2024 Reviews received at journal 28 Mar, 2024 Reviewers agreed at journal 22 Mar, 2024 Reviewers agreed at journal 21 Mar, 2024 Reviewers invited by journal 21 Mar, 2024 Editor assigned by journal 20 Mar, 2024 Editor invited by journal 15 Mar, 2024 Submission checks completed at journal 15 Mar, 2024 First submitted to journal 02 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4006620","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":280963138,"identity":"8e9c4961-9841-413a-914f-9cda199c957b","order_by":0,"name":"Aleksandra Drozd-Rzoska","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYNCCAwxyDAyMDchCFgS1GKNrkSCoJbEBTQi3Fv7Zxx8+/HHGLn3D7ea2xxUVdfYMEsnPJBh34NYicS4h2ZjnRnLuhjsH2w3PnDmc2CCRZibBeAaPw84wHJNm+MCcu+FGYptkY9uBBAbpBLMbjG24tcifYWyT/PGhPt0ArOUf0GHS6d/wajE4w8wmwXPjcAJESwMzY4N0Dn5bDM+wMRvznDluOPNGYrthw7HDiW3yb8p/JOLxi9wZdmCIHauW57uR/uxhQ02dPT/P8c0GH3fY4PY+EmBDkBjRhFcLGKCmhFEwCkbBKBjhAACRI1b2BjyycQAAAABJRU5ErkJggg==","orcid":"","institution":"Institute of High Pressure Physics Polish Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Aleksandra","middleName":"","lastName":"Drozd-Rzoska","suffix":""},{"id":280963139,"identity":"0c56dd80-154d-44b3-9ca6-3ee6186321dc","order_by":1,"name":"Agata Sojecka","email":"","orcid":"","institution":"University of Economics in Katowice, Dept. of Marketing, ul. 1 Maja 50, 40-257 Katowice, Poland","correspondingAuthor":false,"prefix":"","firstName":"Agata","middleName":"","lastName":"Sojecka","suffix":""}],"badges":[],"createdAt":"2024-03-02 13:38:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4006620/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4006620/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-60589-3","type":"published","date":"2024-04-29T19:58:02+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":56042977,"identity":"809e3559-1362-498b-a1ba-9110aa9ccb22","added_by":"auto","created_at":"2024-05-07 20:09:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":659958,"visible":true,"origin":"","legend":"","description":"","filename":"AgatkaSojeckaNatureSustainGlobalcorr2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4006620/v1_covered_4bda7ef3-1e85-4bd7-85ab-ae6e9ca60bd8.pdf"},{"id":52972383,"identity":"d0bfee83-ea3b-4000-b326-07e869af89f3","added_by":"auto","created_at":"2024-03-19 08:35:50","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":21083,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-4006620/v1/3af618c14c46d4096ffb77e9.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Global Population: from Super-Malthus behavior to Doomsday Criticality","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Global population growth, Super Malthus behavior, distortions-sensitive analysis, constrained criticality, Doomsday criticality, physics of complex systems, Weibull distribution, historical impacts","lastPublishedDoi":"10.21203/rs.3.rs-4006620/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4006620/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\left(t\\right)={P}_{0}exp{\\left[\\pm \\left(t/\\right)\\right]}^{}\\)\u003c/span\u003e\u003c/span\u003e, and SM-2 is the Malthus-type relation with the time-dependent growth rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(r\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e or relaxation time \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(t\\right)=1/r\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\left(t\\right)={P}_{0}exp\\left(r\\left(t\\right)\\times t\\right)={P}_{0}exp\\left[/\\left(t\\right)\\right]\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003ePopulation data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~3\u0026nbsp;billion): from the compressed exponential behavior (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\u0026gt;1)\\)\u003c/span\u003e\u003c/span\u003e to the stretched exponential one (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\u0026lt;1\\)\u003c/span\u003e\u003c/span\u003e). For SM-2 dependence, linear changes of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(T\\right)\\)\u003c/span\u003e\u003c/span\u003e during the Industrial Revolutions period, since ~\u0026thinsp;1700, led to the constrained critical behavior \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\left(t\\right)={P}_{0}exp\\left[b{\\prime }t/\\left({T}_{C}-t\\right)\\right]\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{C}\\approx 2216\\)\u003c/span\u003e\u003c/span\u003e is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.\u003c/p\u003e","manuscriptTitle":"Global Population: from Super-Malthus behavior to Doomsday Criticality","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-19 08:35:45","doi":"10.21203/rs.3.rs-4006620/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-04-09T09:10:37+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-03-28T15:02:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"b653712d-607c-4d00-9085-61bce2e01e8f","date":"2024-03-22T06:09:27+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"03272009-5c9f-406e-837f-ba4515d33d59","date":"2024-03-21T19:30:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-21T19:05:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-03-20T10:06:10+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-03-15T14:38:22+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-15T14:25:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-03-02T13:36:50+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4f55f492-c9fe-4ddb-b82b-cbcaacecf08e","owner":[],"postedDate":"March 19th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":29585308,"name":"Biological sciences/Ecology"},{"id":29585309,"name":"Biological sciences/Evolution"},{"id":29585310,"name":"Earth and environmental sciences/Ecology"},{"id":29585311,"name":"Earth and environmental sciences/Environmental social sciences"},{"id":29585312,"name":"Earth and environmental sciences/Planetary science"},{"id":29585313,"name":"Physical sciences/Mathematics and computing"},{"id":29585314,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2024-05-07T20:06:32+00:00","versionOfRecord":{"articleIdentity":"rs-4006620","link":"https://doi.org/10.1038/s41598-024-60589-3","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-04-29 19:58:02","publishedOnDateReadable":"April 29th, 2024"},"versionCreatedAt":"2024-03-19 08:35:45","video":"","vorDoi":"10.1038/s41598-024-60589-3","vorDoiUrl":"https://doi.org/10.1038/s41598-024-60589-3","workflowStages":[]},"version":"v1","identity":"rs-4006620","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4006620","identity":"rs-4006620","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}