A First Order Piece-Wise Linear Differential Equation Explains Alternate Bearing In Perennial Plants

A First Order Piece-Wise Linear Differential Equation Explains Alternate Bearing In Perennial Plants | 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 Research Article A First Order Piece-Wise Linear Differential Equation Explains Alternate Bearing In Perennial Plants Kartika Panwar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7171447/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The phenomenon of Alternate Bearing observed in polycarpic plants has long been a problem of interest for ecologists and biologists due to its cascading ecological and socio-economical effects. The discrete Resource Budget Model (RBM) with tent-map equations was the first mathematical attempt to model the underlying physical mechanism behind the phenomenon. In this work, the presence of resource budgeting of photosynthate in plants confirmed by past experimental studies was modeled as a continuous process and an ordinary, first-order, and piece-wise linear differential equation was derived in compliance with the discrete model. This led to the emergence of additional parameters that introduced an evolutionary window to understand the onset of flowering and fruiting phenophases of different plant species. The new parameters were dependent on the plant’s internal reproductive clock evolutionarily set by the regional duration of favorable weather conditions and defined the duration of flowering and fruiting phenophases of the species. This could not be explained by the discrete model. The continuous model also allowed for different annual onset times of flowering phenophase for different species. Modifications to RBM have been made in the literature to address problems related to alternate-bearing in individual trees and masting in a coupled population of trees but those models do not address the storage of photosynthate as a continuous process as done in this work. The incorporation of coupling between plants in the continuous RBM to explain the problem of masting is the subject of our future studies. Mathematical and Theoretical Biology Alternate Bearing Biophysical Modelling Chaotic Solutions First Order Differential Equation Mathematical Modelling Piece-Wise Linear Differential Equation Resource Budget Model Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7171447","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":488136444,"identity":"04347a76-d018-4549-85b7-42d04e2afee3","order_by":0,"name":"Kartika Panwar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYBACCRCRcADGrWBgMACL4NfC2IDQcoZYLQwwLYxtUC34gGT72ecPHpyxy+Of3WP4uXLeYXlz9uYDDA934NYizZNu2JBwI7lY4s4ZY8mz2w4b7uw5lsCQeAa3FjmGNKBfPjAnNtzI3SDZuO0w44YbOQYMiW14tPA/A2mpT5x/I3fzz8Y5h+0JapGWANly43Dihhu52yQbG0AMAlokZzxjnJFw5nix4Y38b5YNx9KTN5w5lnAAnxaJ82kMH38cq86Tu5GWfLOhxtp2w/Hmgw9/4tECAwlQuhlMHiCsAaGljhjFo2AUjIJRMMIAAN/UYB+ini51AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-8849-3409","institution":"Department of Physics and Astrophysics, University of Delhi","correspondingAuthor":true,"prefix":"","firstName":"Kartika","middleName":"","lastName":"Panwar","suffix":""}],"badges":[],"createdAt":"2025-07-20 19:02:41","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7171447/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7171447/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87294818,"identity":"7cb358c2-686c-4b2d-ab48-ef9557f6d090","added_by":"auto","created_at":"2025-07-22 12:13:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":644693,"visible":true,"origin":"","legend":"","description":"","filename":"JMBRBMCont.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7171447/v1_covered_fcd02e44-3fb2-4d4c-bf29-2063752f4716.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eA First Order Piece-Wise Linear Differential Equation Explains Alternate Bearing In Perennial Plants\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[{"identity":"f3d87cf5-d7ae-4adb-9a41-a321ece9eb56","identifier":"10.13039/501100001501","name":"University Grants Commission","awardNumber":"1320 (CSIR-UGC NET JUNE 2017)","order_by":0}],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Delhi","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Alternate Bearing, Biophysical Modelling, Chaotic Solutions, First Order Differential Equation, Mathematical Modelling, Piece-Wise Linear Differential Equation, Resource Budget Model","lastPublishedDoi":"10.21203/rs.3.rs-7171447/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7171447/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe phenomenon of Alternate Bearing observed in polycarpic plants has long been a problem of interest for ecologists and biologists due to its cascading ecological and socio-economical effects. The discrete Resource Budget Model (RBM) with tent-map equations was the first mathematical attempt to model the underlying physical mechanism behind the phenomenon. In this work, the presence of resource budgeting of photosynthate in plants confirmed by past experimental studies was modeled as a continuous process and an ordinary, first-order, and piece-wise linear differential equation was derived in compliance with the discrete model. This led to the emergence of additional parameters that introduced an evolutionary window to understand the onset of flowering and fruiting phenophases of different plant species. The new parameters were dependent on the plant\u0026rsquo;s internal reproductive clock evolutionarily set by the regional duration of favorable weather conditions and defined the duration of flowering and fruiting phenophases of the species. This could not be explained by the discrete model. The continuous model also allowed for different annual onset times of flowering phenophase for different species.\u003c/p\u003e\u003cp\u003eModifications to RBM have been made in the literature to address problems related to alternate-bearing in individual trees and masting in a coupled population of trees but those models do not address the storage of photosynthate as a continuous process as done in this work. 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