Semigroup Basesfor Genetic Breeding Programs 1 Application of Basis-Pruning Algorithms

Semigroup Basesfor Genetic Breeding Programs 1 Application of Basis-Pruning Algorithms | 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 Semigroup Basesfor Genetic Breeding Programs 1 Application of Basis-Pruning Algorithms Marshal Sampson, Rafiat Bada Abubakar, Ubong Akpan, Itoro Tim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7643818/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 Genetic breeding programs combine parental lines through crossing operations to produce new varieties. The space of possible crosses and breeding procedures can be very large, but often a much smaller set of crossing primitives suffices to generate the same set of achievable lines. We adapt semigroup basis pruning algorithms by to the breeding setting by modeling breeding operations as transformations on a finite population state space. We provide formal definitions, proofs of algorithmic correctness and termination for the finite case, and a worked example using a small set of parental lines. The example includes an executable Python implementation which identifies a minimal generating set of crosses for the target breeding outcomes. The approach offers a principled method to reduce complexity in breeding programs, identify critical parental lines, and prioritize crosses under resource constraints. Full Text Additional Declarations No competing interests reported. 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-7643818","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":518191989,"identity":"718b5161-a866-4d43-8984-fc632ec15b67","order_by":0,"name":"Marshal Sampson","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFUlEQVRIiWNgGAWjYJACZgYGCxjbhkECTLMR1CIBY6eRruUwYS267Wcffy6okbDnn3b28IePO87LS/afMWD4UHaYwZx/AVYtZmfSzaRnHJNInHE7L01y5pnbhrMlcgwYZ5w7zGA54wF2LQfS2Jh52CQSGG7nmDHztt1mnCfBYwBkHGYwuHEAu5bzz5g/8/yTsJe/nWP8mbftnP08/jMGzH/xabmRxiDN2ybBuOF2jgGQcSBxNkOOATMjSMv5BhxanrFJ8/ZJJG4E+6UtOXnmjLSCgz3n0nkMbmAPMbPzaUCHfbOxl7udCwyxNjvbGecPb3zwo8xazuA8dochAR4E8wCYCwwT4rVAAD9BW0bBKBgFo2BkAABPpV+MHB/kOgAAAABJRU5ErkJggg==","orcid":"","institution":"Akwa Ibom State University","correspondingAuthor":true,"prefix":"","firstName":"Marshal","middleName":"","lastName":"Sampson","suffix":""},{"id":518191990,"identity":"7f0c4ebc-103c-45ec-b8ae-663072597642","order_by":1,"name":"Rafiat Bada Abubakar","email":"","orcid":"","institution":"Federal University Otuoke","correspondingAuthor":false,"prefix":"","firstName":"Rafiat","middleName":"Bada","lastName":"Abubakar","suffix":""},{"id":518191991,"identity":"4460b634-307e-4830-a523-9574ec2b0066","order_by":2,"name":"Ubong Akpan","email":"","orcid":"","institution":"Akwa Ibom State University","correspondingAuthor":false,"prefix":"","firstName":"Ubong","middleName":"","lastName":"Akpan","suffix":""},{"id":518191992,"identity":"43adfba3-9813-4830-bef1-58ad82dfe772","order_by":3,"name":"Itoro Tim","email":"","orcid":"","institution":"Akwa Ibom State University","correspondingAuthor":false,"prefix":"","firstName":"Itoro","middleName":"","lastName":"Tim","suffix":""}],"badges":[],"createdAt":"2025-09-17 23:23:17","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-7643818/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7643818/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91932647,"identity":"c5188973-530e-42a9-bb0c-7142a8ab7692","added_by":"auto","created_at":"2025-09-23 02:35:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":393306,"visible":true,"origin":"","legend":"","description":"","filename":"SemigroupBasesforGeneticBreedingPrograms2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7643818/v1_covered_d539a0e4-b702-408c-b79d-0b5d9f1362ae.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eSemigroup Basesfor Genetic Breeding Programs 1 Application of Basis-Pruning Algorithms\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"","lastPublishedDoi":"10.21203/rs.3.rs-7643818/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7643818/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGenetic breeding programs combine parental lines through crossing operations to produce new varieties. 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