On the use of Algebra in Genetics: From Phenotype to Genotype

On the use of Algebra in Genetics: From Phenotype to Genotype | 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 On the use of Algebra in Genetics: From Phenotype to Genotype Ioannis G. Diamataris, Ioanna Maroulakou, Georgios C. Boulougouris This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6666111/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 In this work, we propose a mathematical framework based on linear algebra that connects the observed phenotype frequencies in finite population samples with the underlying genetic information encoded in genotype and allele frequencies, and the allelic interactions that govern dominance in gene expression. In cases where a genotype uniquely determines the observed phenotype, we derive an analytical relationship between phenotype frequency, genotypic frequencies, and allelic interactions. Given known dominant recessive allelic interactions and the observed phenotypic frequencies in a population sample, we express all compatible genotypic frequencies in a closed algebraic form. Furthermore, under the assumption of complete (100%) penetrance, and given both phenotypic and genotypic frequencies in a population sample, we derive a matrix representation of the allelic dominance relationships. Future implementations of the proposed framework could incorporate high throughput genomic data, thereby enhancing our ability to investigate the genotype phenotype relationship a crucial step in understanding complex traits, genetic disorders, and disease susceptibilities. 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-6666111","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":459929907,"identity":"ac142919-faf2-4d81-9c1b-e92527e4ff45","order_by":0,"name":"Ioannis G. 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