{"paper_id":"41441e1e-6cfb-4b71-8302-a63813879dbb","body_text":"Leveraging Power-Law Distributions to Map Impact Origins in Product Supply Chains | 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 Leveraging Power-Law Distributions to Map Impact Origins in Product Supply Chains Venkat Roy, Fu Zhao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8427560/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 Tracing a single product's environmental footprint—greenhouse gas emissions, water consumption, toxic releases, ecosystem damage—requires tracking thousands of processes across global supply chains to their fundamental environmental interactions: ore extraction, agricultural inputs, industrial water use spanning continents and ecosystems. Life Cycle Assessment (LCA) quantifies these impacts comprehensively. However, this comprehensive scope comes at a cost: impacts are aggregated into locationless scores, obscuring where damage likely occurs. Full spatial resolution has remained impractical: regionalizing all processes would require millions of location-specific datasets. This limitation prevents targeted mitigation, especially for spatially-dependent impacts like freshwater ecotoxicity, where the same emission generates orders-of-magnitude different consequences depending on ecosystem sensitivity and baseline contamination. We find that environmental impacts follow power-law distributions across diverse product systems: fewer than 2% of processes account for over 95% of total impact (mean Gini coefficient 0.982, n=449 product-impact combinations). This concentration enables selective spatialization—focusing analytical resources on only critical processes. We present Impact Origin Mapping, a framework combining network-based pathway tracing with AI-assisted geographic attribution to map impacts to affected ecosystems. Applied to lithium carbonate production, the framework traces freshwater ecotoxicity from a Nevada clay deposit to specific water bodies across multiple US states, transforming aggregated LCA scores into ecosystem-level impact maps that enable targeted interventions. Earth and environmental sciences/Environmental social sciences/Sustainability Earth and environmental sciences/Environmental social sciences/Environmental impact spatial life cycle assessment power-law distributions geographic attribution impact concentration ecosystem mapping Full Text Additional Declarations There is NO Competing Interest. 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-8427560\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":572230782,\"identity\":\"4be48507-ff74-4b48-8492-d7b421eb8a60\",\"order_by\":0,\"name\":\"Venkat Roy\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYLCCDyDiAIhgI1IH4wyStTDzkKTF4PbhY9K2Ow7n891IPsDwoewwEVrOpaVJ5545bDnzRloC44xzRGiR7OExk85tO2xgcCPHgJm3jVgtlmAt+R+Y/xKjhZ8HqIURYgsDMyNxWtiSLXvPpBtInnlmcLDnXDphLWw8zAdv/NxhbcB3PPnhgx9l1oS1AAGLBGMDhHWAKPVAwPwBpmUUjIJRMApGAVYAAFs6OdGyYRkyAAAAAElFTkSuQmCC\",\"orcid\":\"https://orcid.org/0009-0003-6493-868X\",\"institution\":\"Purdue University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Venkat\",\"middleName\":\"\",\"lastName\":\"Roy\",\"suffix\":\"\"},{\"id\":572230783,\"identity\":\"6ba098af-3880-4147-a233-7b3e93f2ce48\",\"order_by\":1,\"name\":\"Fu Zhao\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Purdue University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Fu\",\"middleName\":\"\",\"lastName\":\"Zhao\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-12-22 17:55:52\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-8427560/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-8427560/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":100017278,\"identity\":\"b005db88-3022-4dc3-9137-962baf28f5d9\",\"added_by\":\"auto\",\"created_at\":\"2026-01-12 07:10:03\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"acdc-reference\",\"size\":4693806,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"impactoriginmappingNatureCommslong.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8427560/v1/e77061d720b6a2ef484d38d9.pdf\"},{\"id\":100017281,\"identity\":\"0bf77419-cfdf-427e-95af-5ee0a88cb06a\",\"added_by\":\"auto\",\"created_at\":\"2026-01-12 07:10:05\",\"extension\":\"json\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"acdc-reference\",\"size\":4409,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"NCOMMS25104091.json\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8427560/v1/481a73bc2bc3cef4c4523b86.json\"},{\"id\":107480516,\"identity\":\"3a52608c-9627-4d89-9291-3830cd02c5a1\",\"added_by\":\"auto\",\"created_at\":\"2026-04-22 02:11:30\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":2283939,\"visible\":true,\"origin\":\"\",\"legend\":\"Article File\",\"description\":\"\",\"filename\":\"impactoriginmappingNatureCommslong.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8427560/v1_covered_4f8d6fa8-aacb-4693-8d04-45310451e9c7.pdf\"}],\"financialInterests\":\"There is \\u003cb\\u003eNO\\u003c/b\\u003e Competing Interest.\",\"formattedTitle\":\"Leveraging Power-Law Distributions to Map Impact Origins in Product Supply Chains\",\"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\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"spatial life cycle assessment, power-law distributions, geographic attribution, impact concentration, ecosystem mapping\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8427560/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8427560/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"Tracing a single product's environmental footprint—greenhouse gas emissions, water consumption, toxic releases, ecosystem damage—requires tracking thousands of processes across global supply chains to their fundamental environmental interactions: ore extraction, agricultural inputs, industrial water use spanning continents and ecosystems. Life Cycle Assessment (LCA) quantifies these impacts comprehensively. However, this comprehensive scope comes at a cost: impacts are aggregated into locationless scores, obscuring where damage likely occurs. Full spatial resolution has remained impractical: regionalizing all processes would require millions of location-specific datasets. This limitation prevents targeted mitigation, especially for spatially-dependent impacts like freshwater ecotoxicity, where the same emission generates orders-of-magnitude different consequences depending on ecosystem sensitivity and baseline contamination. We find that environmental impacts follow power-law distributions across diverse product systems: fewer than 2% of processes account for over 95% of total impact (mean Gini coefficient 0.982, n=449 product-impact combinations). This concentration enables selective spatialization—focusing analytical resources on only critical processes. We present Impact Origin Mapping, a framework combining network-based pathway tracing with AI-assisted geographic attribution to map impacts to affected ecosystems. Applied to lithium carbonate production, the framework traces freshwater ecotoxicity from a Nevada clay deposit to specific water bodies across multiple US states, transforming aggregated LCA scores into ecosystem-level impact maps that enable targeted interventions.\",\"manuscriptTitle\":\"Leveraging Power-Law Distributions to Map Impact Origins in Product Supply Chains\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-01-12 07:09:11\",\"doi\":\"10.21203/rs.3.rs-8427560/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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}}],\"origin\":\"\",\"ownerIdentity\":\"e03bc9bb-abb2-449f-a77d-8eb9ac617a2b\",\"owner\":[],\"postedDate\":\"January 12th, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":60897964,\"name\":\"Earth and environmental sciences/Environmental social sciences/Sustainability\"},{\"id\":60897965,\"name\":\"Earth and environmental sciences/Environmental social sciences/Environmental impact\"}],\"tags\":[],\"updatedAt\":\"2026-04-15T14:06:27+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2026-01-12 07:09:11\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-8427560\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-8427560\",\"identity\":\"rs-8427560\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}