[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-438425-105":59,"doc-detail-438425-en":129},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":122,"head_meta":124,"extra_data":126,"updated_unix":128},105,"en","universal-niche-geometry-governs-the-response-of-ecosystems-to-environmental-perturbations","Universal Niche Geometry Governs the Response of Ecosystems to Environmental Perturbations","","Ecosystems’ responses to environmental perturbations remain difficult to predict due to strong coupling between species and their environment. This work presents a theoretical framework to compute steady-state responses in generalized consumer-resource models. It applies to systems with nonreciprocal interactions, crossfeeding, and nonlinear growth and consumption. Near steady state, geometric transformations map perturbations in resource availability and mortality rates to shifts in niche structure, illustrated with pH-induced bacterial toxicity in denitrification and discussed for biological implications, including limits on distinguishing cooperation from competition via external perturbations.",{"@graph":69,"@context":121},[70,84,104],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/universal-niche-geometry-governs-the-response-of-ecosystems-to-environmental-perturbations/438425/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":98,"encodingFormat":97,"isAccessibleForFree":99,"interactionStatistic":100},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/universal-niche-geometry-governs-the-response-of-ecosystems-to-environmental-perturbations/438425.png","ImageObject",300,407,{"name":92,"@type":93},"pixelkiddo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-29",true,{"@type":101,"interactionType":102,"userInteractionCount":4},"InteractionCounter",{"@type":103},"ViewAction",{"@type":105,"mainEntity":106},"FAQPage",[107,113,117],{"name":108,"@type":109,"acceptedAnswer":110},"What is the main goal of the framework presented in the document?","Question",{"text":111,"@type":112},"To calculate the steady-state response of ecosystems to environmental perturbations within generalized consumer-resource models.","Answer",{"name":114,"@type":109,"acceptedAnswer":115},"Which types of ecological model features does the framework support?",{"text":116,"@type":112},"It is applicable to systems with nonreciprocal interactions, crossfeeding, and nonlinear growth or consumption rates.",{"name":118,"@type":109,"acceptedAnswer":119},"How does the framework connect environmental perturbations to changes in niches?",{"text":120,"@type":112},"Near a steady state, geometric transformations directly map perturbations in resource availability and mortality rates to shifts in niche structure.","https://schema.org",{"og:url":83,"og:type":123,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":125,"canonical":83},"index,follow",{"doc_id":127,"site_id":62},438425,1790685339,{"code":4,"msg":5,"data":130},{"doc_id":127,"user_id":131,"nickname":92,"user_avatar":132,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":138,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":128,"read_time":143},962090883892,"https://ap-avatar.wpscdn.com/avatar/e00115db34f3e0f11b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1790152879550218658","Author Manuscr ipt Author Manuscr ipt Author Manuscr ipt Author Manuscript  \n\n| | HHS Public Access\u003Cbr>Author manuscript\u003Cbr>PRX Life. Author manuscript; available in PMC 2026 January 06. |\n| --- | --- |\n\nPublished in final edited form as:  \nPRX Life. 2025 ; 3(1): . doi:10.1103/prxlife.3.013010 .  \nUniversal Niche Geometry Governs the Response of Ecosystems to Environmental Perturbations  \nAkshit Goyal 1,2,* , Jason W. Rocks3 , Pankaj Mehta3,4,†  \n1 Department of Physics, Massachusetts Insitute of Technology, Cambridge, Massachusetts 02139, USA  \n2 International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India  \n3 Department of Physics, Boston University, Boston, Massachusetts 02215, USA  \n4 Faculty of Computing and Data Sciences, Boston University, Boston, Massachusetts 02215, USA  \nAbstract  \nHow ecosystems respond to environmental perturbations is a fundamental question in ecology, made especially challenging due to the strong coupling between species and their environment. Here, we introduce a theoretical framework for calculating the steady-state response of ecosystems to environmental perturbations in generalized consumer-resource models. Our construction is applicable to a wide class of systems, including models with nonreciprocal interactions, crossfeeding, and nonlinear growth/consumption rates. Within our framework, all ecological variables are embedded into four distinct vector spaces, and ecological interactions are represented by geometric transformations between these spaces. We show that, near a steady state, such geometric transformations directly map environmental perturbations—in resource availability and mortality rates—to shifts in niche structure. We illustrate these ideas in a variety of settings including a minimal model for pH-induced toxicity in bacterial denitrification. We end by discussing the biological implications of our framework. We show that it is extremely difficult to distinguish cooperative and competitive interactions by measuring the responses of species to external perturbations.  \nI. INTRODUCTION  \nOne of the most challenging and interesting problems in theoretical ecology is to  \ndevelop methods for understanding how ecosystems respond to environmental perturbations [1,2] . This problem is especially acute in diverse ecosystems where species and environment are often strongly coupled due to environmental feedback. Characterizing how ecosystems respond to changes in their environment has important practical and theoretical consequences. Practically, understanding how ecosystems respond to changes in resource  \nPublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.  \n*Contact author: [akshitg@icts.res.in](akshitg@icts.res.in).†[Contact author: pankajm@bu.edu](Contact author: pankajm@bu.edu).  \nAuthor Manuscr ipt Author Manuscr ipt Author Manuscr ipt Author Manuscript  \nGoyal et al. Page 2  \nconcentrations is a fundamental concern of environmental science and human health and disease [3,4] . For example, how does perturbing the nitrification process affect water quality [5]? How do changes in diet affect the composition and function of the human gut microbiome [6,7]?  \nFrom a theoretical vantage point, we know that one of the most successful ways to investigate physical systems is to analyze how they respond to perturbations [8,9] .  \nThis is true for both classical and quantum systems, where objects like static and  \ndynamic susceptibilities are a staple of theoretical treatments of subjects as diverse as electromagnetism, thermodynamics, and quantum field theory [10, 11] . For this reason, the theory of linear response has become a pillar of modern theoretical physics. In the context of ecology, techniques for characterizing ecological re","cbCaicak3fGyoj4V","https://ap.wps.com/l/cbCaicak3fGyoj4V","pdf",2675312,46,"English","# Abstract\n# I. Introduction\n## Ecological responses to perturbations\n## Linear response theory in physics and ecology\n## Generalized consumer-resource models (CRMs)","[{\"question\":\"What is the main goal of the framework presented in the document?\",\"answer\":\"To calculate the steady-state response of ecosystems to environmental perturbations within generalized consumer-resource models.\"},{\"question\":\"Which types of ecological model features does the framework support?\",\"answer\":\"It is applicable to systems with nonreciprocal interactions, crossfeeding, and nonlinear growth or consumption rates.\"},{\"question\":\"How does the framework connect environmental perturbations to changes in niches?\",\"answer\":\"Near a steady state, geometric transformations directly map perturbations in resource availability and mortality rates to shifts in niche structure.\"}]","Universal Niche Geometry Governs the Response of Ecosystems to Environmental Perturbations | PDF",116]