{"id":"https://openalex.org/W4294992201","doi":"https://doi.org/10.1371/journal.pcbi.1010521","title":"Stability criteria for the consumption and exchange of essential resources","display_name":"Stability criteria for the consumption and exchange of essential resources","publication_year":2022,"publication_date":"2022-09-08","ids":{"openalex":"https://openalex.org/W4294992201","doi":"https://doi.org/10.1371/journal.pcbi.1010521","pmid":"https://pubmed.ncbi.nlm.nih.gov/36074781"},"language":"en","primary_location":{"id":"doi:10.1371/journal.pcbi.1010521","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pcbi.1010521","pdf_url":null,"source":{"id":"https://openalex.org/S86033158","display_name":"PLoS Computational Biology","issn_l":"1553-734X","issn":["1553-734X","1553-7358"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS Computational Biology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1371/journal.pcbi.1010521","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087275461","display_name":"Theo Gibbs","orcid":"https://orcid.org/0000-0002-1515-8420"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Theo Gibbs","raw_affiliation_strings":["Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey, United States of America"],"raw_orcid":"https://orcid.org/0000-0002-1515-8420","affiliations":[{"raw_affiliation_string":"Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey, United States of America","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071536338","display_name":"Yifan Zhang","orcid":"https://orcid.org/0000-0001-8238-9723"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yifan Zhang","raw_affiliation_strings":["Department of Plant Biology, University of Illinois, Urbana, Illinois, United States of America"],"raw_orcid":"https://orcid.org/0000-0001-8238-9723","affiliations":[{"raw_affiliation_string":"Department of Plant Biology, University of Illinois, Urbana, Illinois, United States of America","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040055814","display_name":"Zachary R. Miller","orcid":"https://orcid.org/0000-0001-9762-8301"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zachary R. Miller","raw_affiliation_strings":["Department of Ecology & Evolution, University of Chicago, Chicago, Illinois, United States of America"],"raw_orcid":"https://orcid.org/0000-0001-9762-8301","affiliations":[{"raw_affiliation_string":"Department of Ecology & Evolution, University of Chicago, Chicago, Illinois, United States of America","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019708820","display_name":"James P. O\u2019Dwyer","orcid":"https://orcid.org/0000-0003-1180-8622"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James P. O\u2019Dwyer","raw_affiliation_strings":["Department of Plant Biology, University of Illinois, Urbana, Illinois, United States of America"],"raw_orcid":"https://orcid.org/0000-0003-1180-8622","affiliations":[{"raw_affiliation_string":"Department of Plant Biology, University of Illinois, Urbana, Illinois, United States of America","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087275461"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":{"value":2655,"currency":"USD","value_usd":2655},"apc_paid":{"value":2655,"currency":"USD","value_usd":2655},"fwci":4.7503,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.94831414,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"18","issue":"9","first_page":"e1010521","last_page":"e1010521"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10932","display_name":"Microbial Metabolic Engineering and Bioproduction","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6375702023506165},{"id":"https://openalex.org/keywords/resource","display_name":"Resource (disambiguation)","score":0.6257619857788086},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5685042142868042},{"id":"https://openalex.org/keywords/consumption","display_name":"Consumption (sociology)","score":0.5657821297645569},{"id":"https://openalex.org/keywords/competition","display_name":"Competition (biology)","score":0.5483555793762207},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5197727084159851},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3916463255882263},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.3820878863334656},{"id":"https://openalex.org/keywords/environmental-economics","display_name":"Environmental economics","score":0.37562820315361023},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.36611002683639526},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.34425097703933716},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.15759310126304626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09498581290245056}],"concepts":[{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6375702023506165},{"id":"https://openalex.org/C206345919","wikidata":"https://www.wikidata.org/wiki/Q20380951","display_name":"Resource (disambiguation)","level":2,"score":0.6257619857788086},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5685042142868042},{"id":"https://openalex.org/C30772137","wikidata":"https://www.wikidata.org/wiki/Q5164762","display_name":"Consumption (sociology)","level":2,"score":0.5657821297645569},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.5483555793762207},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5197727084159851},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3916463255882263},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.3820878863334656},{"id":"https://openalex.org/C134560507","wikidata":"https://www.wikidata.org/wiki/Q753291","display_name":"Environmental economics","level":1,"score":0.37562820315361023},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.36611002683639526},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.34425097703933716},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.15759310126304626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09498581290245056},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010829","descriptor_name":"Physiological Phenomena","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010829","descriptor_name":"Physiological Phenomena","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010829","descriptor_name":"Physiological Phenomena","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011157","descriptor_name":"Population Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011157","descriptor_name":"Population Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011157","descriptor_name":"Population Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017753","descriptor_name":"Ecosystem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017753","descriptor_name":"Ecosystem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017753","descriptor_name":"Ecosystem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D018533","descriptor_name":"Biomass","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D018533","descriptor_name":"Biomass","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D018533","descriptor_name":"Biomass","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":5,"locations":[{"id":"doi:10.1371/journal.pcbi.1010521","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pcbi.1010521","pdf_url":null,"source":{"id":"https://openalex.org/S86033158","display_name":"PLoS Computational Biology","issn_l":"1553-734X","issn":["1553-734X","1553-7358"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS Computational Biology","raw_type":"journal-article"},{"id":"pmid:36074781","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36074781","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLoS computational biology","raw_type":null},{"id":"pmh:oai:uchicago.tind.io:5009","is_oa":true,"landing_page_url":"http://knowledge.uchicago.edu/record/5009","pdf_url":null,"source":{"id":"https://openalex.org/S4306402460","display_name":"Knowledge@UChicago (University of Chicago)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40347166","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/I40347166"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://knowledge.uchicago.edu/record/5009","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:ef05d92970a14aca8cae4646056944ee","is_oa":true,"landing_page_url":"https://doaj.org/article/ef05d92970a14aca8cae4646056944ee","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"PLoS Computational Biology, Vol 18, Iss 9, p e1010521 (2022)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9488833","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9488833","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"PLoS Comput Biol","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1371/journal.pcbi.1010521","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pcbi.1010521","pdf_url":null,"source":{"id":"https://openalex.org/S86033158","display_name":"PLoS Computational Biology","issn_l":"1553-734X","issn":["1553-734X","1553-7358"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS Computational Biology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3368294025","display_name":null,"funder_award_id":"2039656","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G727702052","display_name":null,"funder_award_id":"1746045","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7447253409","display_name":null,"funder_award_id":"DGE-2039656","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7724506614","display_name":null,"funder_award_id":"220020439","funder_id":"https://openalex.org/F4320306183","funder_display_name":"James S. McDonnell Foundation"},{"id":"https://openalex.org/G8380571957","display_name":null,"funder_award_id":"DGE-1746045","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8670966305","display_name":null,"funder_award_id":"376199","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320306183","display_name":"James S. McDonnell Foundation","ror":"https://ror.org/03dy4aq19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W1512220826","https://openalex.org/W1593658962","https://openalex.org/W1946886856","https://openalex.org/W1969238253","https://openalex.org/W1978809795","https://openalex.org/W1990498142","https://openalex.org/W2012994611","https://openalex.org/W2028915685","https://openalex.org/W2033890928","https://openalex.org/W2035346239","https://openalex.org/W2043231452","https://openalex.org/W2049459598","https://openalex.org/W2049546703","https://openalex.org/W2059037247","https://openalex.org/W2061666069","https://openalex.org/W2061867342","https://openalex.org/W2062626613","https://openalex.org/W2066119558","https://openalex.org/W2069994241","https://openalex.org/W2078708516","https://openalex.org/W2091671027","https://openalex.org/W2103393468","https://openalex.org/W2104810457","https://openalex.org/W2109242001","https://openalex.org/W2110224558","https://openalex.org/W2111298353","https://openalex.org/W2118123652","https://openalex.org/W2123569104","https://openalex.org/W2127746569","https://openalex.org/W2144683622","https://openalex.org/W2157471218","https://openalex.org/W2162185058","https://openalex.org/W2299167651","https://openalex.org/W2413154614","https://openalex.org/W2416065856","https://openalex.org/W2515996996","https://openalex.org/W2574782663","https://openalex.org/W2597588799","https://openalex.org/W2603036206","https://openalex.org/W2606411644","https://openalex.org/W2614283331","https://openalex.org/W2616923088","https://openalex.org/W2750868503","https://openalex.org/W2765970410","https://openalex.org/W2806126901","https://openalex.org/W2883800094","https://openalex.org/W2906957660","https://openalex.org/W2909333924","https://openalex.org/W2950714739","https://openalex.org/W2951604240","https://openalex.org/W2952758388","https://openalex.org/W2968654899","https://openalex.org/W2985324331","https://openalex.org/W2995486710","https://openalex.org/W3003984566","https://openalex.org/W3010770048","https://openalex.org/W3021904993","https://openalex.org/W3030066800","https://openalex.org/W3046882971","https://openalex.org/W3132416946","https://openalex.org/W3155064590","https://openalex.org/W3158704851","https://openalex.org/W3169774877","https://openalex.org/W3176697880","https://openalex.org/W3188650615","https://openalex.org/W3195365295","https://openalex.org/W3206560497","https://openalex.org/W3206997815","https://openalex.org/W4225854602","https://openalex.org/W4237774156"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2942366970","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2194570607"],"abstract_inverted_index":{"Models":[0],"of":[1,15,33,52,80,86,100,125,163,215],"consumer":[2,16,53,91],"effects":[3],"on":[4,67,76,178,228],"a":[5,77,122,212],"shared":[6],"resource":[7,19,36,48,69,180,219,258],"environment":[8],"have":[9,60],"helped":[10],"clarify":[11],"how":[12,250],"the":[13,31,41,47,50,68,84,143,152,179,191,204],"interplay":[14],"traits":[17],"and":[18,109,156,186,218,260],"supply":[20],"impact":[21],"stable":[22,62,173],"coexistence.":[23],"Recent":[24],"models":[25,39,58,74],"generalize":[26],"this":[27,161],"picture":[28],"to":[29,90,158,211,240],"include":[30],"exchange":[32,261],"resources":[34,87,196],"alongside":[35],"competition.":[37],"These":[38],"exemplify":[40],"fact":[42],"that":[43,129,167,203],"although":[44],"consumers":[45,101],"shape":[46,254],"environment,":[49,144],"outcome":[51],"interactions":[54],"is":[55,118],"context-dependent:":[56],"such":[57],"can":[59,170,253],"either":[61,172],"or":[63,174],"unstable":[64],"equilibria,":[65],"depending":[66,177],"supply.":[70],"However,":[71],"these":[72,126],"recent":[73],"focus":[75],"simplified":[78],"version":[79],"microbial":[81],"metabolism":[82],"where":[83,106,224],"depletion":[85,155],"always":[88],"leads":[89],"growth.":[92],"Here,":[93],"we":[94,165,201],"model":[95],"an":[96],"arbitrarily":[97],"large":[98],"system":[99],"governed":[102],"by":[103,121,147],"Liebig's":[104],"law,":[105],"species":[107,226],"require":[108],"deplete":[110],"multiple":[111,225],"resources,":[112],"but":[113,133,247],"each":[114],"consumer's":[115],"growth":[116,157],"rate":[117],"only":[119,229],"limited":[120],"single":[123],"one":[124,230],"resources.":[127],"Resources":[128],"are":[130,139,197,262],"taken":[131],"up":[132],"not":[134],"incorporated":[135],"into":[136,142],"new":[137],"biomass":[138],"leaked":[140],"back":[141],"possibly":[145],"transformed":[146],"intracellular":[148],"reactions,":[149],"thereby":[150],"tying":[151],"mismatch":[153],"between":[154],"cross-feeding.":[159],"For":[160],"set":[162],"dynamics,":[164],"show":[166],"feasible":[168],"equilibria":[169],"be":[171],"unstable,":[175],"again":[176],"environment.":[181],"We":[182],"identify":[183],"special":[184],"consumption":[185],"production":[187],"networks":[188],"which":[189],"protect":[190],"community":[192],"from":[193],"instability":[194],"when":[195,257],"scarce.":[198],"Using":[199],"simulations,":[200],"demonstrate":[202,249],"qualitative":[205],"stability":[206,235,242],"patterns":[207,256],"derived":[208],"analytically":[209],"apply":[210],"broader":[213],"class":[214],"network":[216],"structures":[217],"inflow":[220],"profiles,":[221],"including":[222],"cases":[223],"coexist":[227],"externally":[231],"supplied":[232],"resource.":[233],"Our":[234],"criteria":[236],"bear":[237],"some":[238],"resemblance":[239],"classic":[241],"results":[243],"for":[244],"pairwise":[245],"interactions,":[246],"also":[248],"environmental":[251],"context":[252],"coexistence":[255],"limitation":[259],"modeled":[263],"directly.":[264]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}