{"id":"https://openalex.org/W2037329599","doi":"https://doi.org/10.1137/s003613999935319x","title":"How Many Species Can Two Essential Resources Support?","display_name":"How Many Species Can Two Essential Resources Support?","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2037329599","doi":"https://doi.org/10.1137/s003613999935319x","mag":"2037329599"},"language":"en","primary_location":{"id":"doi:10.1137/s003613999935319x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003613999935319x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://conservancy.umn.edu/bitstreams/84303b76-ac74-4bf4-b1ae-960b7e7498dd/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017820212","display_name":"Bingtuan Li","orcid":"https://orcid.org/0000-0002-1444-6201"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]},{"id":"https://openalex.org/I4210143137","display_name":"University of Louisville Hospital","ror":"https://ror.org/04sq8k219","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210143137"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bingtuan Li","raw_affiliation_strings":["University of Louisville","University of Utah"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Louisville","institution_ids":["https://openalex.org/I4210143137"]},{"raw_affiliation_string":"University of Utah","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109396218","display_name":"Hal L. Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152479","display_name":"Statistical Service","ror":"https://ror.org/05vydvf11","country_code":"CY","type":"government","lineage":["https://openalex.org/I4210152479"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Hal Smith","raw_affiliation_strings":["CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)","institution_ids":["https://openalex.org/I4210152479"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6907,"has_fulltext":true,"cited_by_count":51,"citation_normalized_percentile":{"value":0.89620902,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"62","issue":"1","first_page":"336","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9951000213623047,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9876000285148621,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chemostat","display_name":"Chemostat","score":0.9166246652603149},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.6532461643218994},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.6254642009735107},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5445913672447205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41241690516471863},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.3659104108810425},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3564451336860657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27379146218299866},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.23570281267166138}],"concepts":[{"id":"https://openalex.org/C125111812","wikidata":"https://www.wikidata.org/wiki/Q902311","display_name":"Chemostat","level":3,"score":0.9166246652603149},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6532461643218994},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.6254642009735107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5445913672447205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41241690516471863},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.3659104108810425},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3564451336860657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27379146218299866},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.23570281267166138},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C523546767","wikidata":"https://www.wikidata.org/wiki/Q10876","display_name":"Bacteria","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s003613999935319x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003613999935319x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:conservancy.umn.edu:11299/3458","is_oa":true,"landing_page_url":"http://purl.umn.edu/3458","pdf_url":"https://conservancy.umn.edu/bitstreams/84303b76-ac74-4bf4-b1ae-960b7e7498dd/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/3458","is_oa":true,"landing_page_url":"http://purl.umn.edu/3458","pdf_url":"https://conservancy.umn.edu/bitstreams/84303b76-ac74-4bf4-b1ae-960b7e7498dd/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037329599.pdf","grobid_xml":"https://content.openalex.org/works/W2037329599.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W257442556","https://openalex.org/W1656967312","https://openalex.org/W1851248039","https://openalex.org/W1946886856","https://openalex.org/W1968201943","https://openalex.org/W1971134127","https://openalex.org/W1974186209","https://openalex.org/W1975472370","https://openalex.org/W1979140770","https://openalex.org/W1988681504","https://openalex.org/W1989998020","https://openalex.org/W1995608339","https://openalex.org/W1995834589","https://openalex.org/W1995986570","https://openalex.org/W2009710695","https://openalex.org/W2015067077","https://openalex.org/W2015217267","https://openalex.org/W2023893235","https://openalex.org/W2027665073","https://openalex.org/W2034171352","https://openalex.org/W2034305650","https://openalex.org/W2035346239","https://openalex.org/W2043616341","https://openalex.org/W2043691077","https://openalex.org/W2054817264","https://openalex.org/W2061011338","https://openalex.org/W2062247832","https://openalex.org/W2067877098","https://openalex.org/W2069653542","https://openalex.org/W2072938666","https://openalex.org/W2080351913","https://openalex.org/W2085722279","https://openalex.org/W2090413088","https://openalex.org/W2153465537","https://openalex.org/W2165565577","https://openalex.org/W3025136633","https://openalex.org/W4211137119","https://openalex.org/W4237564398","https://openalex.org/W4239085533"],"related_works":["https://openalex.org/W1608758340","https://openalex.org/W2123404724","https://openalex.org/W47420346","https://openalex.org/W1505019344","https://openalex.org/W4237795480","https://openalex.org/W2143478158","https://openalex.org/W2042789668","https://openalex.org/W2025026414","https://openalex.org/W2102268782","https://openalex.org/W2064253281"],"abstract_inverted_index":{"A":[0],"chemostat":[1],"model":[2,67],"of":[3,6,54,65,75],"n":[4],"species":[5,28,32],"microorganisms":[7],"competing":[8],"for":[9,21,30],"two":[10,31,103],"perfectly":[11],"complementary,":[12],"growth-limiting":[13],"nutrients":[14],"is":[15,46,68],"considered.":[16],"Sufficient":[17],"conditions":[18],"are":[19],"given":[20],"there":[22],"to":[23,33,38,52],"be":[24],"a":[25],"single":[26],"winning":[27],"and":[29,61,78,92],"coexist,":[34],"driving":[35],"the":[36,41,55,63,66],"others":[37],"extinction.":[39],"In":[40],"case":[42],"when":[43],"n=3,":[44],"it":[45],"shown":[47],"that":[48],"every":[49],"solution":[50],"converges":[51],"one":[53],"single-species":[56],"or":[57],"two-species":[58],"steady":[59],"states,":[60],"hence":[62],"dynamics":[64],"completely":[69],"determined.":[70],"The":[71],"results":[72],"generalize":[73],"those":[74],"Hsu,":[76],"Cheng,":[77],"Hubbell":[79],"[SIAM":[80],"J.":[81],"Appl.":[82],"Math.,":[83],"41":[84],"(1981),":[85],"pp.":[86,99],"422--444]":[87],"as":[88,90],"well":[89],"Butler":[91],"Wolkowicz":[93],"[":[94],"Math.":[95],"Biosci.,":[96],"83":[97],"(1987),":[98],"1--48]":[100],"who":[101],"considered":[102],"species.":[104]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}