{"id":"https://openalex.org/W2002603593","doi":"https://doi.org/10.1086/285203","title":"On Conditions for Evolutionary Stability for a Continuously Varying Character","display_name":"On Conditions for Evolutionary Stability for a Continuously Varying Character","publication_year":1991,"publication_date":"1991-07-01","ids":{"openalex":"https://openalex.org/W2002603593","doi":"https://doi.org/10.1086/285203","mag":"2002603593"},"language":"en","primary_location":{"id":"doi:10.1086/285203","doi":"https://doi.org/10.1086/285203","is_oa":false,"landing_page_url":"https://doi.org/10.1086/285203","pdf_url":null,"source":{"id":"https://openalex.org/S122176235","display_name":"The American Naturalist","issn_l":"0003-0147","issn":["0003-0147","1537-5323"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-3","ki-jl-1","medline","norway-2","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315672","host_organization_name":"University of Chicago Press","host_organization_lineage":["https://openalex.org/P4310315672","https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago Press","University of Chicago"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Naturalist","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011909752","display_name":"F. Christiansen","orcid":"https://orcid.org/0000-0001-9415-0621","observed_orcids":["https://orcid.org/0000-0001-9415-0621"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Freddy Bugge Christiansen","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5011909752"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.7271,"has_fulltext":false,"cited_by_count":450,"citation_normalized_percentile":{"value":0.98446167,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"138","issue":"1","first_page":"37","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.8838000297546387,"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":0.8838000297546387,"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":0.07840000092983246,"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/T10174","display_name":"Animal Behavior and Reproduction","score":0.017899999395012856,"subfield":{"id":"https://openalex.org/subfields/1105","display_name":"Ecology, Evolution, Behavior and Systematics"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/evolutionary-stability","display_name":"evolutionary stability","score":0.9810000061988831},{"id":"https://openalex.org/keywords/evolutionarily-stable-strategy","display_name":"evolutionarily stable strategy","score":0.8700000047683716},{"id":"https://openalex.org/keywords/convergence-stability","display_name":"convergence stability","score":0.781000018119812},{"id":"https://openalex.org/keywords/polymorphism","display_name":"polymorphism","score":0.597000002861023}],"concepts":[{"id":"https://openalex.org/C2519700","wikidata":"https://www.wikidata.org/wiki/Q1069992","display_name":"Evolutionarily stable strategy","level":3,"score":0.683856725692749},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6626830697059631},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5419713854789734},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5326900482177734},{"id":"https://openalex.org/C171578705","wikidata":"https://www.wikidata.org/wiki/Q5418700","display_name":"Evolutionary dynamics","level":3,"score":0.532243013381958},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5272102355957031},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.5036737322807312},{"id":"https://openalex.org/C131892835","wikidata":"https://www.wikidata.org/wiki/Q770985","display_name":"Intraspecific competition","level":2,"score":0.41600269079208374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37233561277389526},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.3629528880119324},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35979437828063965},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.32034939527511597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.180768221616745},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.17200878262519836},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.16175204515457153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12840673327445984},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.1057596504688263},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08471545577049255},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1086/285203","doi":"https://doi.org/10.1086/285203","is_oa":false,"landing_page_url":"https://doi.org/10.1086/285203","pdf_url":null,"source":{"id":"https://openalex.org/S122176235","display_name":"The American Naturalist","issn_l":"0003-0147","issn":["0003-0147","1537-5323"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-3","ki-jl-1","medline","norway-2","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315672","host_organization_name":"University of Chicago Press","host_organization_lineage":["https://openalex.org/P4310315672","https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago Press","University of Chicago"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Naturalist","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/f570d9f0-9dec-11de-a092-000ea68e967b","doi":null,"is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/f570d9f0-9dec-11de-a092-000ea68e967b","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Christiansen, F 1991, 'On conditions for evolutionary stability for a continuously varying character', American Naturalist, vol. 138, pp. 37\u201350.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W138950840","https://openalex.org/W1513240596","https://openalex.org/W1590824230","https://openalex.org/W1967272454","https://openalex.org/W1967829443","https://openalex.org/W1972569416","https://openalex.org/W1994507967","https://openalex.org/W2009479360","https://openalex.org/W2036034149","https://openalex.org/W2037575679","https://openalex.org/W2039102755","https://openalex.org/W2047647995","https://openalex.org/W2055107977","https://openalex.org/W2076558112","https://openalex.org/W2077856214","https://openalex.org/W2094216703","https://openalex.org/W2101784227","https://openalex.org/W2105973197","https://openalex.org/W2303043072","https://openalex.org/W2327161309","https://openalex.org/W2328268168","https://openalex.org/W3014992565"],"related_works":["https://openalex.org/W4386332491","https://openalex.org/W2032744614","https://openalex.org/W1977271028","https://openalex.org/W2116862131","https://openalex.org/W2055480527","https://openalex.org/W2017476532","https://openalex.org/W6940523319","https://openalex.org/W2055107977","https://openalex.org/W4206213492","https://openalex.org/W1972573843"],"abstract_inverted_index":{"The":[0,17,61,126,223],"two":[1,51],"conditions":[2,52],"for":[3,23,56,69,230],"stability":[4,63,86,91,129,152,188],"of":[5,26,41,75,92,103,137,140,150,153,160,173,185,201,204],"an":[6,109,143],"evolutionary":[7,98,110,144,155,163,202,220],"equilibrium,":[8,31],"the":[9,12,24,27,30,33,42,50,54,67,83,90,97,101,138,148,151,154,158,170,186,198],"m-stability":[10,18],"and":[11,32,82,207,210,238],"\u03b4-stability":[13,34],"conditions,":[14],"are":[15],"discussed.":[16],"condition":[19,22,35,55,64,87,130],"is":[20,113,225],"a":[21,38,57,79,93,135,161,194,228],"convergence":[25,62,70,114,187,208],"population":[28,95],"toward":[29,216],"coresponds":[36],"to":[37,66,72,89,123,134,147],"local":[39,84,118,127,211],"version":[40],"classic":[43],"evolutionarily":[44,240],"stable":[45,59,209,221,241],"strategy":[46],"(ESS)":[47],"condition.":[48],"Together":[49],"provide":[53],"continuous":[58],"strategy.":[60],"corresponds":[65,88],"requirement":[68],"due":[71],"initial":[73,171,199],"increase":[74,102,172],"rare":[76,104,174],"alleles":[77],"in":[78,197],"monomorphic":[80,94,237],"population,":[81],"ESS":[85,119,128,212],"at":[96,142],"equilibrium":[99,111,145,164],"against":[100],"alleles.":[105],"In":[106],"this":[107,179],"way,":[108],"that":[112,234],"stable,":[115,120],"but":[116],"not":[117],"will":[121],"tend":[122],"become":[124],"polymorphic.":[125],"therefore":[131],"contributes":[132],"more":[133],"description":[136,149],"dynamics":[139],"variation":[141],"than":[146],"equilibrium.":[156],"However,":[157],"characterization":[159],"polymorphic":[162,219,239],"cannot":[165,181],"be":[166],"reached":[167],"by":[168],"studying":[169],"variant":[175],"alleles,":[176],"just":[177],"as":[178],"method":[180],"describe":[182],"all":[183],"aspects":[184],"either.":[189],"Combining":[190],"these":[191],"analyses":[192],"provides":[193],"powerful":[195],"tool":[196],"exploration":[200],"equilibriums":[203,214],"complicated":[205],"systems,":[206],"unstable":[213],"point":[215],"very":[217],"interesting":[218],"states.":[222],"analysis":[224],"illustrated":[226],"on":[227],"model":[229],"intraspecific":[231],"exploitative":[232],"competition":[233],"may":[235],"show":[236],"equilibriums.":[242]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":35},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":27},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":14}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}