{"doi":"10.1007/s13235-025-00646-2","title":"Hyper Diversity, Species Richness, and Community Structure in ESS and Non-ESS Communities","abstract":"Abstract In mathematical models of eco-evolutionary dynamics with a quantitative trait, two species with different strategies can coexist only if they are separated by a valley or peak of the adaptive landscape. A community is ecologically and evolutionarily stable if each species’ trait sits on global, equal fitness peaks, forming a saturated ESS community. However, the adaptive landscape may allow communities with fewer ( undersaturated ) or more ( hypersaturated ) species than the ESS. Non-ESS communities at ecological equilibrium exhibit invasion windows of strategies that can successfully invade. Hypersaturated communities can arise through mutual invasibility where each non-ESS species’ strategy lies in another’s invasion window. Hypersaturation in ESS communities with more than 1 species remains poorly understood. We use the G -function approach to model niche coevolution and Darwinian dynamics in a Lotka–Volterra competition model. We confirm that up to 2 species can coexist in a hypersaturated community with a single-species ESS if the strategy is scalar-valued, or 3 species if the strategy is bivariate. We conjecture that at most $$n \\cdot \\left( {s + 1} \\right)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>·</mml:mo> <mml:mfenced> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> species can form a hypersaturated community, where $$n$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> </mml:math> is the number of ESS species at the strategy’s dimension $$s$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>s</mml:mi> </mml:math> . For a scalar-valued 2-species ESS, 4 species coexist by “straddling” the would-be ESS traits. When our model has a 5-species ESS, we can get 7 or 8, but not 9 or 10, species coexisting in the hypersaturated community. In a bivariate model with a single-species ESS, an infinite number of 3-species hypersaturated communities can exist. We offer conjectures and discuss their relevance to ecosystems that may be non-ESS due to invasive species, climate change, and human-altered landscapes.","journal":"Dynamic Games and Applications","year":2025,"id":552999,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9512,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2025-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1449739,"name":"Tania L.S. Vincent","orcid":null,"position":1,"is_corresponding":false},{"id":1449305,"name":"Gordon G. McNickle","orcid":"0000-0002-7188-7265","position":2,"is_corresponding":false},{"id":1449306,"name":"Roel Dobbe","orcid":"0000-0003-4633-7023","position":3,"is_corresponding":false},{"id":314572,"name":"Kateřina Staňková","orcid":"0000-0002-4519-0325","position":4,"is_corresponding":false},{"id":294827,"name":"Joel S. Brown","orcid":"0000-0002-0958-9494","position":5,"is_corresponding":false},{"id":1449740,"name":"Joseph Apaloo","orcid":null,"position":6,"is_corresponding":false},{"id":1449304,"name":"Kailas Shankar Honasoge","orcid":"0000-0001-5127-6945","position":0,"is_corresponding":true}],"reference_count":38,"raw_metadata":null,"created_at":"2026-07-19T02:54:37.527189Z","pmid":"41020141","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}