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A community is ecologically and evolutionarily stable if each species\u2019 trait sits on global, equal fitness peaks, forming a\n                    <jats:italic>saturated<\/jats:italic>\n                    ESS community. However, the adaptive landscape may allow communities with fewer (\n                    <jats:italic>undersaturated<\/jats:italic>\n                    ) or more (\n                    <jats:italic>hypersaturated<\/jats:italic>\n                    ) species than the ESS. Non-ESS communities at ecological equilibrium exhibit\n                    <jats:italic>invasion windows<\/jats:italic>\n                    of strategies that can successfully invade.\n                    <jats:italic>Hypersaturated<\/jats:italic>\n                    communities can arise through\n                    <jats:italic>mutual invasibility<\/jats:italic>\n                    where each non-ESS species\u2019 strategy lies in another\u2019s invasion window. Hypersaturation in ESS communities with more than 1 species remains poorly understood. We use the\n                    <jats:italic>G<\/jats:italic>\n                    -function approach to model niche coevolution and Darwinian dynamics in a Lotka\u2013Volterra 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                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$n \\cdot \\left( {s + 1} \\right)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\u00b7<\/mml:mo>\n                            <mml:mfenced>\n                              <mml:mrow>\n                                <mml:mi>s<\/mml:mi>\n                                <mml:mo>+<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:mfenced>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    species can form a hypersaturated community, where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$n$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>n<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is the number of ESS species at the strategy\u2019s dimension\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$s$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>s<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . For a scalar-valued 2-species ESS, 4 species coexist by \u201cstraddling\u201d 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.\n                  <\/jats:p>","DOI":"10.1007\/s13235-025-00646-2","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T02:43:42Z","timestamp":1748573022000},"page":"1424-1444","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hyper Diversity, Species Richness, and Community Structure in ESS and Non-ESS Communities"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5127-6945","authenticated-orcid":false,"given":"Kailas Shankar","family":"Honasoge","sequence":"first","affiliation":[]},{"given":"Tania L. 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