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Hyper Diversity, Species Richness, and Community Structure in ESS and Non-ESS Communities

Kailas Shankar Honasoge (), Tania L. S. Vincent, Gordon G. McNickle, Roel Dobbe, Kateřina Staňková, Joel S. Brown and Joseph Apaloo
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Kailas Shankar Honasoge: Delft University of Technology
Gordon G. McNickle: University of Illinois at Chicago
Roel Dobbe: Delft University of Technology
Kateřina Staňková: Delft University of Technology
Joel S. Brown: Moffitt Cancer Center
Joseph Apaloo: St. Francis Xavier University

Dynamic Games and Applications, 2025, vol. 15, issue 4, No 15, 1424-1444

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 $$n \cdot \left( {s + 1} \right)$$ n · s + 1 species can form a hypersaturated community, where $$n$$ n is the number of ESS species at the strategy’s dimension $$s$$ s . 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.

Keywords: Hypersaturated communities; Non-ESS communities; Mutual invasibility; Niche coevolution; Darwinian Dynamics; Evolutionary game theory (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-025-00646-2

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