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

Area of Science:

• Eco-evolutionary dynamics
• Theoretical ecology
• Mathematical biology

Background:

• Species coexistence in ecological communities is often limited by adaptive landscapes, requiring valleys or peaks for stability.
• Evolutionarily Stable Strategy (ESS) communities are stable when species traits align with global fitness peaks.
• Communities can be undersaturated (fewer species than ESS) or hypersaturated (more species than ESS), with hypersaturation arising from mutual invasibility.

Purpose of the Study:

• To investigate the mechanisms and limits of hypersaturation in eco-evolutionary dynamics using mathematical modeling.
• To explore how hypersaturated communities can exceed the number of species predicted by ESS.
• To analyze the conditions under which hypersaturation occurs in Lotka-Volterra competition models.

Main Methods:

• Utilized the G-function approach to model niche coevolution and Darwinian dynamics.
• Employed a Lotka-Volterra competition model to simulate species interactions and trait evolution.
• Analyzed scalar-valued and bivariate strategy spaces to determine coexistence limits.

Main Results:

• Confirmed that hypersaturated communities with up to 2 species (scalar strategy) or 3 species (bivariate strategy) can exist with a single-species ESS.
• Demonstrated that for a 2-species ESS, 4 species can coexist by 'straddling' ESS traits.
• Observed that with a 5-species ESS, 7 or 8 species can coexist, but not 9 or 10; an infinite number of 3-species hypersaturated communities can exist in a bivariate model with a single-species ESS.

Conclusions:

• Hypersaturated communities can harbor more species than predicted by single-species or multi-species ESS, particularly in models with lower-dimensional strategies.
• The findings suggest a conjecture for the maximum number of species in hypersaturated communities: n*(s+1), where n is the number of ESS species and s is the strategy dimension.
• The study's insights are relevant for understanding real-world ecosystems affected by invasive species, climate change, and human-altered landscapes, which may deviate from ESS.