Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions.

Area of Science:

• Ecology
• Evolutionary Biology
• Mathematical Biology

Background:

• Biodiversity persistence is challenged by Darwinian selection and pairwise competition.
• Higher-order interactions (beyond pairwise) significantly influence social phenotypes and community dynamics.
• Understanding these complex interactions is crucial for ecological stability.

Purpose of the Study:

• To investigate the impact of higher-order interactions on the evolution of social phenotypes.
• To develop a novel perspective on species coexistence using perturbed interaction networks.
• To demonstrate how network perturbations can predict community equilibrium.

Main Methods:

• Development of a simple mathematical model for higher-order interactions.
• Analysis of perturbed intransitive competitive networks.
• Application of a mathematical technique to determine coexistence equilibrium, bypassing large systems of ordinary differential equations.

Main Results:

• Perturbed interaction networks can rapidly determine species coexistence equilibrium.
• The system can split into multiple feasible cluster states based on perturbation levels.
• The ratio of unperturbed to perturbed species is inversely proportional to the perturbation magnitude.

Conclusions:

• Nonlinear dynamical systems and interaction topologies are crucial for understanding species coexistence under adverse conditions.
• Reduced competition between species enhances their abundance and competitive success.
• This framework offers insights into maintaining biodiversity in complex ecological communities.