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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities.

Katherine Betz¹, Feng Fu^2,3, Naoki Masuda^4,5,6

¹Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, 14260-2900, USA.

Bulletin of Mathematical Biology

|June 7, 2024

Summary

This summary is machine-generated.

This study introduces an eco-evolutionary game model on networks with two communities. It reveals how community structure influences population dynamics and game strategy evolution.

Keywords:

Bifurcation analysis Evolutionary game theory Feedback-evolving games Oscillatory dynamics

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Area of Science:

Evolutionary Game Theory
Mathematical Biology
Network Science

Background:

Eco-evolutionary models demonstrate that feedback between behavior and environment alters game payoffs and population dynamics.
Environmental states can be localized (edge-based) rather than global, influencing interactions.

Purpose of the Study:

To propose and analyze an eco-evolutionary game dynamics model on a two-community network.
To investigate how differing interaction rates within and between communities affect dynamics.
To explore the impact of edge-based environmental states on game evolution.

Main Methods:

Analytical determination of equilibria and stability under symmetric population structure.
Numerical study of replicator dynamics for the general model.
Modeling pairwise interactions on network edges with community structure.

Main Results:

The model exhibits complex dynamics, including multiple transcritical bifurcations and multistability.
Anti-synchronous oscillations were observed, indicating rich emergent behavior.
Community structure significantly impacts eco-evolutionary dynamics within and between niches.

Conclusions:

The proposed model provides a framework for understanding eco-evolutionary dynamics in structured populations.
Community structure and interaction rates are crucial factors shaping evolutionary outcomes.
Edge-based environmental states introduce novel dynamics compared to node-based or global states.