A replicator model with transport dynamics on networks for species evolution.

Area of Science:

• Ecological modeling
• Network theory
• Evolutionary game theory

Background:

• Marine ecosystems face complex dynamics influenced by local species evolution and inter-reserve species exchange.
• Understanding these multi-scale interactions is crucial for effective conservation and management strategies.

Purpose of the Study:

• To propose and analyze a network-based framework for modeling marine ecosystem evolution and dynamics.
• To investigate how inter-reserve species exchange affects ecosystem equilibria and stability.
• To assess the model's capability in reproducing phenomena like synchronization.

Main Methods:

• A multi-scale model incorporating local species evolution (replicator equation) and network-level transport (transport function).
• Analysis of evolutionary stable states and their asymptotic stability conditions based on network properties.
• Implementation of a fourth-order P-(EC)k Gauss-Legendre Runge Kutta scheme for numerical simulations.
• Validation through numerical experiments on single-node and multi-node network structures.

Main Results:

• Established conditions for the asymptotic stability of evolutionarily stable states, dependent on network velocity transfer and maximum degree.
• Demonstrated the model's ability to capture local and network-wide dynamics, including synchronization phenomena.
• Characterized the model's capabilities and limitations through various numerical experiments on different network topologies.

Conclusions:

• The proposed network framework provides valuable insights into marine ecosystem stability, resilience, and long-term behavior.
• The model offers a robust tool for ecological research, conservation planning, and ecosystem management.
• The study highlights the importance of considering both local and network-level interactions in ecological dynamics.