Spatio-temporal evolution of cooperation: multistability, pattern formation, and chaos in resource-driven...

Area of Science:

• Evolutionary Biology
• Ecology
• Mathematical Biology

Background:

• Cooperative behavior is vital for organism survival but is challenged by selfish individuals exploiting finite resources.
• Interactions between cooperation and resource availability create feedback loops, driving co-evolution of behaviors and environments.

Purpose of the Study:

• To model the interplay between cooperative strategies and resource dynamics in both well-mixed and spatially heterogeneous populations.
• To analyze how resource feedback mechanisms influence evolutionary dynamics across temporal and spatial scales.

Main Methods:

• Integration of population dynamics with replicator dynamics.
• Development of models for homogeneous and heterogeneous spatial distributions with resource feedback.
• Analysis of evolutionary dynamics including bifurcations and chaotic behavior.

Main Results:

• Temporal models show multistability and bifurcations; spatial models exhibit Turing instability, Turing-Hopf bifurcation, and chaos.
• Homogeneous distributions yield stable periodic solutions, while heterogeneous distributions lead to chaotic dynamics.
• Sustaining cooperation is favored by higher initial cooperator density, faster resource growth, and lower initial resource stock.

Conclusions:

• Resource dynamics and spatial diffusion critically shape the evolution of cooperation.
• Payoffs alone do not guarantee cooperation; resource abundance is a key factor.
• Findings offer insights for ecosystem management, conservation biology, and understanding animal social behavior.