Dynamics of cooperation evolution in fluctuating populations with environmental feedback

Cooperation is an important driver of resource regeneration and ecological maintenance, and a favorable environment enables the evolution of cooperation. In order to explore the dynamic relationship among environmental fluctuations and individual behaviors in biological systems, this paper designs an evolutionary game model in dynamic populations to examine the interactions between resources and cooperative evolution. The results suggest that the sustainable evolution of populations ensures that the initial population size is within the environmental carrying capacity, otherwise the system may be at risk of collapse. The strength of environmental feedbacks and synergistic factors together determine the expansion or contraction of populations and cooperation. Theoretical predictions agree with numerical simulations, thus elucidating the conditions in which cooperative behavior could be sustained in a system with limited resources. There hope that this work provides new theoretical support for the evolution of cooperation in dynamical systems and for the construction of more adaptive evolutionary models.