Stochastic ecoevolutionary dynamics under coupled behavioral and environmental feedback

The behavioral patterns and dynamics of biological populations are shaped by the combined influences of interaction outcomes and environmental resources. Numerous coevolutionary mechanisms proposed in previous studies have extended the exploration of biological behavior into system level modeling, deepening our understanding of long-term population dynamics. Yet from a modeling perspective, deterministic dynamical frameworks often fail to capture many subtle real world factors, thereby limiting their predictive reliability, particularly for critical system outcomes. To address this limitation, this study extends existing approaches by introducing independent stochastic processes to construct a stochastic dynamical model with bidirectional feedback mechanisms. The model characterizes the coevolutionary dynamics between collective behavior and environmental states, and analytical conditions for internal equilibrium points and stochastic asymptotic stability are derived. Numerical simulations not only verify the theoretical results but also reveal multiple dynamic regimes that emerge under different levels of stochasticity, including small oscillations near equilibrium, amplified oscillations, and unstable fluctuations. This research deepens our comprehension of the coevolution of behavior and environment from a stochastic dynamics perspective and provides a fundamental theoretical framework.