Lotka–Volterra Dynamics and Sustainable Regulation of Agroecosystems: Coupled Framework of Monte Carlo Simulation and Multi-Objective Optimisation

Addressing the dual challenges of agricultural productivity and ecological sustainability, this study develops an integrated framework combining Lotka–Volterra dynamics, Monte Carlo simulation, and multi-objective optimisation to quantify agroecosystem responses under anthropogenic interventions. Key innovations include the incorporation of carbon sequestration dynamics and low-carbon agricultural practices into ecological–economic trade-off analysis. Our findings demonstrate the following: (1) Seasonal carbon fertilisation effects enhance producer growth by up to 30%, while energy recycling from consumer mortality offsets 22% of pesticide-induced carbon emissions. (2) The strategic introduction of dual-function species synergistically improves carbon sink capacity by 18–25% through enhanced producer efficiency and reduced chemical reliance. (3) Multi-objective optimisation reveals that integrated pest management coupled with organic amendments achieves a 51.2% net benefit improvement, while reducing agrochemical carbon footprints by 40–55%. The proposed framework bridges critical gaps in sustainable agriculture by simultaneously addressing yield stability, biodiversity conservation, and climate mitigation imperatives. This work advances the dynamic modelling of agroecosystems through probabilistic risk assessment and carbon-aware decision-making, providing actionable pathways for low-carbon agricultural intensification.