Resilience prediction and tipping point control of multilayer ecological networks based on dimensionality reduction method

The collapse of ecosystems often leads to irreversible and catastrophic outcomes. Analyzing and controlling these collapses are challenging due to the complex nature, high dimensionality, multilayer structure, and dynamic behavior of ecosystems, influenced by factors such as interaction topology. While dimensionality reduction techniques can simplify system dynamics, most existing methods focus on individual interaction, hindering comprehensive analysis of diverse species and interactions in complex ecological networks. This paper presents a framework for a plant–pollinator–parasite multilayer network that incorporates mutualistic and parasitic interactions using diagonal coupling. A downscaling approach is devised to transform the high-dimensional system into a low-dimensional effective system with overall variables and layer structure variables. The simplified model accurately captures the fundamental characteristics and dynamics of the original system. Through this framework, we systematically elucidate the resilience patterns of multilayer networks under coupled interactions and the collapse scenarios of three species types, highlighting hysteresis phenomena, multiple tipping points, and first-order or multistage phase transitions within the system. Additionally, two control strategies are introduced to manage collapse critical points via intra- and inter-layer influence, with a low-dimensional model employed to forecast control outcomes. The study demonstrates that the low-dimensional model and control measures are instrumental in evaluating, foreseeing, and controlling the resilience and collapse tipping points of multilayer ecosystems. This framework is versatile and can be extended to diverse multilayer dynamic networks, exposing the fundamental mechanisms and resilience phenomena of these systems.