The source region of Yangtze River and Yellow River plays an important role in the carbon source/sink cycle and is a focal point for ecological environment management; however, it is also one of China's most vulnerable ecological systems. This vulnerability is due to human and livestock population expansion; large area of alpine meadow are experiencing overgrazing and climate change, with barren patches developing and connecting with each other. Barren patches develop in a range of sizes and shapes, presenting an infertile "black soil" type landscape in the final stage of grassland degradation. The driving mechanisms of alpine meadow degradation are complex and remain controversial, making it difficult to determine individual causes of degradation and to take effective measures to counter them. Thus, this investigation employed "black box" theory to avoid these uncertain elements in its examination of spatial patterns and temporal evolution in barren patches. This investigation aimed to clarify the role barren patch evolution and connectivity plays in alpine meadow degradation, providing an increased understanding of alpine meadow ecosystems as the basis for ecological maintenance, restoration and management.
A simulation method of complexity science, cellular automata, was used to model the development of barren patches in this study. The initial iteration data for the model were obtained from observations of moderately degraded meadows with the lowest barren patch percentage, and were used to draw a matrix in which each cell was represented as either 0 or 1; 0 representing a cell where vegetation cover was lower than 50% and 1 representing cells where vegetation cover was over 50%. Based on field observations of barren patch percentage and landscape structure, including the experience of local herdsman whose livelihoods are inextricably linked to the grassland, the simulation time step was set to one year per iteration. Further field observations of barren patch evolution and other features of their spatial distribution at different stages of degradation were used to define the rules of the model, and Matlab 7.0 was used as a platform for simulation. Cell neighborhoods were defined as the Moore type and cellular space was treated according to the reflective boundary rule. Using this combination of field research techniques and cellular automata simulation, realistic developmental graphs modeling the connectivity of barren patches from the initial degradation stage to the collapse of the alpine meadow system were established. The goodness of fit for the simulation analyses averaged 93.9%. Results further indicated that in the degradation sequence, there were three defined degradation stages: a low-speed connectivity stage from 0 to 2 years, a jump stage from 2 to 7 years and an irreversible connectivity stage from 7 to 9 years. Additionally, a sudden change was found to occur at the beginning of each stage, identifying a threshold characteristic in the process of barren patch connectivity. Through comparative analysis of the performances of grassland ecology and restoration between the jump stage and the irreversible connectivity stage, the connectivity threshold was calculated at 54.5% as a protection index of the alpine meadow. The irreversibility of ecological harm associated with large barren patches highlights the importance of determining and using the connectivity threshold to identify and determine priority sites for restoration.