Coupling input and output intensity to explore the sustainable agriculture intensification path in mainland China

Sustainable intensification (SI) of agriculture is widely regarded as an important way to alleviate the contradiction between the food gap and ecosystem health. Correlate input intensity and output intensity have been regarded as an important dimension in most estimation frameworks of SI. But in practice, this correlation is generally expressed in terms of efficiency metrics and calculated as the ratio of output intensity to input intensity, which cannot quantitatively explain the impact of input intensity on output intensity and provide a threshold value for estimating the suitability of SI. This study's goals are to propose an input—output coupled method to explain the impact of input intensity on output intensity and thereby estimate the suitability of provincial SI. Provincial annual input intensity and output intensity were estimated from an emergy-based perspective by taking China as a case study. The K-means algorithm was used to identify the structural pattern of arable land input intensity. A sliding window-based partial correlation index method was proposed and applied to reveal the interaction process between input intensity and output intensity. The results show that there are two main change paths in the pattern of input intensity: one path in the western irrigation regions and the other path in the eastern northeast China Plain and middle-lower Yangtze Plain. The former path can be expressed as a small increase in fertilizer and agro-machinery input intensity with a decrease in labour force input intensity. The latter path shows a larger increase in fertilizer and pesticide input intensity. For each type of input intensity except mulching film, its correlation to output intensity has experienced a similar coupling—decoupling—recoupling process in both plain provinces and mountainous or plateau provinces. According to Landau's theory of phase transition, the complex coupling of input and output undergoes a phase transition process from order to disorder and then to order, depicted by the sliding window-based partial correlation coefficient as the order parameter from a holistic perspective. The inflection points of coupling relation changes show that the phenomenon of fertilizer and pesticide overuse has steadily occupied most provinces in eastern China and is spreading westwards. Although the “zero growth action for fertilizers and pesticides” has made considerable achievements in reducing the input intensity of fertilizer and pesticides sinc