Fig. 3

Synergistic effects among the GBCD corpus, Human Footprint (HF), and international migration of scholars (IMS). (a,b) Correlation analysis using the Convergent Cross Mapping (CCM) method reveals a strong association between GBCD and IMS, with a correlation coefficient exceeding 0.9 from 2013 to 2020. In contrast, the correlation coefficient between GBCD and HF diverges significantly, dropping below 0.2, indicating no evident intrinsic relationship. (c–f) When GBCD and IMS are used as observed values for each other, their estimated value distributions exhibit a high degree of similarity and a linear pattern. However, when HF serves as the observed value, the GBCD distribution becomes highly convergent, consistent with the trends observed in the correlation coefficient. These findings highlight the synergistic effects between GBCD and IMS, while suggesting a lack of association between GBCD and HF.