Fig. 5: Conceptual framework of glacier lake ecosystem dynamics via structural equation modeling.

This figure offers a visual schematic and their statistical relations based on SEM analyses, depicting the state of the glacier lake ecosystem under varying rates of ecological response relative to the pace of climate change. Panels a, b delineate the ecosystem’s condition in two distinct phases: the normal phase (prior to ~1980s) and the accelerated phase (post- ~1980s), respectively. a In the normal phase, the ecosystem and climate changes are in relative equilibrium, with the thickness of arrow segments representing the moderate strength of ecological driving forces. b The accelerated phase shows intensified ecological responses to climate change, highlighted by thicker arrow segments that denote increased force strengths. The color arrows signify the primary drivers within the lake ecosystem (the sum of total algae pigment concentrations), with adjacent numbers quantifying the impact magnitude of each driver. Continuous arrows indicate positive effect while dashed arrows indicate negative effect. The red and black color show significant (*p < 0.05, **p < 0.01, ***p < 0.001) and not significant (ns) path, respectively (see Supplementary Fig. 25 and Supplementary Table 7 for more statistical parameters). Goodness of fit statistics are evaluated as follows: Chi-square, Degrees of freedom, probability level, NFI (Normed fit index), CFI (Comparative fit index), AIC (Akaike information criterion), etc. For comprehensive data and a more detailed explanation of these dynamics, refer to the Supplementary Note 10.