Fig. 5

Anticipating abrupt community shifts. a Energy gap index. In the framework of the energy landscape analysis, difference between the energy of a current community state from that of the local energy minimum is defined as the “energy gap” index for anticipating drastic community changes. b Stable-state entropy index. Shannon’s entropy estimates based on random-walk simulations towards alternative stable states are expected to represent instability of current community states on energy landscapes (see “Methods” section for details). c Relationship between the degree of community-compositional changes (abruptness) and each signal index. Note that a high score of energy gap, stable-state entropy, or local Lyapunov/structural stability potentially represents an unstable state. Significant/non-significant regressions within respective replicates are shown with solid/dashed lines for each panel [false discovery rate (FDR) < 0.05]. See Additional file 13: Figure S13 for detailed results