Landscape quantifies the intermediate state and transition dynamics in ecological networks
Fig 5
Barrier height serves as a new EWS to predict collapse.
(A and B) The process of system collapse (A) and recovery (B) is simulated from the Langevin equation. We present two-dimensional landscape, in which the same coordinates are used to ensure comparability. The left arrow indicates the proportion of each state (H: blue, I: green, L: gold). The transitions between attractors are marked by thick arrows. (C) Calculated RBH between low and intermediate states with increasing κ. We regard the point as an EWS when the BDS statistic for the sequence up to this point is significant (blue: p<0.05, gold: p<0.01, red: p<0.001). (D) For complete collapse to the low state, the RBH can serve as the earliest warning signal compared with other metrics based on time series, such as AR(1), variance (Var), coefficient of variation (CV) and fano factor (fano). The color in RBH has the same meaning as (C), indicating the predicted critical κ value based on different p-values.