Extended Data Fig. 2: Chaotic dynamics in relation to predictability and monotonic trend.

(a) Proportion of time series classified as chaotic using the Jacobian method and (b) values of the Lyapunov exponent (LE) in relation to leave-one-out prediction R² for abundance. (c) Proportion of time series classified as chaotic using the Jacobian method and (d) values of the LE in relation to monotonic trend, as measured by the squared Spearman rank correlation coefficient. In (A) and (C), the line is a logistic regression, associated band is the 95% confidence interval, and points are vertically jittered to reduce overlap. Point colour indicates taxonomic group.