Fig. 1: Overview of the possible transient system dynamics in the absence of a stable equilibrium point.

The transient dynamics of the human consumer-renewable resource system exhibit either overshoot and collapse dynamics (case I; a, b), or overshoot and crumble dynamics (case II; c, d). a State space portrait showing the population isoclines and resource isocline of a system exhibiting overshoot and collapse dynamics. For this system, the slope of the crumbling trajectory is negative, and therefore not appearing in the positive quadrant of the state space. b Temporal dynamics of overshoot and collapse scenario. c State space portrait showing the population isoclines and resource isocline of a system exhibiting overshoot and crumble dynamics. For this system, the slope of the crumbling trajectory is larger than the slope of the population isocline, facilitating the crumbling dynamics. d Temporal dynamics of overshoot and crumble scenario. Here, the baseline model system is shown, but dynamics are similar for the extended model (Supplementary Fig. 1). Parameter values: Overshoot and collapse: c = 0.0022 year⁻¹, h = 0.0088 individual⁻¹  year⁻¹; Overshoot and crumble: c = 0.0131 year⁻¹, h = 0.0088 individual⁻¹ year⁻¹; other parameters as in Table 1.