Figure 1

A schematic illustration of early ecosystem collapse induced by period-doubling route to chaos in seasonally forced systems. Items in blue color represent the prevailing paradigm of ecosystem collapse across a tipping point, and the narrow range of critical slowing down that precedes the collapse in which existing early-warning signals apply. Items in red represent generic dynamical behaviors of seasonally forced systems. They include a cascade of period-doubling bifurcations, chaotic dynamics and early ecosystem collapse. The label P_SN represents a threshold of an environmental parameter, such as precipitation, at which the functional state that describes resonant oscillations ceases to exist, the label P_PD represents the threshold at which the oscillation period of the functional state doubles, and the label P_C represents the threshold at which collapse to a dysfunctional state occurs.