Ecosystems off track: rate-induced critical transitions in ecological models

Siteur et al. provide a relatively thorough description of a particular type of critical transition in ecology: those that are rate-induced. A classical state-based or threshold-based critical transition occurs when a state variable of one part of an ecological model/system shifts enough to eliminate a previously stable basin of attraction resulting in a shift in the equilibrial state of the system. A focus on this type of critical-transition relies on an assumption that one component of the system (the slow component) changes sufficiently more slowly than the fast component to treat it as constant during fast dynamics. Humans are, however, significantly increasing the rate of change of environmental processes, particularly climate, which have previously been considered sufficiently slow to satisfy the assumption of a constant value for most ecological dynamics. The authors use a simulation to show that as the rate of change of the slow system increases the fast state variable tends to lag behind the stable steady state dynamics at a given value of the slow system. The value of this lag can be calculated analytically under a relatively narrow set of circumstances (if the lag depends only on the rate of change in the slow system and not the actual current state of the system). Their simulation also shows that at a certain rate of change in the slow system the fast system becomes unstable and decays to zero, representing a critical transition away from the steady-state equilibrium to the alternative stable state of zero. They proceed to demonstrate how to determine this “critical rate of change” using both analytical and graphical approaches. They again provide the caveat that these tools only apply to systems with a single fast state-variable and even then do not necessarily precisely replicate the critical rate of change that can be recovered from model simulations. This paper offers a clear overview of this particular type of critical transition and makes a convincing argument for how easily they occur in ecological models and how relevant this problem is to our rapidly changing world. Their rationale for prescriptions for human development on the basis of critical rates as well as critical levels seems sound. It would be interesting to see some clear empirical systems demonstrating these dynamics though they suggest that these might be relatively difficult to identify.

Siteur, Koen, et al. “Ecosystems off track: rate‐induced critical transitions in ecological models.” Oikos 125.12 (2016): 1689-1699.