Evolutionary rescue can prevent rate-induced tipping in predator-prey systems

Nowadays, populations are faced with unprecedented rates of global climate change, habitat fragmentation and destruction causing an accelerating conversion of their living conditions. Critical transitions in ecosystems, often called regime shifts, lead to sudden shifts in the dominance of species or even to species’ extinction and decline of biodiversity. Many regime shifts are explained as transitions between alternative stable states caused by (i) certain bifurcations when certain parameters or external forcing cross critical thresholds, (ii) fluctuations or (iii) extreme events. We address a fourth mechanism which does not require alternative states but instead, the system performs a large excursion away from its usual behaviour when environmental  conditions change too fast. During this excursion, the system can embrace dangerously, unexpected states. We demonstrate that predator-prey systems can exhibit a population collapse if the rate of environmental change crosses a certain critical rate. In reference to this critical rate of change which has to be surpassed, this transition is called rate-induced tipping (R-tipping). A further difference to the other three tipping mechanisms is that R-tipping mainly manifests during the transient dynamics – the dynamics before the long-term dynamics are reached.  Whether a system will track its usual state or will tip with the consequence of a possible extinction of a species depends crucially on the time scale relations between the ecological timescale and the time scale of environmental change as well as the initial condition. However, populations have the ability to respond to environmental change due to rapid evolution. Employing an eco-evolutionary model we show how such kind of adaptation can prevent rate-induced tipping in predator-prey systems. The corresponding mechanism, called evolutionary rescue, introduces a third timescale which needs to be taken into account. Only a large genetic variation within a population reflecting rapid evolution would be able to successfully counteract an overcritically fast environmental change.