Persistence and extinction dynamics driven by the rate of environmental change in a predator–prey metacommunity

Early warning indicators capture catastrophic transitions driven by explicit rates of environmental change

In response to external changes, ecosystems can undergo catastrophic transitions. Early warning indicators aim to predict such transitions based on the phenomenon of critical slowing down at bifurcation points found under a constant environment. When an explicit rate of environmental change is considered, catastrophic transitions can become distinct phenomena from bifurcations, and result from a delayed response to noncatastrophic bifurcations. We use a trophic metacommunity model where transitions in time series and bifurcations of the system are distinct phenomena. We calculate early warning indicators from the time series of the continually changing system and show that they predict not the bifurcation of the underlying system but the actual catastrophic transition driven by the explicit rate of change. Predictions based on the bifurcation structure could miss catastrophic transitions that can still be captured by early warning signals calculated from time series. Our results expand the repertoire of mechanistic models used to anticipate catastrophic transitions to nonequilibrium ecological systems exposed to a constant rate of environmental change.

An SIRS model with nonmonotone incidence and saturated treatment in a changing environment

Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values [Formula: see text] and [Formula: see text] for the treatment rate r: (i) when [Formula: see text], the disease will disappear; (ii) when [Formula: see text], the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when [Formula: see text] predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change.

Evolutionary rescue can prevent rate-induced tipping

The transformation of ecosystems proceeds at unprecedented rates. Recent studies suggest that high rates of environmental change can cause rate-induced tipping. In ecological models, the associated rate-induced critical transition manifests during transient dynamics in which populations drop to dangerously low densities. In this work, we study how indirect evolutionary rescue—due to the rapid evolution of a predator’s trait—can save a prey population from the rate-induced collapse. Therefore, we explicitly include the time-dependent dynamics of environmental change and evolutionary adaptation in an eco-evolutionary system. We then examine how fast the evolutionary adaptation needs to be to counteract the response to environmental degradation and express this relationship by means of a critical rate. Based on this critical rate, we conclude that indirect evolutionary rescue is more probable if the predator population possesses a high genetic variation and, simultaneously, the environmental change is slow. Hence, our results strongly emphasize that the maintenance of biodiversity requires a deceleration of the anthropogenic degradation of natural habitats.