Tracking unstable states: ecosystem dynamics in a changing world

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.

Stoichiometry and environmental change drive dynamical complexity and unpredictable switches in an intraguild predation model

We incorporate stoichiometry (the balance of key elements) into an intraguild predation (IGP) model. Theoretical and numerical results show that our system exhibits complex dynamics, including chaos and multiple types of both bifurcations and bistability. Types of bifurcation present include saddle-node, Hopf, and transcritical bifurcations, and types of bistability present include node-node, node-cycle, and cycle-cycle bistability; cycle-cycle bistability has never been observed in IGP ordinary differential equation models. Stoichiometry can stabilize or destabilize the system via the disappearance or appearance of chaos. The species represented in the model can coexist for moderate levels of light intensity and nutrient availability. When the amount of light or nutrients present is extremely high or low, coexistence of the species becomes impossible, potentially harming biodiversity. Interestingly, stoichiometry can facilitate the re-emergence of severely endangered species as light intensity increases. In a temporally changing environment, the system can jump between different unstable states following changes in light intensity, with the trajectory followed depending strongly on initial conditions.

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.

Two classes of functional connectivity in dynamical processes in networks

The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines-from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity-one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes-excitations, regular and chaotic oscillators-and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.

Metacommunity persistence to environmental change: Stabilizing and destabilizing effects of individual species dispersal

Ecological communities face a high risk of extinction to climate change which can destabilize ecological systems. In the face of accelerating environmental change, understanding the factors and the mechanisms that stabilize the ecological communities is a central focus in ecology. Although dispersal has been widely used as an important stabilizing process, it remains unclear how individual species dispersal affects the stability and persistence of an ecological community. In this study, using a spatially coupled predator-prey community, we address the effects of individual species dispersal and nutrient enrichment on metacommunity stability in constant and varying environments. We show two contrasting effects of dispersal on metacommunity persistence in temporally constant and varying environments. Specifically, predator dispersal in constant environments shows stronger stability through inhomogeneous (asynchronized) states, whereas prey dispersal shows an increasing extinction risk through a homogeneous (synchronized) state. On the contrary, the metacommunity dynamics in temporally varying environments reveal that predator dispersal causes a local extinction through tracking unstable states and also a delayed shift between dynamical states. Moreover, our results emphasize that metacommunity persistence depends on individual species dispersal and environmental variations. Thus, our findings of the individual species dispersal can help to develop conservation measures that are tailored to varying environmental conditions.