Synchronization and entrainment of metapopulations: A trade-off among time-induced heterogeneity, dispersal, and seasonal force

Stability of ecosystems under oscillatory driving with frequency modulation

Consumer-resource cycles are widespread in ecosystems, and seasonal forcing is known to influence them profoundly. Typically, seasonal forcing perturbs an ecosystem with time-varying frequency; however, previous studies have explored the dynamics of such systems under oscillatory forcing with constant frequency. Studies of the effect of time-varying frequency on ecosystem stability are lacking. Here we investigate isolated and network models of a cyclic consumer-resource ecosystem with oscillatory driving subjected to frequency modulation. We show that frequency modulation can induce stability in the system in the form of stable synchronized solutions, depending on intrinsic model parameters and extrinsic modulation strength. The stability of synchronous solutions is determined by calculating the maximal Lyapunov exponent, which determines that the fraction of stable synchronous solution increases with an increase in the modulation strength. We also uncover intermittent synchronization when synchronous dynamics are intermingled with episodes of asynchronous dynamics. Using the phase-reduction method for the network model, we reduce the system into a phase equation that clearly distinguishes synchronous, intermittently synchronous, and asynchronous solutions. While investigating the role of network topology, we find that variation in rewiring probability has a negligible effect on the stability of synchronous solutions. This study deepens our understanding of ecosystems under seasonal perturbations.

Effects of time-varying habitat connectivity on metacommunity persistence

Network structure or connectivity patterns are critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure, though most real network structures change in time, forming time-varying networks. This raises the question, in metacommunities, how does the pattern of synchrony vary with temporal evolution in the network structure. The synchronous dynamics among species are known to reduce metacommunity persistence. Here we consider a time-varying metacommunity small-world network consisting of a chaotic three-species food chain oscillator in each patch or node. The rate of change in the network connectivity is determined by the natural frequency or its subharmonics of the constituent oscillator to allow sufficient time for the evolution of species in between successive rewirings. We find that over a range of coupling strengths and rewiring periods, even higher rewiring probabilities drive a network from asynchrony towards synchrony. Moreover, in networks with a small rewiring period, an increase in average degree (more connected networks) pushes the asynchronous dynamics to synchrony. On the other hand, in networks with a low average degree, a higher rewiring period drives the synchronous dynamics to asynchrony resulting in increased species persistence. Our results also follow the calculation of synchronization time and are robust across other ecosystem models. Overall, our study opens the possibility of developing temporal connectivity strategies to increase species persistence in ecological networks.

Role of limiting dispersal on metacommunity stability and persistence

The role of dispersal on the stability and synchrony of a metacommunity is a topic of considerable interest in theoretical ecology. Dispersal is known to promote both synchrony, which enhances the likelihood of extinction, and spatial heterogeneity, which favors the persistence of the population. Several efforts have been made to understand the effect of diverse variants of dispersal in the spatially distributed ecological community. Despite that environmental change strongly affects the dispersal, the effects of controlled dispersal on the metacommunity stability and their persistence remain unknown. We study the influence of limiting the immigration using two-patch prey-predator metacommunity at both local and spatial scales. We find that the spread of the inhomogeneous stable steady states (asynchronous states) decreases monotonically upon limiting the predator dispersal. Nevertheless, at the local scale, the spread of the inhomogeneous steady states increases up to a critical value of the limiting factor, favoring the metacommunity persistence, and then starts decreasing for a further decrease in the limiting factor with varying local interaction. Interestingly, limiting the prey dispersal promotes inhomogeneous steady states in a large region of the parameter space, thereby increasing the metacommunity persistence at both spatial and local scales. Further, we show similar qualitative dynamics in an entire class of complex networks consisting of a large number of patches. We also deduce various bifurcation curves and stability conditions for the inhomogeneous steady states, which we find to agree well with the simulation results. Thus, our findings on the effect of the limiting dispersal can help to develop conservation measures for ecological communities.

Synchronization within synchronization: transients and intermittency in ecological networks

Transients are fundamental to ecological systems with significant implications to management, conservation and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator–prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e. synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry—henceforth the phenomenon of  ‘synchronization within synchronization.’ Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.

Dynamic environment-induced multistability and critical transition in a metacommunity ecosystem

We study a metacommunity model of consumer-resource populations coupled via dispersal under an environment-dependent framework, and we explore the occurrence of multistability and critical transition. By emphasizing two magnitudes acting on a dynamic environment at temporal and spatial scales, the coupled system with simple diffusive coupling and the nonlinear environmental coupling enables various interesting complex dynamics such as bistability, multistability, and critical transitions. Using the basin stability measure, we find the probability of attaining each alternative state in a multistable region. In addition, critical transitions (one from a high to a low species density and the other from a low to a high species density) are identified at different magnitudes in the presence of stochastic fluctuations. We also explore the robustness of critical slowing-down indicators, e.g., lag-1 autocorrelation and variance, to forewarn the critical transition in the metacommunity model. Further, a network structure also identifies synchronization and multiclustering for a different choice of initial conditions. In contrast with the earlier studies on dynamic environmental coupling, our results based on the defined magnitudes provide important insights into environmental heterogeneity, which determines the set of environmental conditions to predict metacommunity stability and persistence.