Increased persistence via asynchrony in oscillating ecological populations with long-range interaction

Patterns of neuronal synchrony in higher-order networks

Synchrony in neuronal networks is crucial for cognitive functions, motor coordination, and various neurological disorders. While traditional research has focused on pairwise interactions between neurons, recent studies highlight the importance of higher-order interactions involving multiple neurons. Both types of interactions lead to complex synchronous spatiotemporal patterns, including the fascinating phenomenon of chimera states, where synchronized and desynchronized neuronal activity coexist. These patterns are thought to resemble pathological states such as schizophrenia and Parkinson's disease, and their emergence is influenced by neuronal dynamics as well as by synaptic connections and network structure. This review integrates the current understanding of how pairwise and higher-order interactions contribute to different synchrony patterns in neuronal networks, providing a comprehensive overview of their role in shaping network dynamics. We explore a broad range of connectivity mechanisms that drive diverse neuronal synchrony patterns, from pairwise long-range temporal interactions and time-delayed coupling to adaptive communication and higher-order, time-varying connections. We cover key neuronal models, including the Hindmarsh-Rose model, the stochastic Hodgkin-Huxley model, the Sherman model, and the photosensitive FitzHugh-Nagumo model. By investigating the emergence and stability of various synchronous states, this review highlights their significance in neurological systems and indicates directions for future research in this rapidly evolving field.

Transient chaos and memory effect in the Rosenzweig-MacArthur system with dynamics of consumption rates

We consider the system of the Rosenzweig-MacArthur equations with one consumer and two resources. Recently, the model has been generalized by including an optimization of the consumption rates β_{i} [P. Gawroński et al., Chaos 32, 093121 (2022)1054-150010.1063/5.0105340]. Also, we have assumed that β_{1}+β_{2}=1, which reflects the limited amount of time that can be devoted to a given type of resource. Here we investigate the transition to the phase where one of the resources becomes extinct. The goal is to show that the stability of the phase with two resources strongly depends on the initial value of β_{i}. Our second goal is to demonstrate signatures of transient chaos in the time evolution.

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.

Noise-induced symmetry breaking in a network of excitable ecological systems

Noise-induced symmetry breaking has barely been unveiled on the ecological grounds, though its occurrence may elucidate mechanisms responsible for maintaining biodiversity and ecosystem stability. Here, for a network of excitable consumer-resource systems, we show that the interplay of network structure and noise intensity manifests a transition from homogeneous steady states to inhomogeneous steady states, resulting in noise-induced symmetry breaking. On further increasing the noise intensity, there exist asynchronous oscillations, leading to heterogeneity crucial for maintaining a system's adaptive capacity. The observed collective dynamics can be understood analytically in the framework of linear stability analysis of the corresponding deterministic system.

Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources

The system of two resources _R and _R and one consumer C is investigated within the Rosenzweig-MacArthur model with a Holling type II functional response. The rates of consumption of particular resources are normalized as to keep their sum constant. Dynamic switching is introduced as to increase the variable C in a process of finite speed. The space of parameters where both resources coexist is explored numerically. The results indicate that oscillations of C and mutually synchronized _R, which appear equal for the rates of consumption, are destabilized when these rates are modified. Then, the system is driven to one of fixed points or to a limit cycle with a much smaller amplitude. As a consequence of symmetry between the resources, the consumer cannot change the preferred resource once it is chosen.

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.

Foraging behaviour and patch size distribution jointly determine population dynamics in fragmented landscapes

Increased fragmentation caused by habitat loss represents a major threat to the persistence of animal populations. How fragmentation affects populations depends on the rate at which individuals move between spatially separated patches. Whereas negative effects of habitat loss on biodiversity are well known, the effects of fragmentation per se on population dynamics and ecosystem stability remain less well understood. Here, we use a spatially explicit predator-prey model to investigate how the interplay between fragmentation and optimal foraging behaviour affects predator-prey interactions and, subsequently, ecosystem stability. We study systems wherein prey occupies isolated patches and are consumed by predators that disperse following Lévy random walks. Our results show that the Lévy exponent and the degree of fragmentation jointly determine coexistence probabilities. In highly fragmented landscapes, Brownian and ballistic predators go extinct and only scale-free predators can coexist with prey. Furthermore, our results confirm that predation causes irreversible habitat loss in fragmented landscapes owing to overexploitation of smaller patches of prey. Moreover, we show that predator dispersal can reduce, but not prevent or minimize, the amount of lost habitat. Our results suggest that integrating optimal foraging theory into population and landscape ecology is crucial to assessing the impact of fragmentation on biodiversity and ecosystem stability.

Dynamical robustness of complex networks subject to long-range connectivity

In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the concept of long-range interactions among the dynamical units of complex networks and demonstrate for the first time that such a characteristic can have noteworthy impacts on the dynamical robustness of networked systems, regardless of the underlying network topology. We present a comprehensive analysis of this phenomenon on top of diverse network architectures. Such dynamical damages being able to substantially affect the network performance, determining mechanisms that boost the robustness of networks becomes a fundamental question. In this work, we put forward a prescription based upon self-feedback that can efficiently resurrect global rhythmicity of complex networks composed of active and inactive dynamical units, and thus can enhance the network robustness. We have been able to delineate the whole proposition analytically while dealing with all d -path adjacency matrices, having an excellent agreement with the numerical results. For the numerical computations, we examine scale-free networks, Watts–Strogatz small-world model and also Erdös–Rényi random network, along with Landau–Stuart oscillators for casting the local dynamics.

Neuronal synchronization in long-range time-varying networks

We study synchronization in neuronal ensembles subject to long-range electrical gap junctions which are time-varying. As a representative example, we consider Hindmarsh-Rose neurons interacting based upon temporal long-range connections through electrical couplings. In particular, we adopt the connections associated with the direct 1-path network to form a small-world network and follow-up with the corresponding long-range network. Further, the underlying direct small-world network is allowed to temporally change; hence, all long-range connections are also temporal, which makes the model much more realistic from the neurological perspective. This time-varying long-range network is formed by rewiring each link of the underlying 1-path network stochastically with a characteristic rewiring probability p_r, and accordingly all indirect k(>1)-path networks become temporal. The critical interaction strength to reach complete neuronal synchrony is much lower when we take up rapidly switching long-range interactions. We employ the master stability function formalism in order to characterize the local stability of the state of synchronization. The analytically derived stability condition for the complete synchrony state agrees well with the numerical results. Our work strengthens the understanding of time-varying long-range interactions in neuronal ensembles.

Long-range dispersal promotes species persistence in climate extremes

Anthropogenic global warming in this century can act as a leading factor for large scale species extinctions in the near future. Species, in order to survive, need to develop dispersal strategies depending upon their environmental niche. Based on empirical evidence only a few previous studies have addressed how dispersal can evolve with changing temperature. However, for the analytical tractability, there is a need to develop an explicit model to ask how the temperature-dependent dispersal alters ecological dynamics. We investigate the persistence of species in a spatial ecological model, where dispersal is considered as a function of temperature. Spatial persistence is of major concern and dispersal is reasonably an important factor for extinction risk in the context of promoting synchrony. Our study yields how the temperature influences species decision of dispersal, resulting in either short-range or long-range dispersal. We examine synchronous or asynchronous behavior of species under their thermal dependence of dispersal. Moreover, we also analyze the transients to study the collective behavior of species away from their final or asymptotic dynamics. One of the key findings is at the most unfavorable environmental conditions long-range dispersal works out as the driving force for the persistence of species.

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.

Occasional long distance dispersal increases spatial synchrony of population cycles

Spatially separated populations of the same species often exhibit correlated fluctuations in abundance, a phenomenon known as spatial synchrony. Dispersal can generate spatial synchrony. In nature, most individuals disperse short distances with a minority dispersing long distances. The effect of occasional long distance dispersal on synchrony is untested, and theoretical predictions are contradictory. Occasional long distance dispersal might either increase both overall synchrony and the spatial scale of synchrony, or reduce them. We conducted a protist microcosm experiment to test whether occasional long distance dispersal increases or decreases overall synchrony and the spatial scale of synchrony. We assembled replicate 15-patch ring metapopulations of the protist predator Euplotes patella and its protist prey Tetrahymena pyriformis. All metapopulations experienced the same dispersal rate, but differed in dispersal distance. Some metapopulations experienced strictly short distance (nearest neighbour) dispersal, others experienced a mixture of short- and long distance dispersal. Occasional long distance dispersal increased overall spatial synchrony and the spatial scale of synchrony for both prey and predators, though the effects were not statistically significant for predators. As predicted by theory, dispersal generated spatial synchrony by entraining the phases of the predator-prey cycles in different patches, a phenomenon known as phase locking. Our results are consistent with theoretical models predicting that occasional long distance dispersal increases spatial synchrony. However, our results also illustrate that the spatial scale of synchrony need not match the spatial scale of the processes generating synchrony. Even strictly short distance dispersal maintained high spatial synchrony for many generations at spatial scales much longer than the dispersal distance, thanks to phase locking.

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

Demographic and environmental heterogeneities are prevalent across many natural systems. Earlier studies on metapopulation models have mostly considered heterogeneities either in the demographic parameters or in the interaction strength and topology between the spatially separated patches. In contrast, here we study the dynamics of a metapopulation model where each of the uncoupled patches has different periods of oscillations (period mismatch). We show different synchronization dynamics governed by both period mismatch and dispersal in neighboring patches. Indeed, we find both appearance and disappearance of phase synchronization, quasiperiodic oscillations, and period doubling of limit cycle. We also quantify the effect of seasonal variation (entrainment) and dispersal on species synchrony using phase-response curve and a synchrony measure, which thereof identify the influence of stochasticity on species persistence through trade-off mechanisms. Our results show that trade-offs among period mismatch, dispersal, and external force can drive entrained oscillations as well as asynchronous population dynamics that structure ecological communities.

Lévy flight movements prevent extinctions and maximize population abundances in fragile Lotka-Volterra systems

Multiple-scale mobility is ubiquitous in nature and has become instrumental for understanding and modeling animal foraging behavior. However, the impact of individual movements on the long-term stability of populations remains largely unexplored. We analyze deterministic and stochastic Lotka-Volterra systems, where mobile predators consume scarce resources (prey) confined in patches. In fragile systems (that is, those unfavorable to species coexistence), the predator species has a maximized abundance and is resilient to degraded prey conditions when individual mobility is multiple scaled. Within the Lévy flight model, highly superdiffusive foragers rarely encounter prey patches and go extinct, whereas normally diffusing foragers tend to proliferate within patches, causing extinctions by overexploitation. Lévy flights of intermediate index allow a sustainable balance between patch exploitation and regeneration over wide ranges of demographic rates. Our analytical and simulated results can explain field observations and suggest that scale-free random movements are an important mechanism by which entire populations adapt to scarcity in fragmented ecosystems.

Survivability of a metapopulation under local extinctions

A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability (in the form of global oscillation) of a metapopulation on top of diverse dispersal topologies extremely crucial. However, among various dispersal topologies in ecological networks, which one can provide higher metapopulation survivability under local extinction is still not well explored. In this article, we scrutinize the robustness of an ecological network consisting of prey-predator patches having Holling type I functional response, against progressively extinct population patches. We present a comprehensive study on this while considering global, small-world, and scale-free dispersal of the subpopulations. Furthermore, we extend our work in enhancing survivability in the form of sustained global oscillation by introducing asymmetries in the dispersal rates of the considered species. Our findings affirm that the asynchrony among the patches plays an important role in the survivability of a metapopulation. In order to demonstrate the model independence of the observed phenomenon, we perform a similar analysis for patches exhibiting Holling type II functional response. On the grounds of the obtained results, our work is expected to provide a better perception of the influence of dispersal arrangements on the global survivability of ecological networks.