Phase-locking and environmental fluctuations generate synchrony in a predator-prey community

Insights Into Spatial Synchrony Enabled by Long-Term Data

Spatial synchrony, the tendency for temporal fluctuations in an ecological variable to be positively associated in different locations, is a widespread and important phenomenon in ecology. Understanding of the nature and mechanisms of synchrony, and how synchrony is changing, has developed rapidly over the past 2 decades. Many recent developments have taken place through the study of long-term data sets. Here, we review and synthesise some important recent advances in spatial synchrony, with a focus on how long-term data have facilitated new understanding. Longer time series do not just facilitate better testing of existing ideas or more precise statistical results; more importantly, they also frequently make possible the expansion of conceptual paradigms. We discuss several such advances in our understanding of synchrony, how long-term data led to these advances, and how future studies can continue to improve the state of knowledge.

Metapopulations, the Inflationary Effect, and Consequences for Public Health

AbstractThe metapopulation concept offers significant explanatory power in ecology and evolutionary biology. Metapopulations, a set of spatially distributed populations linked by dispersal, and their community and ecosystem level analogs, metacommunity and meta-ecosystem models, tend to be more stable regionally than locally. This fact is largely attributable to the interplay of spatiotemporal heterogeneity and dispersal (the inflationary effect). We highlight this underappreciated (but essential) role of spatiotemporal heterogeneity in metapopulation biology, present a novel expression for quantifying and defining the inflationary effect, and provide a mechanistic interpretation of how it arises and impacts population growth and abundance. We illustrate the effect with examples from infectious disease dynamics, including the hypothesis that policy decisions made during the COVID-19 pandemic generated spatiotemporal heterogeneity that enhanced the spread of disease. We finish by noting how spatiotemporal heterogeneity generates emergent population processes at large scales across many topics in the history of ecology, as diverse as natural enemy-victim dynamics, species coexistence, and conservation biology. Embracing the complexity of spatiotemporal heterogeneity is vital for future research on the persistence of populations.

Long-living transients in ecological models: Recent progress, new challenges, and open questions

Traditionally, mathematical models in ecology placed an emphasis on asymptotic, long-term dynamics. However, a large number of recent studies highlighted the importance of transient dynamics in ecological and eco-evolutionary systems, in particular 'long transients' that can last for hundreds of generations or even longer. Many models as well as empirical studies indicated that a system can function for a long time in a certain state or regime (a 'metastable regime') but later exhibits an abrupt transition to another regime not preceded by any parameter change (or following the change that occurred long before the transition). This scenario where tipping occurs without any apparent source of a regime shift is also referred to as 'metastability'. Despite considerable evidence of the presence of long transients in real-world systems as well as models, until recently research into long-living transients in ecology has remained in its infancy, largely lacking systematisation. Within the past decade, however, substantial progress has been made in creating a unifying theory of long transients in deterministic as well as stochastic systems. This has considerably accelerated further studies on long transients, in particular on those characterised by more complicated patterns and/or underlying mechanisms. The main goal of this review is to provide an overview of recent research on long transients and related regime shifts in models of ecological dynamics. We pay special attention to the role of environmental stochasticity, the effect of multiple timescales (slow-fast systems), transient spatial patterns, and relation between transients and spatial synchronisation. We also discuss current challenges and open questions in understanding transients with applications to ecosystems dynamics.

Mohamad M, Myers JA, Nathalang A, Pérez ÁJ, Phumsathan S, Pongpattananurak N, Ren H, Rodriguez LJV, Sukumar R, Sun IF, Suresh HS, Thomas DW, Thompson J, Uriarte M, Valencia R, Wang X, Wolf AT, Zimmerman JK. Assessing the spatial scale of synchrony in forest tree population dynamics

Populations of forest trees exhibit large temporal fluctuations, but little is known about the synchrony of these fluctuations across space, including their sign, magnitude, causes and characteristic scales. These have important implications for metapopulation persistence and theoretical community ecology. Using data from permanent forest plots spanning local, regional and global spatial scales, we measured spatial synchrony in tree population growth rates over sub-decadal and decadal timescales and explored the relationship of synchrony to geographical distance. Synchrony was high at local scales of less than 1 km, with estimated Pearson correlations of approximately 0.6-0.8 between species' population growth rates across pairs of quadrats. Synchrony decayed by approximately 17-44% with each order of magnitude increase in distance but was still detectably positive at distances of 100 km and beyond. Dispersal cannot explain observed large-scale synchrony because typical seed dispersal distances (<100 m) are far too short to couple the dynamics of distant forests on decadal timescales. We attribute the observed synchrony in forest dynamics primarily to the effect of spatially synchronous environmental drivers (the Moran effect), in particular climate, although pests, pathogens and anthropogenic drivers may play a role for some species.

Dispersal evolution and eco-evolutionary dynamics in antagonistic species interactions

Dispersal evolution modifies diverse spatial processes, such as range expansions or biological invasions of single species, but we are currently lacking a realistic vision for metacommunities. Focusing on antagonistic species interactions, we review existing theory of dispersal evolution between natural enemies, and explain how this might be relevant for classic themes in host-parasite evolutionary ecology, namely virulence evolution or local adaptation. Specifically, we highlight the importance of considering the simultaneous (co)evolution of dispersal and interaction traits. Linking such multi-trait evolution with reciprocal demographic and epidemiological feedbacks might change basic predictions about coevolutionary processes and spatial dynamics of interacting species. Future challenges concern the integration of system-specific disease ecology or spatial modifiers, such as spatial network structure or environmental heterogeneity.

Dispersal synchronizes giant kelp forests

Spatial synchrony is the tendency for population fluctuations to be correlated among different locations. This phenomenon is a ubiquitous feature of population dynamics and is important for ecosystem stability, but several aspects of synchrony remain unresolved. In particular, the extent to which any particular mechanism, such as dispersal, contributes to observed synchrony in natural populations has been difficult to determine. To address this gap, we leveraged recent methodological improvements to determine how dispersal structures synchrony in giant kelp (Macrocystis pyrifera), a global marine foundation species that has served as a useful system for understanding synchrony. We quantified population synchrony and fecundity with satellite imagery across 11 years and 880 km of coastline in southern California, USA, and estimated propagule dispersal probabilities using a high-resolution ocean circulation model. Using matrix regression models that control for the influence of geographic distance, resources (seawater nitrate), and disturbance (destructive waves), we discovered that dispersal was an important driver of synchrony. Our findings were robust to assumptions about propagule mortality during dispersal and consistent between two metrics of dispersal: (1) the individual probability of dispersal and (2) estimates of demographic connectivity that incorporate fecundity (the number of propagules dispersing). We also found that dispersal and environmental conditions resulted in geographic clusters with distinct patterns of synchrony. This study is among the few to statistically associate synchrony with dispersal in a natural population and the first to do so in a marine organism. The synchronizing effects of dispersal and environmental conditions on foundation species, such as giant kelp, likely have cascading effects on the spatial stability of biodiversity and ecosystem function.

Understanding temporal variability across trophic levels and spatial scales in freshwater ecosystems

A tenet of ecology is that temporal variability in ecological structure and processes tends to decrease with increasing spatial scales (from locales to regions) and levels of biological organization (from populations to communities). However, patterns in temporal variability across trophic levels and the mechanisms that produce them remain poorly understood. Here we analyzed the abundance time series of spatially structured communities (i.e., metacommunities) spanning basal resources to top predators from 355 freshwater sites across three continents. Specifically, we used a hierarchical partitioning method to disentangle the propagation of temporal variability in abundance across spatial scales and trophic levels. We then used structural equation modeling to determine if the strength and direction of relationships between temporal variability, synchrony, biodiversity, and environmental and spatial settings depended on trophic level and spatial scale. We found that temporal variability in abundance decreased from producers to tertiary consumers but did so mainly at the local scale. Species population synchrony within sites increased with trophic level, whereas synchrony among communities decreased. At the local scale, temporal variability in precipitation and species diversity were associated with population variability (linear partial coefficient, β = 0.23) and population synchrony (β = -0.39) similarly across trophic levels, respectively. At the regional scale, community synchrony was not related to climatic or spatial predictors, but the strength of relationships between metacommunity variability and community synchrony decreased systematically from top predators (β = 0.73) to secondary consumers (β = 0.54), to primary consumers (β = 0.30) to producers (β = 0). Our results suggest that mobile predators may often stabilize metacommunities by buffering variability that originates at the base of food webs. This finding illustrates that the trophic structure of metacommunities, which integrates variation in organismal body size and its correlates, should be considered when investigating ecological stability in natural systems. More broadly, our work advances the notion that temporal stability is an emergent property of ecosystems that may be threatened in complex ways by biodiversity loss and habitat fragmentation.

Spatial heterogeneity of biomass turnover has contrasting effects on synchrony and stability in trophic metacommunities

Spatial heterogeneity is a fundamental feature of ecosystems, and ecologists have identified it as a factor promoting the stability of population dynamics. In particular, differences in interaction strengths and resource supply between patches generate an asymmetry of biomass turnover with a fast and a slow patch coupled by a mobile predator. Here, we demonstrate that asymmetry leads to opposite stability patterns in metacommunities receiving localized perturbations depending on the characteristics of the perturbed patch. Perturbing prey in the fast patch synchronizes the dynamics of prey biomass between the two patches and destabilizes predator dynamics by increasing the predator's temporal variability. Conversely, perturbing prey in the slow patch decreases the synchrony of the prey's dynamics and stabilizes predator dynamics. Our results have implications for conservation ecology and suggest reinforcing protection policies in fast patches to dampen the effects of perturbations and promote the stability of population dynamics at the regional scale.

Niche Modification by Sulfate-Reducing Bacteria Drives Microbial Community Assembly in Anoxic Marine Sediments

Sulfate-reducing bacteria (SRB) are essential functional microbial taxa for degrading organic matter (OM) in anoxic marine environments. However, there are little experimental data regarding how SRB regulates microbial communities. Here, we applied a top-down microbial community management approach by inhibiting SRB to elucidate their contributions to the microbial community during OM degradation. Based on the highly replicated microcosms (n = 20) of five different incubation stages, we found that many microbial community properties were influenced after inhibiting SRB, including the composition, structure, network, and community assembly processes. We also found a strong coexistence pattern between SRB and other abundant phylogenetic lineages via positive frequency-dependent selection. The relative abundances of the families Synergistaceae, Peptostreptococcaceae, Dethiosulfatibacteraceae, Prolixibacteraceae, Marinilabiliaceae, and Marinifilaceae were simultaneously suppressed after inhibiting SRB during OM degradation. A close association between SRB and the order Marinilabiliales among coexisting taxa was most prominent. They contributed to preserved modules during network successions, were keystone nodes mediating the networked community, and contributed to homogeneous ecological selection. The molybdate tolerance test of the isolated strains of Marinilabiliales showed that inhibited SRB (not the inhibitor of SRB itself) triggered a decrease in the relative abundance of Marinilabiliales. We also found that inhibiting SRB resulted in reduced pH, which is unsuitable for the growth of most Marinilabiliales strains, while the addition of pH buffer (HEPES) in SRB-inhibited treatment microcosms restored the pH and the relative abundances of these bacteria. These data supported that SRB could modify niches to affect species coexistence. IMPORTANCE Our model offers insight into the ecological properties of SRB and identifies a previously undocumented dimension of OM degradation. This targeted inhibition approach could provide a novel framework for illustrating how functional microbial taxa associate the composition and structure of the microbial community, molecular ecological network, and community assembly processes. These findings emphasize the importance of SRB during OM degradation. Our results proved the feasibility of the proposed study framework, inhibiting functional taxa at the community level, for illustrating when and to what extent functional taxa can contribute to ecosystem services.

Individual species and site dynamics are the main drivers of spatial scaling of stability in aquatic communities

Introduction

Any measure of ecological stability scales with the spatial and temporal extent of the data on which it is based. The magnitude of stabilization effects at increasing spatial scale is determined by the degree of synchrony between local and regional species populations.

Methods

We applied two recently developed approaches to quantify these stabilizing effects to time series records from three aquatic monitoring data sets differing in environmental context and organism type.

Results and Discussion

We found that the amount and general patterns of stabilization with increasing spatial scale only varied slightly across the investigated species groups and systems. In all three data sets, the relative contribution of stabilizing effects via asynchronous dynamics across space was higher than compensatory dynamics due to differences in biomass fluctuations across species and populations. When relating the stabilizing effects of individual species and sites to species and site-specific characteristics as well as community composition and aspects of spatial biomass distribution patterns, however, we found that the effects of single species and sites showed large differences and were highly context dependent, i.e., dominant species can but did not necessarily have highly stabilizing or destabilizing effects on overall community biomass. The sign and magnitude of individual contributions depended on community structure and the spatial distribution of biomass and species in space. Our study therefore provides new insights into the mechanistic understanding of ecological stability patterns across scales in natural species communities.

From pattern to process? Dual travelling waves, with contrasting propagation speeds, best describe a self-organised spatio-temporal pattern in population growth of a cyclic rodent

The dynamics of cyclic populations distributed in space result from the relative strength of synchronising influences and the limited dispersal of destabilising factors (activators and inhibitors), known to cause multi‐annual population cycles. However, while each of these have been well studied in isolation, there is limited empirical evidence of how the processes of synchronisation and activation–inhibition act together, largely owing to the scarcity of datasets with sufficient spatial and temporal scale and resolution. We assessed a variety of models that could be underlying the spatio‐temporal pattern, designed to capture both theoretical and empirical understandings of travelling waves using large‐scale (>35,000 km²), multi‐year (2011–2017) field monitoring data on abundances of common vole (Microtus arvalis), a cyclic agricultural rodent pest. We found most support for a pattern formed from the summation of two radial travelling waves with contrasting speeds that together describe population growth rates across the region.

Synchrony and Stability in Trophic Metacommunities: When Top Predators Navigate in a Heterogeneous World

Ecosystem stability strongly depends on spatial aspects since localized perturbations spread across an entire region through species dispersal. Assessing the synchrony of the response of connected populations is fundamental to understand stability at different scales because if populations fluctuate asynchronously, the risk of their simultaneous extinction is low, thus reducing the species' regional extinction risk. Here, we consider a metacommunity model consisting of two food chains connected by dispersal and we review the various mechanisms governing the transmission of small perturbations affecting populations in the vicinity of equilibrium. First, we describe how perturbations propagate vertically (i.e., within food chains through trophic interactions) and horizontally (i.e., between food chains through dispersal) in metacommunities. Then, we discuss the mechanisms susceptible to alter synchrony patterns such as density-depend dispersal or spatial heterogeneity. Density-dependent dispersal, which is the influence of prey or predator abundance on dispersal, has a major impact because the species with the highest coefficient of variation of biomass governs the dispersal rate of the dispersing species and determines the synchrony of its populations, thus bypassing the classic vertical transmission of perturbations. Spatial heterogeneity, which is a disparity between patches of the attack rate of predators on prey in our model, alters the vertical transmission of perturbations in each patch, thus making synchrony dependent on which patch is perturbed. Finally, by combining our understanding of the impact of each of these mechanisms on synchrony, we are able to full explain the response of realistic metacommunities such as the model developed by Rooney et al. (2006). By disentangling the main mechanisms governing synchrony, our metacommunity model provides a broad insight into the consequences of spacial aspects on food web stability.

Noise-induced versus intrinsic oscillation in ecological systems

Studies of oscillatory populations have a long history in ecology. A first-principles understanding of these dynamics can provide insights into causes of population regulation and help with selecting detailed predictive models. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing oscillations. We employ statistical physics concepts, including measures of spatial synchrony, that incorporate patterns at all scales and are novel to ecology, to show that spatial patterns can, under broad and well-defined circumstances, elucidate drivers of population dynamics. We find that when neighbours are coupled (e.g. by dispersal), noisy intrinsic oscillations become distinguishable from noise-induced oscillations at a transition point related to synchronisation that is distinct from the deterministic bifurcation point. We derive this transition point and show that it diverges from the deterministic bifurcation point as stochasticity increases. The concept of universality suggests that the results are robust and widely applicable.

Network topology and patch connectivity affect dynamics in experimental and model metapopulations

Biological populations are rarely isolated in space and instead interact with others via dispersal in metapopulations. Theory predicts that network connectivity patterns can have critical effects on network robustness, as certain topologies, such as scale-free networks, are more tolerant to disturbances than other patterns. However, at present, experimental evidence of how these topologies affect population dynamics in a metapopulation framework is lacking. We used experimental metapopulations of the aquatic protist Paramecium tetraurelia to determine how network topology influences occupation patterns. We created metapopulations engineered to be comparable in linkage density, but differing in their degree distribution. We compared random networks to scale-free networks by evaluating local population occupancy and abundance throughout 18-30 protist generations. In parallel, we used simulations to explore differences in patch occupation patterns among topologies. Our experimental results highlighted the importance of the balance between dispersal and extinction in the interaction with spatial network topology. Under low dispersal conditions, random metapopulations of P. tetraurelia reached higher abundance and higher occupancy (proportion of occupied patches) compared to scale-free systems in both experimental and simulated systems. Under high dispersal conditions, we did not detect differences between types of metapopulations. Increasing patch degree (i.e. number of connections per patch) reduced the probability of extinction of local populations in both types of networks. We suggest the interaction between colonization/extinction rates and network topology alters the likelihood of rescue effects which results in differential patterns of occupancy and abundance in metapopulations.

Age-dependent patterns of spatial autocorrelation in fish populations

The degree of spatial autocorrelation in population fluctuations increases with dispersal and geographical covariation in the environment, and decreases with strength of density dependence. Because the effects of these processes can vary throughout an individual's lifespan, we studied how spatial autocorrelation in abundance changed with age in three marine fish species in the Barents Sea. We found large interspecific differences in age-dependent patterns of spatial autocorrelation in density. Spatial autocorrelation increased with age in cod, the reverse trend was found in beaked redfish, while it remained constant among age classes in haddock. We also accounted for the average effect of local cohort dynamics, i.e. the expected local density of an age class given last year's local density of the cohort, with the goal of disentangling spatial autocorrelation patterns acting on an age class from those formed during younger age classes and being carried over. We found that the spatial autocorrelation pattern of older age classes became increasingly determined by the distribution of the cohort during the previous year. Lastly, we found high degrees of autocorrelation over long distances for the three species, suggesting the presence of far-reaching autocorrelating processes on these populations. We discuss how differences in the species' life history strategies could cause the observed differences in age-specific variation in spatial autocorrelation. As spatial autocorrelation can differ among age classes, our study indicates that fluctuations in age structure can influence the spatio-temporal variation in abundance of marine fish populations.

Predator avoidance and foraging for food shape synchrony and response to perturbations in trophic metacommunities

The response of species to perturbations strongly depends on spatial aspects in populations connected by dispersal. Asynchronous fluctuations in biomass among populations lower the risk of simultaneous local extinctions and thus reduce the regional extinction risk. However, dispersal is often seen as passive diffusion that balances species abundance between distant patches, whereas ecological constraints, such as predator avoidance or foraging for food, trigger the movement of individuals. Here, we propose a model in which dispersal rates depend on the abundance of the species interacting with the dispersing species (e.g., prey or predators) to determine how density-dependent dispersal shapes spatial synchrony in trophic metacommunities in response to stochastic perturbations. Thus, unlike those with passive dispersal, this model with density-dependent dispersal bypasses the classic vertical transmission of perturbations due to trophic interactions and deeply alters synchrony patterns. We show that the species with the highest coefficient of variation of biomass governs the dispersal rate of the dispersing species and determines the synchrony of its populations. In addition, we show that this mechanism can be modulated by the relative impact of each species on the growth rate of the dispersing species. Species affected by several constraints disperse to mitigate the strongest constraints (e.g., predation), which does not necessarily experience the highest variations due to perturbations. Our approach can disentangle the joint effects of several factors implied in dispersal and provides a more accurate description of dispersal and its consequences on metacommunity dynamics.

Synchrony and Perturbation Transmission in Trophic Metacommunities

AbstractIn a world where natural habitats are ever more fragmented, the dynamics of metacommunities are essential to properly understand species responses to perturbations. If species' populations fluctuate asynchronously, the risk of their simultaneous extinction is low, thus reducing the species' regional extinction risk. However, identifying synchronizing or desynchronizing mechanisms in systems containing several species and when perturbations affect multiple species is challenging. We propose a metacommunity model consisting of two food chains connected by dispersal to study the transmission of small perturbations affecting populations in the vicinity of an equilibrium. In spite of the complex responses produced by such a system, two elements enable us to understand the key processes that rule the synchrony between populations: (1) knowing which species have the strongest response to perturbations and (2) the relative importance of dispersal processes compared with local dynamics for each species. We show that perturbing a species in one patch can lead to asynchrony between patches if the perturbed species is not the most affected by dispersal. The synchrony patterns of rare species are the most sensitive to the relative strength of dispersal to demographic processes, thus making biomass distribution critical to understanding the response of trophic metacommunities to perturbations. We further partition the effect of each perturbation on species synchrony when perturbations affect multiple trophic levels. Our approach allows disentangling and predicting the responses of simple trophic metacommunities to perturbations, thus providing a theoretical foundation for future studies considering more complex spatial ecological systems.

Coupled phase-amplitude dynamics in heterogeneous metacommunities

Spatial synchrony of population fluctuations is an important tool for predicting regional stability. Its application to natural systems is still limited by the complexity of ecological time series displaying great variation in the frequency and amplitude of their fluctuations, which are not fully resolved by current ecological theories of spatial synchrony. In particular, while environmental fluctuations and limited dispersal can each control the dynamics of frequency and amplitude of population fluctuations, ecological theories of spatial synchrony still need to resolve their role on synchrony and stability in heterogeneous metacommunities. Here, we adopt a heterogeneous predator-prey metacommunity model and study the response of dispersal-driven phase locking and frequency modulation to among-patch heterogeneity in carrying capacity. We find that frequency modulation occurs at intermediate values of dispersal and habitat heterogeneity. We also show how frequency modulation can emerge in metacommunities of autonomously oscillating populations as well as through the forcing of local communities at equilibrium. Frequency modulation was further found to produce temporal variation in population amplitudes, promoting local and regional stability through cyclic patterns of local and regional variability. Our results highlight the importance of approaching spatial synchrony as a non-stationary phenomenon, with implications for the assessment and interpretation of spatial synchrony observed in experimental and natural systems.

Combined Impacts of Predation, Mutualism and Dispersal on the Dynamics of a Four-Species Ecological System

Multi-species and ecosystem models have provided ecologist with an excellent opportunity to study the effects of multiple biotic interactions in an ecological system. Predation and mutualism are among the most prevalent biotic interactions in the multi-species system. Several ecological studies exist, but they are based on one-or two-species interactions, and in real life, multiple interactions are natural characteristics of a multi-species community. Here, we use a system of partial differential equations to study the combined effects of predation, mutualism and dispersal on the multi-species coexistence and community stability in the ecological system. Our results show that predation provided a defensive mechanism against the negative consequences of the multiple species interactions by reducing the net effect of competition. Predation is critical in the stability and coexistence of the multi-species community. The combined effects of predation and dispersal enhance the multiple species coexistence and persistence. Dispersal exerts a positive effect on the system by supporting multiple species coexistence and stability of community structures. Dispersal process also reduces the adverse effects associated with multiple species interactions. Additionally, mutualism induces oscillatory behaviour on the system through Hopf bifurcation. The roles of mutualism also support multiple species coexistence mechanisms (for some threshold values) by increasing the stable coexistence and the stable limit cycle regions. We discover that the stability and coexistence mechanisms are controlled by the transcritical and Hopf bifurcation that occurs in this system. Most importantly, our results show the important influences of predation, mutualism and dispersal in the stability and coexistence of the multi-species communities

Dynamical Ising model of spatially coupled ecological oscillators

Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of 'universal' properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system's dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.

Temporal patterns of dispersal-induced synchronization in population dynamics

The mechanisms and properties of synchronization of oscillating ecological populations attract attention because it is a fairly common phenomenon and because spatial synchrony may elevate a risk of extinction and may lead to other environmental impacts. Conditions for stable synchronization in a system of linearly coupled predator-prey oscillators have been considered in the past. However, the spatial dispersal coupling may be relatively weak and may not necessarily lead to a stable, complete synchrony. If the coupling between oscillators is too weak to induce a stable synchrony, oscillators may be engaged into intermittent synchrony, when episodes of synchronized dynamics are interspersed with the episodes of desynchronized dynamics. In the present study we consider the temporal patterning of this kind of intermittent synchronized dynamics in a system of two dispersal-coupled Rosenzweig-MacArthur predator-prey oscillators. We consider the properties of the distributions of durations of desynchronized intervals and their dependence on the model parameters. We show that the temporal patterning of synchronous dynamics (an ecological network phenomenon) may depend on the properties of individual predator-prey patch (individual oscillator) and may vary independently of the strength of dispersal. We also show that if the dynamics of predator is slow relative to the dynamics of the prey (a situation that may promote brief but large outbreaks), dispersal-coupled predator-prey oscillating populations exhibit numerous short desynchronizations (as opposed to few long desynchronizations) and may require weaker dispersal in order to reach strong synchrony.

Hidden similarities in the dynamics of a weakly synchronous marine metapopulation

Populations of many marine species are only weakly synchronous, despite coupling through larval dispersal and exposure to synchronous environmental drivers. Although this is often attributed to observation noise, factors including local environmental differences, spatially variable dynamics, and chaos might also reduce or eliminate metapopulation synchrony. To differentiate spatially variable dynamics from similar dynamics driven by spatially variable environments, we applied hierarchical delay embedding. A unique output of this approach, the "dynamic correlation," quantifies similarity in intrinsic dynamics of populations, independently of whether their abundance is correlated through time. We applied these methods to 17 populations of blue crab (Callinectes sapidus) along the US Atlantic coast and found that their intrinsic dynamics were broadly similar despite largely independent fluctuations in abundance. The weight of evidence suggests that the latitudinal gradient in temperature, filtered through a unimodal response curve, is sufficient to decouple crab populations. As unimodal thermal performance is ubiquitous in ectotherms, we suggest that this may be a general explanation for the weak synchrony observed at large distances in many marine species, although additional studies are needed to test this hypothesis.

Population spatial synchrony enhanced by periodicity and low detuning with environmental forcing

Explaining why fluctuations in abundances of spatially disjunct populations often are correlated through time is a major goal of population ecologists. We address two hypotheses receiving little to no testing in wild populations: (i) that population cycling facilitates synchronization given weak coupling among populations, and (ii) that the ability of periodic external forces to synchronize oscillating populations is a function of the mismatch in timescales (detuning) between the force and the population. Here, we apply new analytical methods to field survey data on gypsy moth outbreaks. We report that at timescales associated with gypsy moth outbreaks, spatial synchrony increased with population periodicity via phase locking. The extent to which synchrony in temperature and precipitation influenced population synchrony was associated with the degree of mismatch in dominant timescales of oscillation. Our study provides new empirical methods and rare empirical evidence that population cycling and low detuning can promote population spatial synchrony.

Spatial synchrony in sub-arctic geometrid moth outbreaks reflects dispersal in larval and adult life cycle stages

Spatial synchrony in population dynamics can be caused by dispersal or spatially correlated variation in environmental factors like weather (Moran effect). Distinguishing between these mechanisms is challenging for natural populations, and the study of dispersal-induced synchrony in particular has been dominated by theoretical modelling and laboratory experiments. The goal of the present study was to evaluate the evidence for dispersal as a cause of meso-scale (distances of tens of kilometres) spatial synchrony in natural populations of the two cyclic geometrid moths Epirrita autumnata and Operophtera brumata in sub-arctic mountain birch forest in northern Norway. To infer the role of dispersal in geometrid synchrony, we applied three complementary approaches, namely estimating the effect of design-based dispersal barriers (open sea) on synchrony, comparing the strength of synchrony between E. autumnata (winged adults) and the less dispersive O. brumata (wingless adult females), and relating the directionality (anisotropy) of synchrony to the predominant wind directions during spring, when geometrid larvae engage in windborne dispersal (ballooning). The estimated effect of dispersal barriers on synchrony was almost three times stronger for the less dispersive O. brumata than E. autumnata. Inter-site synchrony was also weakest for O. brumata at all spatial lags. Both observations argue for adult dispersal as an important synchronizing mechanism at the spatial scales considered. Further, synchrony in both moth species showed distinct anisotropy and was most spatially extensive parallel to the east-west axis, coinciding closely to the overall dominant wind direction. This argues for a synchronizing effect of windborne larval dispersal. Congruent with most extensive dispersal along the east-west axis, E. autumnata also showed evidence for a travelling wave moving southwards at a speed of 50-80 km/year. Our results suggest that dispersal processes can leave clear signatures in both the strength and directionality of synchrony in field populations, and highlight wind-driven dispersal as promising avenue for further research on spatial synchrony in natural insect populations.

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.

Thermal variability alters the impact of climate warming on consumer-resource systems

Thermal variation through space and time are prominent features of ecosystems that influence processes at multiple levels of biological organization. Yet, it remains unclear how populations embedded within biological communities will respond to climate warming in thermally variable environments, particularly as climate change alters existing patterns of thermal spatial and temporal variability. As environmental temperatures increase above historical ranges, organisms may increasingly rely on extreme habitats to effectively thermoregulate. Such locations desirable in their thermal attributes (e.g., thermal refugia) are often suboptimal for resource acquisition (e.g., underground tunnels). Thus, via the expected increase in both mean temperatures and diel thermal variation, climate warming may heighten the trade-off for consumers between behaviors maximizing thermal performance and those maximizing resource acquisition. Here, we integrate behavioral, physiological, and trophic ecology to provide a general framework for understanding how temporal thermal variation, mediated by access to a thermal refugium, alters the response of consumer-resource systems to warming. We use this framework to predict how temporal variation and access to thermal refugia affect the persistence of consumers and resources during climate warming, how the quality of thermal refugia impact consumer-resource systems, and how consumer-resource systems with fast vs. slow ecological dynamics respond to warming. Our results show that the spatial thermal variability provided by refugia can elevate consumer biomass at warmer temperatures despite reducing the fraction of time consumers spend foraging, that temporal variability detrimentally impacts consumers at high environmental temperatures, and that consumer-resource systems with fast ecological dynamics are most vulnerable to climate warming. Thus, incorporating both estimates of thermal variability and species interactions may be necessary to accurately predict how populations respond to warming.

Temporal scale of environmental correlations affects ecological synchrony

Population densities of a species measured in different locations are often correlated over time, a phenomenon referred to as synchrony. Synchrony results from dispersal of individuals among locations and spatially correlated environmental variation, among other causes. Synchrony is often measured by a correlation coefficient. However, synchrony can vary with timescale. We demonstrate theoretically and experimentally that the timescale-specificity of environmental correlation affects the overall magnitude and timescale-specificity of synchrony, and that these effects are modified by population dispersal. Our laboratory experiments linked populations of flour beetles by changes in habitat size and dispersal. Linear filter theory, applied to a metapopulation model for the experimental system, predicted the observed timescale-specific effects. The timescales at which environmental covariation occurs can affect the population dynamics of species in fragmented habitats.

Metapopulation dynamics in a changing climate: Increasing spatial synchrony in weather conditions drives metapopulation synchrony of a butterfly inhabiting a fragmented landscape

Habitat fragmentation and climate change are both prominent manifestations of global change, but there is little knowledge on the specific mechanisms of how climate change may modify the effects of habitat fragmentation, for example, by altering dynamics of spatially structured populations. The long-term viability of metapopulations is dependent on independent dynamics of local populations, because it mitigates fluctuations in the size of the metapopulation as a whole. Metapopulation viability will be compromised if climate change increases spatial synchrony in weather conditions associated with population growth rates. We studied a recently reported increase in metapopulation synchrony of the Glanville fritillary butterfly (Melitaea cinxia) in the Finnish archipelago, to see if it could be explained by an increase in synchrony of weather conditions. For this, we used 23 years of butterfly survey data together with monthly weather records for the same period. We first examined the associations between population growth rates within different regions of the metapopulation and weather conditions during different life-history stages of the butterfly. We then examined the association between the trends in the synchrony of the weather conditions and the synchrony of the butterfly metapopulation dynamics. We found that precipitation from spring to late summer are associated with the M. cinxia per capita growth rate, with early summer conditions being most important. We further found that the increase in metapopulation synchrony is paralleled by an increase in the synchrony of weather conditions. Alternative explanations for spatial synchrony, such as increased dispersal or trophic interactions with a specialist parasitoid, did not show paralleled trends and are not supported. The climate driven increase in M. cinxia metapopulation synchrony suggests that climate change can increase extinction risk of spatially structured populations living in fragmented landscapes by altering their dynamics.

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.

Scale-dependent portfolio effects explain growth inflation and volatility reduction in landscape demography

Population demography is central to fundamental ecology and for predicting range shifts, decline of threatened species, and spread of invasive organisms. There is a mismatch between most demographic work, carried out on few populations and at local scales, and the need to predict dynamics at landscape and regional scales. Inspired by concepts from landscape ecology and Markowitz's portfolio theory, we develop a landscape portfolio platform to quantify and predict the behavior of multiple populations, scaling up the expectation and variance of the dynamics of an ensemble of populations. We illustrate this framework using a 35-y time series on gypsy moth populations. We demonstrate the demography accumulation curve in which the collective growth of the ensemble depends on the number of local populations included, highlighting a minimum but adequate number of populations for both regional-scale persistence and cross-scale inference. The attainable set of landscape portfolios further suggests tools for regional population management for both threatened and invasive species.

Spatial and temporal variation in the range-wide cyclic dynamics of greater sage-grouse

Periodic changes in abundance, or population cycles, are common in a variety of species and is one of the most widely studied ecological phenomena. The strength of, and synchrony between population cycles can vary across time and space and understanding these patterns can provide insight into the mechanisms generating population cycles and their variability within and among species. Here, we used wavelet and spectral analysis on a range-wide dataset of abundance for the greater sage-grouse (Centrocercus urophasianus) to test for regional differences in temporal cyclicity. Overall, we found that most populations (11 of 15) were cyclic at some point in a 50-year time series (1965-2015), but the patterns varied over both time and space. Several peripheral populations demonstrated amplitude dampening or loss of cyclicity following population lows in the mid-1990s. Populations through the core of the range in the Great and Wyoming Basins had more consistent cyclic dynamics, but period length appeared to shorten from 10-12 to 6-8 years. In one time period, where cyclicity was greatest overall, increased pairwise population synchrony was correlated with cycle intensity. Our work represents a comprehensive range-wide assessment of cyclic dynamics and revealed substantial variation in temporal and spatial trends of cyclic dynamics across populations.

The geography of spatial synchrony

Spatial synchrony, defined as correlated temporal fluctuations among populations, is a fundamental feature of population dynamics, but many aspects of synchrony remain poorly understood. Few studies have examined detailed geographical patterns of synchrony; instead most focus on how synchrony declines with increasing linear distance between locations, making the simplifying assumption that distance decay is isotropic. By synthesising and extending prior work, we show how geography of synchrony, a term which we use to refer to detailed spatial variation in patterns of synchrony, can be leveraged to understand ecological processes including identification of drivers of synchrony, a long-standing challenge. We focus on three main objectives: (1) showing conceptually and theoretically four mechanisms that can generate geographies of synchrony; (2) documenting complex and pronounced geographies of synchrony in two important study systems; and (3) demonstrating a variety of methods capable of revealing the geography of synchrony and, through it, underlying organism ecology. For example, we introduce a new type of network, the synchrony network, the structure of which provides ecological insight. By documenting the importance of geographies of synchrony, advancing conceptual frameworks, and demonstrating powerful methods, we aim to help elevate the geography of synchrony into a mainstream area of study and application.

Center of mass in complex networks

Network dynamics is always a big challenge in nonlinear dynamics. Although great advancements have been made in various types of complex systems, an universal theoretical framework is required. In this paper, we introduce the concept of center of ‘mass’ of complex networks, where ‘mass’ stands for node importance or centrality in contrast to that of particle systems, and further prove that the phase transition and evolutionary state of the system can be characterized by the activity of center of ‘mass’. The steady states of several complex networks (gene regulatory networks and epidemic spreading systems) are then studied by analytically calculating the decoupled equation of the dynamic activity of center of ‘mass’, which is derived from the dynamic equation of the complex networks. The limitations of this method are also pointed out, such as the dynamical problems that related with the relative activities among components, and those systems that consist of oscillatory or chaotic motions.