Noise and determinism in synchronized sheep dynamics

Climate change could amplify weak synchrony in large marine ecosystems

Climate change is increasing the frequency of large-scale, extreme environmental events and flattening environmental gradients. Whether such changes will cause spatially synchronous, large-scale population declines depends on mechanisms that limit metapopulation synchrony, thereby promoting rescue effects and stability. Using long-term data and empirical dynamic models, we quantified spatial heterogeneity in density dependence, spatial heterogeneity in environmental responses, and environmental gradients to assess their role in inhibiting synchrony across 36 marine fish and invertebrate species. Overall, spatial heterogeneity in population dynamics was as important as environmental drivers in explaining population variation. This heterogeneity leads to weak synchrony in the California Current Ecosystem, where populations exhibit diverse responses to shared, large-scale environmental change. In contrast, in the Northeast U.S. Shelf Ecosystem, gradients in average environmental conditions among locations, filtered through nonlinear environmental response curves, limit synchrony. Simulations predict that environmental gradients and response diversity will continue to inhibit synchrony even if large-scale environmental extremes become common. However, if environmental gradients weaken, synchrony and periods of large-scale population decline may rise sharply among commercially important species on the Northeast Shelf. Our approach thus allows ecologists to 1) quantify how differences among local communities underpin landscape-scale resilience and 2) identify the kinds of future climatic changes most likely to amplify synchrony and erode species stability.

Sporadic Events Have a Greater Influence on the Dynamics of Small, Isolated Populations Than Density Dependence and Environmental Conditions

AbstractDensity dependence is often assumed in population dynamics, but its importance in small, isolated populations has been questioned. We evaluated the relative influence of density dependence, environmental conditions, and sporadic events (disease outbreaks and specialist predators) on annual population growth rate, annual female reproduction, and annual survival of juveniles and adult females in three populations of mountain ungulates. We analyzed long-term (30-47 years) individual-based data on two bighorn sheep populations and one mountain goat population in Alberta, Canada. The effect of cougar predation episodes and pneumonia epizootics on annual population growth rate was twice as strong as that of population density. While pneumonia reduced adult female and juvenile survival and predation episodes decreased all demographic rates, high density lowered only juvenile survival. Long-term studies are pivotal for understanding the dynamics of large herbivore populations, but they are rarely duplicated. Our analysis of three mountain ungulate populations with similar life history and ecological characteristics provides evidence that infrequent sporadic events can have a greater relative influence on annual population growth than density-dependent factors in isolated populations. This result contrasts with studies of larger, well-connected populations, highlighting the importance of considering sporadic events in the management and conservation of isolated populations.

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 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.

Coalescence of limit cycles in the presence of noise

Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional point. Here we ask how dynamics in the vicinity of such a bifurcation are influenced by noise. A pitchfork bifurcation can be used to induce bifurcation behavior. We model a limit cycle with the normal form of the Hopf oscillator, couple it to the pitchfork, and investigate the resulting dynamical system in the presence of noise. We show that the generating functional for the averages of the dynamical variables factorizes between the pitchfork and the oscillator. The statistical properties of the pitchfork in the presence of noise in its various regimes are investigated and a scaling theory is developed for the correlation and response functions, including a possible symmetry-breaking field. The analysis is done by perturbative calculations as well as numerical means. Finally, observables illustrating the coupling of a system with a limit cycle to a pitchfork are discussed and the phase-phase correlations are shown to exhibit nondiffusive behavior with universal scaling.

Climatic effects on the synchrony and stability of temperate headwater invertebrates over four decades

Important clues about the ecological effects of climate change can arise from understanding the influence of other Earth-system processes on ecosystem dynamics but few studies span the inter-decadal timescales required. We, therefore, examined how variation in annual weather patterns associated with the North Atlantic Oscillation (NAO) over four decades was linked to synchrony and stability in a metacommunity of stream invertebrates across multiple, contrasting headwaters in central Wales (UK). Prolonged warmer and wetter conditions during positive NAO winters appeared to synchronize variations in population and community composition among and within streams thereby reducing stability across levels of ecological organization. This climatically mediated synchronization occurred in all streams irrespective of acid-base status and land use, but was weaker where invertebrate communities were more functionally diverse. Wavelet linear models indicated that variation in the NAO explained up to 50% of overall synchrony in species abundances at a timescale of 4-6 years. The NAO appeared to affect ecological dynamics through local variations in temperature, precipitation and discharge, but increasing hydrochemical variability within sites during wetter winters might have contributed. Our findings illustrate how large-scale climatic fluctuations generated over the North Atlantic can affect population persistence and dynamics in inland freshwater ecosystems in ways that transcend local catchment character. Protecting and restoring functional diversity in stream communities might increase their stability against warmer, wetter conditions that are analogues of ongoing climate change. Catchment management could also dampen impacts and provide options for climate change adaptation.

Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.

Seasonality in Environment and Population Processes Alters Population Spatial Synchrony

AbstractPopulation spatial synchrony-the tendency for temporal population fluctuations to be correlated across locations-is common and important to metapopulation stability and persistence. One common cause of spatial synchrony, termed the Moran effect, occurs when populations respond to environmental fluctuations, such as weather, that are correlated over space. Although the degree of spatial synchrony in environmental fluctuations can differ between seasons and different population processes occur in different seasons, the impact on population spatial synchrony is uncertain because prior work has largely assumed that the spatial synchrony of environmental fluctuations and their effect on populations are consistent over annual sampling intervals. We used theoretical models to examine how seasonality in population processes and the spatial synchrony of environmental drivers affect population spatial synchrony. We found that population spatial synchrony can depend not only on the spatial synchrony of environmental drivers but also on the degree to which environmental fluctuations are correlated across seasons, locally, and across space. Moreover, measurements of synchrony from "snapshot" population censuses may not accurately reflect synchrony during other parts of the year. Together, these results show that neglecting seasonality in environmental conditions and population processes is consequential for understanding population spatial synchrony and its driving mechanisms.

Opposing effects of spatiotemporal variation in resources and temporal variation in climate on density dependent population growth in seabirds

Understanding how ecological processes combine to shape population dynamics is crucial in a rapidly changing world. Evidence has been emerging for how fundamental drivers of density dependence in mobile species are related to two differing types of environmental variation-temporal variation in climate, and spatiotemporal variation in food resources. However, to date, tests of these hypotheses have been largely restricted to mid-trophic species in terrestrial environments and thus their general applicability remains unknown. We tested if these same processes can be identified in marine upper trophic level species. We assembled a multi-decadal data set on population abundance of 10 species of colonial seabirds comprising a large component of the UK breeding seabird biomass, and covering diverse phylogenies, life histories and foraging behaviours. We tested for evidence of density dependence in population growth rates using discrete time state-space population models fit to long time-series of observations of abundance at seabird breeding colonies. We then assessed if the strength of density dependence in population growth rates was exacerbated by temporal variation in climate (sea temperature and swell height), and attenuated by spatiotemporal variation in prey resources (productivity and tidal fronts). The majority of species showed patterns consistent with temporal variation in climate acting to strengthen density dependent feedbacks to population growth. However, fewer species showed evidence for a weakening of density dependence with increasing spatiotemporal variation in prey resources. Our findings extend this emerging theory for how different sources of environmental variation may shape the dynamics and regulation of animal populations, demonstrating its role in upper trophic marine species. We show that environmental variation leaves a signal in long-term population dynamics of seabirds with potentially important consequences for their demography and trophic interactions.

Contrasting seasonal effects of climate change influence density in a cold-adapted species

Many ecological processes are profoundly influenced by abiotic factors, such as temperature and snow. However, despite strong evidence linking shifts in these ecological processes to corresponding shifts in abiotic factors driven by climate change, the mechanisms connecting population size to season-specific climate drivers are little understood. Using a 21-year dataset and a Bayesian state space model, we identified biologically informed seasonal climate covariates that influenced densities of snowshoe hares (Lepus americanus), a cold-adapted boreal herbivore. We found that snow and temperature had strong but conflicting season-dependent effects. Reduced snow duration in spring and fall and warmer summers were associated with lowered hare density, whereas warmer winters were associated with increased density. When modeled simultaneously and under two climate change scenarios, the negative effects of reduced fall and spring snow duration and warmer summers overwhelm the positive effect of warmer winters, producing projected population declines. Ultimately, the contrasting population-level impacts of climate change across seasons emphasize the critical need to examine the entire annual climate cycle to understand potential long-term population consequences of climate change.

Using network synchrony to identify drivers of social dynamics

Social animals frequently show dynamic social network patterns, the consequences of which are felt at the individual and group level. It is often difficult, however, to identify what drivers are responsible for changes in these networks. We suggest that patterns of network synchronization across multiple social groups can be used to better understand the relative contributions of extrinsic and intrinsic drivers. When groups are socially separated, but share similar physical environments, the extent to which network measures across multiple groups covary (i.e. network synchrony) can provide an estimate of the relative roles of extrinsic and intrinsic drivers. As a case example, we use allogrooming data from three adjacent vervet monkey groups to generate dynamic social networks. We found that network strength was strongly synchronized across the three groups, pointing to shared extrinsic environmental conditions as the driver. We also found low to moderate levels of synchrony in network modularity, suggesting that intrinsic social processes may be more important in driving changes in subgroup formation in this population. We conclude that patterns of network synchronization can help guide future research in identifying the proximate mechanisms behind observed social dynamics in animal groups.

Periodic synchronisation of dengue epidemics in Thailand over the last 5 decades driven by temperature and immunity

The spatial distribution of dengue and its vectors (spp. Aedes) may be the widest it has ever been, and projections suggest that climate change may allow the expansion to continue. However, less work has been done to understand how climate variability and change affects dengue in regions where the pathogen is already endemic. In these areas, the waxing and waning of immunity has a large impact on temporal dynamics of cases of dengue haemorrhagic fever. Here, we use 51 years of data across 72 provinces and characterise spatiotemporal patterns of dengue in Thailand, where dengue has caused almost 1.5 million cases over the last 30 years, and examine the roles played by temperature and dynamics of immunity in giving rise to those patterns. We find that timescales of multiannual oscillations in dengue vary in space and time and uncover an interesting spatial phenomenon: Thailand has experienced multiple, periodic synchronisation events. We show that although patterns in synchrony of dengue are similar to those observed in temperature, the relationship between the two is most consistent during synchronous periods, while during asynchronous periods, temperature plays a less prominent role. With simulations from temperature-driven models, we explore how dynamics of immunity interact with temperature to produce the observed patterns in synchrony. The simulations produced patterns in synchrony that were similar to observations, supporting an important role of immunity. We demonstrate that multiannual oscillations produced by immunity can lead to asynchronous dynamics and that synchrony in temperature can then synchronise these dengue dynamics. At higher mean temperatures, immune dynamics can be more predominant, and dengue dynamics more insensitive to multiannual fluctuations in temperature, suggesting that with rising mean temperatures, dengue dynamics may become increasingly asynchronous. These findings can help underpin predictions of disease patterns as global temperatures rise.

This study shows that spatially large-scale shifts in temperature can synchronize dengue dynamics across Thailand; however, as average temperatures rise, dengue dynamics may increasingly be dictated by dynamics of immunity, which may in turn mean fewer synchronous outbreaks in the future.

Ecological Analysis of the Helminth Community of Microtus lusitanicus (Gerbe, 1879) (Rodentia) in Asturias (NW Spain)

The Lusitanian pine vole, Microtus lusitanicus, an endemic fossorial rodent of the Iberian Peninsula, has a burrowing behaviour and prefers to live underground. It feeds on bark and roots causing severe damage to trees. In Asturias (NW Spain), where M. lusitanicus is considered a pest in several orchards, a faunistic-ecological study was carried out to describe the helminth community of this species and the main factors that could influence its helminth component species. For this purpose, our own collection of 710 voles from several orchards of various locations in Asturias was used. Eight helminth species, four cestodes and four nematodes, were found. Statistical non-parametric tests were used to analyse the effects of extrinsic and intrinsic factors on the diversity of the helminth community and species prevalence and abundance. The results show the influence of climate variables, the year and season of capture, as well as host age, on the diversity of the helminth community and the infection parameters of some helminth species, underlining the importance of their life cycles. In addition to shedding light on the helminth community of this rodent in Asturias, the results obtained could be used to improve the biological methods applied to fight the M. lusitanicus pest.

Climate variability and density-dependent population dynamics: Lessons from a simple High Arctic ecosystem

Whether the renowned population cycles of small mammals in northern food webs are driven by bottom-up (plant–herbivore) or top-down (predator–prey) interactions is still a debated question but crucial to our understanding of their ecological functions and response to climate change. A long-term study of a graminivorous vole population in an exceptionally simple High Arctic food web allowed us to identify which population dynamics features are present without top-down regulation. Unique features were high-amplitude, noncyclic population fluctuations driven by a combination of stochastic weather events and season-specific density dependence likely arising from plant–herbivore interactions. That such features are not present in more complex food webs points to the importance of top-down regulation in small mammal populations.

Ecologists are still puzzled by the diverse population dynamics of herbivorous small mammals that range from high-amplitude, multiannual cycles to stable dynamics. Theory predicts that this diversity results from combinations of climatic seasonality, weather stochasticity, and density-dependent food web interactions. The almost ubiquitous 3- to 5-y cycles in boreal and arctic climates may theoretically result from bottom-up (plant–herbivore) and top-down (predator–prey) interactions. Assessing, empirically, the roles of such interactions and how they are influenced by environmental stochasticity has been hampered by food web complexity. Here, we take advantage of a uniquely simple High Arctic food web, which allowed us to analyze the dynamics of a graminivorous vole population not subjected to top-down regulation. This population exhibited high-amplitude, noncyclic fluctuations—partly driven by weather stochasticity. However, the predominant driver of the dynamics was overcompensatory density dependence in winter that caused the population to frequently crash. Model simulations showed that the seasonal pattern of density dependence would yield regular 2-y cycles in the absence of stochasticity. While such short cycles have not yet been observed in mammals, they are theoretically plausible if graminivorous vole populations are deterministically bottom-up regulated. When incorporating weather stochasticity in the model simulations, cyclicity became disrupted and the amplitude was increased—akin to the observed dynamics. Our findings contrast with the 3- to 5-y population cycles that are typical of graminivorous small mammals in more complex food webs, suggesting that top-down regulation is normally an important component of such dynamics.

Global hotspots of coherent marine fishery catches

Although different fisheries can be tightly linked to each other by human and ecosystem processes, they are often managed independently. Synchronous fluctuations among fish populations or fishery catches can destabilize ecosystems and economies, respectively, but the degree of synchrony around the world remains unclear. We analyzed 1,092 marine fisheries catch time series over 60 yr to test for the presence of coherence, a form of synchrony that allows for phase-lagged relationships. We found that nearly every fishery was coherent with at least one other fishery catch time series globally and that coherence was strongest in the northeast Atlantic, western central Pacific, and eastern Indian Ocean. Analysis of fish biomass and fishing mortality time series from these hotspots revealed that coherence in biomass or fishing mortality were both possible, though biomass coherence was more common. Most of these relationships were synchronous with no time lags, and across catches in all regions, synchrony was a better predictor of regional catch portfolio effects than catch diversity. Regions with higher synchrony had lower stability in aggregate fishery catches, which can have negative consequences for food security and economic wealth.

The geography of metapopulation synchrony in dendritic river networks

Dendritic habitats, such as river ecosystems, promote the persistence of species by favouring spatial asynchronous dynamics among branches. Yet, our understanding of how network topology influences metapopulation synchrony in these ecosystems remains limited. Here, we introduce the concept of fluvial synchrogram to formulate and test expectations regarding the geography of metapopulation synchrony across watersheds. By combining theoretical simulations and an extensive fish population time‐series dataset across Europe, we provide evidence that fish metapopulations can be buffered against synchronous dynamics as a direct consequence of network connectivity and branching complexity. Synchrony was higher between populations connected by direct water flow and decayed faster with distance over the Euclidean than the watercourse dimension. Likewise, synchrony decayed faster with distance in headwater than mainstem populations of the same basin. As network topology and flow directionality generate fundamental spatial patterns of synchrony in fish metapopulations, empirical synchrograms can aid knowledge advancement and inform conservation strategies in complex habitats.

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.

What Have Long-Term Field Studies Taught Us About Population Dynamics?

Long-term studies have been crucial to the advancement of population biology, especially our understanding of population dynamics. We argue that this progress arises from three key characteristics of long-term research. First, long-term data are necessary to observe the heterogeneity that drives most population processes. Second, long-term studies often inherently lead to novel insights. Finally, long-term field studies can serve as model systems for population biology, allowing for theory and methods to be tested under well-characterized conditions. We illustrate these ideas in three long-term field systems that have made outsized contributions to our understanding of population ecology, evolution, and conservation biology. We then highlight three emerging areas to which long-term field studies are well positioned to contribute in the future: ecological forecasting, genomics, and macrosystems ecology. Overcoming the obstacles associated with maintaining long-term studies requires continued emphasis on recognizing the benefits of such studies to ensure that long-term research continues to have a substantial impact on elucidating population biology.

Spatial heterogeneity in climate change effects decouples the long-term dynamics of wild reindeer populations in the high Arctic

The 'Moran effect' predicts that dynamics of populations of a species are synchronized over similar distances as their environmental drivers. Strong population synchrony reduces species viability, but spatial heterogeneity in density dependence, the environment, or its ecological responses may decouple dynamics in space, preventing extinctions. How such heterogeneity buffers impacts of global change on large-scale population dynamics is not well studied. Here, we show that spatially autocorrelated fluctuations in annual winter weather synchronize wild reindeer dynamics across high-Arctic Svalbard, while, paradoxically, spatial variation in winter climate trends contribute to diverging local population trajectories. Warmer summers have improved the carrying capacity and apparently led to increased total reindeer abundance. However, fluctuations in population size seem mainly driven by negative effects of stochastic winter rain-on-snow (ROS) events causing icing, with strongest effects at high densities. Count data for 10 reindeer populations 8-324 km apart suggested that density-dependent ROS effects contributed to synchrony in population dynamics, mainly through spatially autocorrelated mortality. By comparing one coastal and one 'continental' reindeer population over four decades, we show that locally contrasting abundance trends can arise from spatial differences in climate change and responses to weather. The coastal population experienced a larger increase in ROS, and a stronger density-dependent ROS effect on population growth rates, than the continental population. In contrast, the latter experienced stronger summer warming and showed the strongest positive response to summer temperatures. Accordingly, contrasting net effects of a recent climate regime shift-with increased ROS and harsher winters, yet higher summer temperatures and improved carrying capacity-led to negative and positive abundance trends in the coastal and continental population respectively. Thus, synchronized population fluctuations by climatic drivers can be buffered by spatial heterogeneity in the same drivers, as well as in the ecological responses, averaging out climate change effects at larger spatial scales.

Cumulative weather effects can impact across the whole life cycle

Predicting how species will be affected by future climatic change requires the underlying environmental drivers to be identified. As vital rates vary over the lifecycle, structured population models derived from statistical environment-demography relationships are often used to inform such predictions. Environmental drivers are typically identified independently for different vital rates and demographic classes. However, these rates often exhibit positive temporal covariance, suggesting that vital rates respond to common environmental drivers. Additionally, models often only incorporate average weather conditions during a single, a priori chosen time window (e.g. monthly means). Mismatches between these windows and the period when the vital rates are sensitive to variation in climate decrease the predictive performance of such approaches. We used a demographic structural equation model (SEM) to demonstrate that a single axis of environmental variation drives the majority of the (co)variation in survival, reproduction, and twinning across six age-sex classes in a Soay sheep population. This axis provides a simple target for the complex task of identifying the drivers of vital rate variation. We used functional linear models (FLMs) to determine the critical windows of three local climatic drivers, allowing the magnitude and direction of the climate effects to differ over time. Previously unidentified lagged climatic effects were detected in this well-studied population. The FLMs had a better predictive performance than selecting a critical window a priori, but not than a large-scale climate index. Positive covariance amongst vital rates and temporal variation in the effects of environmental drivers are common, suggesting our SEM-FLM approach is a widely applicable tool for exploring the joint responses of vital rates to environmental change.

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.

Synchrony is more than its top-down and climatic parts: interacting Moran effects on phytoplankton in British seas

Large-scale spatial synchrony is ubiquitous in ecology. We examined 56 years of data representing chlorophyll density in 26 areas in British seas monitored by the Continuous Plankton Recorder survey. We used wavelet methods to disaggregate synchronous fluctuations by timescale and determine that drivers of synchrony include both biotic and abiotic variables. We tested these drivers for statistical significance by comparison with spatially synchronous surrogate data. Identification of causes of synchrony is distinct from, and goes beyond, determining drivers of local population dynamics. We generated timescale-specific models, accounting for 61% of long-timescale (> 4yrs) synchrony in a chlorophyll density index, but only 3% of observed short-timescale (< 4yrs) synchrony. Thus synchrony and its causes are timescale-specific. The dominant source of long-timescale chlorophyll synchrony was closely related to sea surface temperature, through a climatic Moran effect, though likely via complex oceanographic mechanisms. The top-down action of Calanus finmarchicus predation enhances this environmental synchronising mechanism and interacts with it non-additively to produce more long-timescale synchrony than top-down and climatic drivers would produce independently. Our principal result is therefore a demonstration of interaction effects between Moran drivers of synchrony, a new mechanism for synchrony that may influence many ecosystems at large spatial scales.

The size of the annual bloom in phytoplankton can vary similarly from year to year in different parts of the same oceanic region, a phenomenon called spatial synchrony. The growth of phytoplankton near the ocean surface is the foundation of marine food webs, which include numerous commercially exploited species. And spatial synchrony in phytoplankton abundance time series can have consequences for the total production of marine ecosystems. Therefore we studied the spatial synchrony of fluctuations in green phytoplankton abundance in 26 areas in seas around the British Isles. Variation and synchrony can occur differently on long and short timescales. We used a novel wavelet-based approach to examine long- and short-timescale fluctuations separately, and we thereby show that slow synchronous fluctuations in phytoplankton can be explained by the effects of slow synchronous fluctuations in sea surface temperature and related oceanographic phenomena, and by the effects of synchronous fluctuations in a zooplankton predator. Crucially, these drivers reinforce one another in a super-additive way, the interaction constituting a new mechanism of synchrony. Future changes in the climate or changes in predation are likely to influence phytoplankton synchrony via this mechanism and hence may influence the aggregate productivity of British seas.

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.

Synchronization of stochastic hybrid oscillators driven by a common switching environment

Many systems in biology, physics, and chemistry can be modeled through ordinary differential equations (ODEs), which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we suppose that this limit ODE supports a stable limit cycle. We demonstrate that a set of such oscillators can synchronize when they are uncoupled, but they share the same switching Markov jump process. The latter is taken to represent the effect of a common randomly switching environment. We determine the leading order of the Lyapunov coefficient governing the rate of decay of the phase difference in the fast switching limit. The analysis bears some similarities to the classical analysis of synchronization of stochastic oscillators subject to common white noise. However, the discrete nature of the Markov jump process raises some difficulties: in fact, we find that the Lyapunov coefficient from the quasi-steady-state approximation differs from the Lyapunov coefficient one obtains from a second order perturbation expansion in the waiting time between jumps. Finally, we demonstrate synchronization numerically in the radial isochron clock model and show that the latter Lyapunov exponent is more accurate.

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.

Control, synchronization, and enhanced reliability of aperiodic oscillations in the Mercury Beating Heart system

Experiments involving the Mercury Beating Heart (MBH) oscillator, exhibiting irregular (aperiodic) dynamics, are performed. In the first set of experiments, control over irregular dynamics of the MBH oscillator was obtained via a superimposed periodic voltage signal. These irregular (aperiodic) dynamics were recovered once the control was switched off. Subsequently, two MBH oscillators were coupled to attain synchronization of their aperiodic oscillations. Finally, two uncoupled MBH oscillators were subjected, repeatedly, to a common stochastic forcing, resulting in an enhancement of their mutual phase correlation.

Spatial patterns of tree yield explained by endogenous forces through a correspondence between the Ising model and ecology

Explaining correlations across space of cyclic dynamics in ecology is a fundamental challenge. We apply ideas from statistical physics, originally used to explain the behavior of magnets, to a dataset on yield from pistachio trees, obtaining a robust description and potential explanation for the generation of spatial correlations in cyclic dynamics. These results suggest looking for mechanistic underpinnings at the level of interactions between neighboring trees that lead to spatial correlations in dynamics and a surprising correspondence between the descriptions of physical phenomena, magnetization, and ecological dynamics. This work demonstrates with data, and not just models, that correlations in cyclic dynamics can be generated from local interactions and dynamics even in a very noisy ecological system.

Spatial patterning of periodic dynamics is a dramatic and ubiquitous ecological phenomenon arising in systems ranging from diseases to plants to mammals. The degree to which spatial correlations in cyclic dynamics are the result of endogenous factors related to local dynamics vs. exogenous forcing has been one of the central questions in ecology for nearly a century. With the goal of obtaining a robust explanation for correlations over space and time in dynamics that would apply to many systems, we base our analysis on the Ising model of statistical physics, which provides a fundamental mechanism of spatial patterning. We show, using 5 y of data on over 6,500 trees in a pistachio orchard, that annual nut production, in different years, exhibits both large-scale synchrony and self-similar, power-law decaying correlations consistent with the Ising model near criticality. Our approach demonstrates the possibility that short-range interactions can lead to long-range correlations over space and time of cyclic dynamics even in the presence of large environmental variability. We propose that root grafting could be the common mechanism leading to positive short-range interactions that explains the ubiquity of masting, correlated seed production over space through time, by trees.

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.

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.

Hybrid Markov chain models of S-I-R disease dynamics

Deterministic epidemic models are attractive due to their compact nature, allowing substantial complexity with computational efficiency. This partly explains their dominance in epidemic modelling. However, the small numbers of infectious individuals at early and late stages of an epidemic, in combination with the stochastic nature of transmission and recovery events, are critically important to understanding disease dynamics. This motivates the use of a stochastic model, with continuous-time Markov chains being a popular choice. Unfortunately, even the simplest Markovian S-I-R model-the so-called general stochastic epidemic-has a state space of order [Formula: see text], where N is the number of individuals in the population, and hence computational limits are quickly reached. Here we introduce a hybrid Markov chain epidemic model, which maintains the stochastic and discrete dynamics of the Markov chain in regions of the state space where they are of most importance, and uses an approximate model-namely a deterministic or a diffusion model-in the remainder of the state space. We discuss the evaluation, efficiency and accuracy of this hybrid model when approximating the distribution of the duration of the epidemic and the distribution of the final size of the epidemic. We demonstrate that the computational complexity is [Formula: see text] and that under suitable conditions our approximations are highly accurate.

Climate change-related regime shifts have altered spatial synchrony of plankton dynamics in the North Sea

During the 1980s, the North Sea plankton community underwent a well-documented ecosystem regime shift, including both spatial changes (northward species range shifts) and temporal changes (increases in the total abundances of warmer water species). This regime shift has been attributed to climate change. Plankton provide a link between climate and higher trophic-level organisms, which can forage on large spatial and temporal scales. It is therefore important to understand not only whether climate change affects purely spatial or temporal aspects of plankton dynamics, but also whether it affects spatiotemporal aspects such as metapopulation synchrony. If plankton synchrony is altered, higher trophic-level feeding patterns may be modified. A second motivation for investigating changes in synchrony is that the possibility of such alterations has been examined for few organisms, in spite of the fact that synchrony is ubiquitous and of major importance in ecology. This study uses correlation coefficients and spectral analysis to investigate whether synchrony changed between the periods 1959-1980 and 1989-2010. Twenty-three plankton taxa, sea surface temperature (SST), and wind speed were examined. Results revealed that synchrony in SST and plankton was altered. Changes were idiosyncratic, and were not explained by changes in abundance. Changes in the synchrony of Calanus helgolandicus and Para-pseudocalanus spp appeared to be driven by changes in SST synchrony. This study is one of few to document alterations of synchrony and climate-change impacts on synchrony. We discuss why climate-change impacts on synchrony may well be more common and consequential than previously recognized.

Harvested populations are more variable only in more variable environments

The interaction between environmental variation and population dynamics is of major importance, particularly for managed and economically important species, and especially given contemporary changes in climate variability. Recent analyses of exploited animal populations contested whether exploitation or environmental variation has the greatest influence on the stability of population dynamics, with consequences for variation in yield and extinction risk. Theoretical studies however have shown that harvesting can increase or decrease population variability depending on environmental variation, and requested controlled empirical studies to test predictions. Here, we use an invertebrate model species in experimental microcosms to explore the interaction between selective harvesting and environmental variation in food availability in affecting the variability of stage‐structured animal populations over 20 generations. In a constant food environment, harvesting adults had negligible impact on population variability or population size, but in the variable food environments, harvesting adults increased population variability and reduced its size. The impact of harvesting on population variability differed between proportional and threshold harvesting, between randomly and periodically varying environments, and at different points of the time series. Our study suggests that predicting the responses to selective harvesting is sensitive to the demographic structures and processes that emerge in environments with different patterns of environmental variation.

Functional Process Zones Characterizing Aquatic Insect Communities in Streams of the Brazilian Cerrado

Stream ecology studies see to understand ecological dynamics in lotic systems. The characterization of streams into Functional Process Zones (FPZ) has been currently debated in stream ecology because aquatic communities respond to functional processes of river segments. Therefore, we tested if different functional process zones have different number of genera and trophic structure using the aquatic insect community of Neotropical streams. We also assessed whether using physical and chemical variables may complement the approach of using FPZ to model communities of aquatic insects in Cerrado streams. This study was conducted in 101 streams or rivers from the central region of the state of Goiás, Brazil. We grouped the streams into six FPZ associated to size of the river system, presence of riparian forest, and riverbed heterogeneity. We used Bayesian models to compare number of genera and relative frequency of the feeding groups between FPZs. Streams classified in different FPZs had a different number of genera, and the largest and best preserved rivers had an average of four additional genera. Trophic structure exhibited low variability among FPZs, with little difference both in the number of genera and in abundance. Using functional process zones in Cerrado streams yielded good results for Ephemeroptera, Plecoptera, and Trichoptera communities. Thus, species distribution and community structure in the river basin account for functional processes and not necessarily for the position of the community along a longitudinal dimension of the lotic system.

Assessing spatial covariance among time series of abundance

For species of conservation concern, an essential part of the recovery planning process is identifying discrete population units and their location with respect to one another. A common feature among geographically proximate populations is that the number of organisms tends to covary through time as a consequence of similar responses to exogenous influences. In turn, high covariation among populations can threaten the persistence of the larger metapopulation. Historically, explorations of the covariance in population size of species with many (>10) time series have been computationally difficult. Here, we illustrate how dynamic factor analysis (DFA) can be used to characterize diversity among time series of population abundances and the degree to which all populations can be represented by a few common signals. Our application focuses on anadromous Chinook salmon (Oncorhynchus tshawytscha), a species listed under the US Endangered Species Act, that is impacted by a variety of natural and anthropogenic factors. Specifically, we fit DFA models to 24 time series of population abundance and used model selection to identify the minimum number of latent variables that explained the most temporal variation after accounting for the effects of environmental covariates. We found support for grouping the time series according to 5 common latent variables. The top model included two covariates: the Pacific Decadal Oscillation in spring and summer. The assignment of populations to the latent variables matched the currently established population structure at a broad spatial scale. At a finer scale, there was more population grouping complexity. Some relatively distant populations were grouped together, and some relatively close populations – considered to be more aligned with each other – were more associated with populations further away. These coarse‐ and fine‐grained examinations of spatial structure are important because they reveal different structural patterns not evident in other analyses.

Detecting and modelling delayed density-dependence in abundance time series of a small mammal (Didelphis aurita)

We study the population size time series of a Neotropical small mammal with the intent of detecting and modelling population regulation processes generated by density-dependent factors and their possible delayed effects. The application of analysis tools based on principles of statistical generality are nowadays a common practice for describing these phenomena, but, in general, they are more capable of generating clear diagnosis rather than granting valuable modelling. For this reason, in our approach, we detect the principal temporal structures on the bases of different correlation measures, and from these results we build an ad-hoc minimalist autoregressive model that incorporates the main drivers of the dynamics. Surprisingly our model is capable of reproducing very well the time patterns of the empirical series and, for the first time, clearly outlines the importance of the time of attaining sexual maturity as a central temporal scale for the dynamics of this species. In fact, an important advantage of this analysis scheme is that all the model parameters are directly biologically interpretable and potentially measurable, allowing a consistency check between model outputs and independent measurements.

Spatial synchrony in population dynamics: The effects of demographic stochasticity and density regulation with a spatial scale

We generalize a previous simple result by Lande et al. (1999) on how spatial autocorrelated noise, dispersal rate and distance as well as strength of density regulation determine the spatial scale of synchrony in population density. It is shown how demographic noise can be incorporated, what effect it has on variance and spatial scale of synchrony, and how it interacts with the point process for locations of individuals under random sampling. Although the effect of demographic noise is a rather complex interaction with environmental noise, migration and density regulation, its effect on population fluctuations and scale of synchrony can be presented in a transparent way. This is achieved by defining a characteristic area dependent on demographic and environmental variances as well as population density, and subsequently using this area to define a spatial demographic coefficient. The demographic noise acts through this coefficient on the spatial synchrony, which may increase or decrease with increasing demographic noise depending on other parameters. A second generalization yields the modeling of density regulation taking into account that regulation at a given location does not only depend on the density at that site but also on densities in the whole territory or home range of individuals. It is shown that such density regulation with a spatial scale reduces the scale of synchrony in population fluctuations relative to the simpler model with density regulation at each location determined only by the local point density, and may even generate negative spatial autocorrelations.