Searching for mechanisms of synchrony in spatially structured gamebird populations

1.  Time series data on five species of gamebird from the Dolomitic Alps were used to examine the relative importance of dispersal and common stochastic events in causing synchrony between spatially structured populations.
2.  Cross-correlation analysis of detrended time series was used to describe the spatial pattern of fluctuations in abundance, while standardized time series were used to describe both fluctuations and the trend in abundance. There were large variations in synchrony both within and between species and only weak negative relationships with distance.
3.  Species in neighbouring habitats were more likely to be in synchrony than species separated by several habitats. Species with similar density-dependent structure were more likely to be in synchrony.
4.  In order to estimate the relative importance of dispersal and environmental stochasticity, we modelled the spatial dynamics of each species using two different approaches. First, we used estimating functions and bootstrapping of time series data to calculate the relative importance of dispersal and stochastic effects for each species. Second, we estimated the intensity of environmental stochasticity from climatic records during the breeding season and then modelled the dispersal rate and dispersal distance for each species. The two models exhibited similar results for rock ptarmigan, black grouse, hazel grouse and rock partridge, while contrasting patterns were observed for capercaillie.
5.  The results suggest that environmental stochasticity plays the dominant role in synchronizing the fluctuations of these galliform species, although there will also be some dispersal between populations.     

Density-dependent dispersal and spatial population dynamics

The synchronization of the dynamics of spatially subdivided populations is of both fundamental and applied interest in population biology. Based on theoretical studies, dispersal movements have been inferred to be one of the most general causes of population synchrony, yet no empirical study has mapped distance-dependent estimates of movement rates on the actual pattern of synchrony in species that are known to exhibit population synchrony. Northern vole and lemming species are particularly well-known for their spatially synchronized population dynamics. Here, we use results from an experimental study to demonstrate that tundra vole dispersal movements did not act to synchronize population dynamics in fragmented habitats. In contrast to the constant dispersal rate assumed in earlier theoretical studies, the tundra vole, and many other species, exhibit negative density-dependent dispersal. Simulations of a simple mathematical model, parametrized on the basis of our experimental data, verify the empirical results, namely that the observed negative density-dependent dispersal did not have a significant synchronizing effect.     

Using mechanistic models to understand synchrony in forest insect populations: the North American gypsy moth as a case study

In many forest insects, subpopulations fluctuate concurrently across large geographical areas, a phenomenon known as population synchrony. Because of the large spatial scales involved, empirical tests to identify the causes of synchrony are often impractical. Simple models are, therefore, a useful aid to understanding, but data often seem to contradict model predictions. For instance, chaotic population dynamics and limited dispersal are not uncommon among synchronous forest defoliators, yet both make it difficult to achieve synchrony in simple models. To test whether this discrepancy can be explained by more realistic models, we introduced dispersal and spatially correlated stochasticity into a mechanistic population model for the North American gypsy moth Lymantria dispar. The resulting model shows both chaotic dynamics and spatial synchrony, suggesting that chaos and synchrony can be reconciled by the incorporation of realistic dynamics and spatial structure. By relating alterations in model structure to changes in synchrony levels, we show that the synchrony is due to a combination of spatial covariance in environmental stochasticity and the origins of chaos in our multispecies model.     

The effects of large and small-scale random events on the synchrony of metapopulation dynamics: a theoretical analysis

We present an analysis of the conditions under which migration and global random factors may determine large scale synchrony in the dynamics of spatially structured populations. We derive an analytic approximation which describes how the desynchronizing influence of local environmental stochasticity combines with the synchronizing influences of larger scale environmental stochastic variation and migration to determine population cross correlation coefficients. Despite the simplifications made by this analysis, computer simulations show that the behaviour of more complicated models is well described by our approximation over considerable regions of parameter space. We conclude that population synchrony is largely determined by the coefficients of variation (CVs) of the local and larger scale stochastic processes, and that migration alone is only likely to maintain population synchrony when the CV of the local stochastic process is very small.     

Nonlinear Effect of Dispersal Rate on Spatial Synchrony of Predator-Prey Cycles

Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.     

Density-dependent demographic variation determines extinction rate of experimental populations

Understanding population extinctions is a chief goal of ecological theory. While stochastic theories of population growth are commonly used to forecast extinction, models used for prediction have not been adequately tested with experimental data. In a previously published experiment, variation in available food was experimentally manipulated in 281 laboratory populations of Daphnia magna to test hypothesized effects of environmental variation on population persistence. Here, half of those data were used to select and fit a stochastic model of population growth to predict extinctions of populations in the other half. When density-dependent demographic stochasticity was detected and incorporated in simple stochastic models, rates of population extinction were accurately predicted or only slightly biased. However, when density-dependent demographic stochasticity was not accounted for, as is usual when forecasting extinction of threatened and endangered species, predicted extinction rates were severely biased. Thus, an experimental demonstration shows that reliable estimates of extinction risk may be obtained for populations in variable environments if high-quality data are available for model selection and if density-dependent demographic stochasticity is accounted for. These results suggest that further consideration of density-dependent demographic stochasticity is required if predicted extinction rates are to be relied upon for conservation planning.     

Canonical functions for dispersal-induced synchrony

Two processes are universally recognized for inducing spatial synchrony in abundance: dispersal and correlated environmental stochasticity. In the present study we seek the expected relationship between synchrony and distance in populations that are synchronized by density-independent dispersal. In the absence of dispersal, synchrony among populations with simple dynamics has been shown to echo the correlation in the environment. We ask what functional form we may expect between synchrony and distance when dispersal is the synchronizing agent. We formulate a continuous-space, continuous-time model that explicitly represents the time evolution of the spatial covariance as a function of spatial distance. Solving this model gives us two simple canonical functions for dispersal-induced covariance in spatially extended populations. If dispersal is rare relative to birth and death, then covariances between nearby points will follow the dispersal distance distribution. At long distances, however, the covariance tails off according to exponential or Bessel functions (depending on whether the population moves in one or two dimensions). If dispersal is common, then the covariances will follow the mixture distribution that is approximately Gaussian around the origin and with an exponential or Bessel tail. The latter mixture results regardless of the original dispersal distance distribution. There are hence two canonical functions for dispersal-induced synchrony     

When can dispersal synchronize populations?

While spatial synchrony of oscillating populations has been observed in many ecological systems, the causes of this phenomenon are still not well understood. The most common explanations have been the Moran effect (synchronous external stochastic influences) and the effect of dispersal among populations. Since ecological systems are typically subject to large spatially varying perturbations which destroy synchrony, a plausible mechanism explaining synchrony must produce rapid convergence to synchrony. We analyze the dynamics through time of the synchronizing effects of dispersal and, consequently, determine whether dispersal can be the mechanism which produces synchrony. Specifically, using methods new to ecology, we analyze a two patch predator-prey model, with identical weak dispersal between the patches. We find that a difference in time scales (i.e. one population has dynamics occurring much faster than the other) between the predator and prey species is the most important requirement for fast convergence to synchrony.     

Dissecting geographic variation in population synchrony using the common vole in central Europe as a test bed

Spatial synchrony of population fluctuations is ubiquitous in nature. Theoretical models suggest that correlated environmental stochasticity, dispersal, and trophic interactions are important promoters of synchrony in nature to leave characteristic signatures of distance‐dependent decays in synchrony. Recent refinements of this theory have clarified how distance‐decay curves may steepen if local dynamics are governed by different density‐dependent feedbacks and how synchrony should vary regionally if the importance and correlation of environmental stochasticity is location‐specific. We analysed spatiotemporal data for the common vole, Microtus arvalis from 49 districts in the Czech Republic to examine the pattern of population synchrony between 2000 and 2014. By extending the nonparametric covariation function, we develop a quantitative method that allows a dissection of the effects of distance and additional variables such as altitude on synchrony. To examine the pattern of local synchrony, we apply the noncentered local‐indicators of spatial association (ncLISA) which highlights areas with different degrees of synchrony than expected by the region‐wide average. Additionally, in order to understand the obtained pattern of local spatial correlations, we have regressed LISA results against the proportion of forest in each district. The common vole abundances fluctuated strongly and exhibited synchronous dynamics with the typical tendency for a decline of synchrony with increasing distance but, not with altitude. The correlation between the neighbor districts decreases as the proportion of forest increases. Forested areas are suboptimum habitats and are strongly avoided by common voles. The investigation of spatiotemporal dynamics in animal populations is a key issue in ecology. Although the majority of studies are focused on testing hypotheses about which mechanisms are involved in shaping this dynamics it is crucial to understand the sources of variation involved in order to understand the underlying processes.     

INTRODUCTION

Foliage-feeding forest insects have served as model systems in the study of animal populations for more than 50 years. Early studies emphasized identification of "key" mortality agents or density-dependent sources of mortality. However, these efforts became burdened by rhetorical ambiguity, and population ecologists are increasingly focusing on characterizing population behavior and identifying the processes that generate that behavior. Two types of behavior seem to be common in forest insect populations: periodic oscillations ("population cycles") and spatial synchrony (synchronous fluctuations over large geographic areas). Several population processes (e.g., host–pathogen interactions) have been demonstrated to be capable of producing periodic oscillations, but the precise identity of these processes remains uncertain for most forest insects and presents a challenge to future research. As part of these efforts, a greater emphasis is needed on the use of statistical methods for detecting periodic behavior and for identifying other types of population behavior (e.g., equilibrium dynamics, limit cycles, transient dynamics). Spatial synchrony appears to be even more ubiquitous in forest insect populations. Dispersal and regional stochasticity ("Moran effect") have been shown to be capable of producing synchrony, but again more research is needed to determine the relative contribution of these processes to synchrony observed in natural populations. In addition, there is a need to search for other types of time–space patterns (e.g., traveling waves, spiral waves) in forest insect populations and to determine their causes. Received: April 25, 2000 / Accepted: September 22, 2000     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

The Moran effect revisited: spatial population synchrony under global warming

The world is spatially autocorrelated. Both abiotic and biotic properties are more similar among neighboring than distant locations, and their temporal co-fluctuations also decrease with distance. P. A. P. Moran realized the ecological importance of such ‘spatial synchrony’ when he predicted that isolated populations subject to identical log-linear density-dependent processes should have the same correlation in fluctuations of abundance as the correlation in environmental noise. The contribution from correlated weather to synchrony of populations has later been coined the ‘Moran effect’. Here, we investigate the potential role of the Moran effect in large-scale ecological outcomes of global warming. Although difficult to disentangle from dispersal and species interaction effects, there is compelling evidence from across taxa and ecosystems that spatial environmental synchrony causes population synchrony. Given this, and the accelerating number of studies reporting climate change effects on local population dynamics, surprisingly little attention has been paid to the implications of global warming for spatial population synchrony. However, a handful of studies of insects, birds, plants, mammals and marine plankton indicate decadal-scale changes in population synchrony due to trends in environmental synchrony. We combine a literature review with modeling to outline potential pathways for how global warming, through changes in the mean, variability and spatial autocorrelation of weather, can impact population synchrony over time. This is particularly likely under a ‘generalized Moran effect’, i.e. when relaxing Moran's strict assumption of identical log-linear density-dependence, which is highly unrealistic in the wild. Furthermore, climate change can influence spatial population synchrony indirectly, through its effects on dispersal and species interactions. Because changes in population synchrony may cascade through food-webs, we argue that the (generalized) Moran effect is key to understanding and predicting impacts of global warming on large-scale ecological dynamics, with implications for extinctions, conservation and management.     

Effects of range position,inter-annual variation and density on demographic transition rates of <Emphasis Type="Italic">Hornungia petraea</Emphasis> populations

The central-marginal model assumes unfavourable and more variable environmental conditions at the periphery of a species’ distribution range to negatively affect demographic transition rates, finally resulting in reduced population sizes and densities. Previous studies on density-dependence as a crucial factor regulating plant population growth have mainly focussed on fecundity and survival. Our objective is to analyse density-dependence in combination with the effect of inter-annual variation and range position on all life stages of an annual plant species, Hornungia petraea, including germination and seed incorporation into the seed bank. As previous studies on H. petraea had revealed a pattern opposite to existing theory with lower population densities at the distribution centre in Italy than at the periphery in Germany, we hypothesised that (1) demographic transition rates are lower, (2) the inter-annual variation in demographic transition rates is higher and (3) the intensity of density-dependence is weaker in Italy than in Germany. To analyse demographic transition rates, we used an autoregressive covariance strategy for repeated measures including density and inter-annual variation. All the three hypotheses were confirmed, but the impact of range position, density-dependence and inter-annual variation differed among the transition steps. All transition rates except fecundity were higher in the German populations than in the Italian populations. Germination rate and incorporation rate into the seed bank were strongly density-dependent. Central populations showed a larger inter-annual variation in fecundity and winter survival rate. Winter survival rate was the only transition step with a stronger density-dependence in peripheral populations. In most cases, these differences between distribution centre and periphery would not have emerged without taking density-dependence and inter-annual variation into account. We conclude that including range position, inter-annual variation and density-dependence in one single statistical model is an important tool for the interpretation of demographic patterns regarding the central-marginal model. Electronic Supplementary Material Supplementary material is available for this article at     

Dispersal and natural enemies interact to drive spatial synchrony and decrease stability in patchy populations

Spatial synchrony is widespread in natural populations but the mechanisms that underpin it are not yet fully understood. Two key biotic drivers of spatial synchrony have been identified: dispersal and trophic interactions (e.g. natural enemies). We used spatially structured, patchy bacterial populations to show that although increased dispersal always enhanced spatial synchrony of fluctuations in bacterial abundance, this effect was far stronger in the presence of a bacteriophage parasite. Bacteriophages drove strong within patch fluctuations in bacterial abundance that became phase locked through dispersal. Furthermore, the way in which stability, measured as constancy, responded to increasing dispersal was qualitatively different depending on whether parasites were present or not. Patch-level constancy decreased with dispersal in the presence of parasites, whereas dispersal increased patch-level constancy in the absence of parasites. Population-level constancy also decreased with dispersal in the presence of parasites, but was unaffected by dispersal in the absence of parasites. These contrasting patterns were likely due to the different role played by dispersal in the presence and absence of parasites, synchronizing dynamics in the former case and averaging stochastic fluctuations in the latter. Taken together, our findings suggest that dispersal and natural enemies can interact to drive spatially synchronous population fluctuations that decrease stability at both the patch and population level.     

Population synchrony and stability in environmentally forced metacommunities

A general prediction from simple metapopulation models is that spatially synchronized forcing can spatially synchronize population dynamics and destabilize metapopulations. In contrast, spatially asynchronous forcing is predicted to decrease population synchrony and promote temporal stability and population persistence, especially in the presence of dispersal. Only recently have studies begun to experimentally address these predictions. Moreover, few studies have experimentally examined how such processes operate in the context of competition communities. Stabilizing processes may continue to operate when placed within a metacommunity context with multiple competing consumers but only at low to intermediate levels of dispersal. High dispersal rates can reverse these predictions and lead to destabilization. We tested this under controlled conditions using an experimental aquatic system composed of three competing species of zooplankton. Metacommunities experienced different levels of dispersal and environmental forcing in the form of spatially synchronous or asynchronous pH perturbations. We found support that dispersal can have contrasting effects on population stability depending on the degree to which population dynamics were synchronized in space. Dispersal under synchronous forcing or no forcing had either neutral of positive effects on spatial population synchrony of all three zooplankton species. In these treatments, dispersal reduced population stability at the local and metapopulation levels for two of three species. In contrast, asynchronously varying environments reduced population synchrony relative to unforced systems, regardless of dispersal level. In these treatments, dispersal enhanced temporal stability and persistence of populations not by reducing population synchrony but by enhancing population minima and spatial averaging of abundances. High dispersal rates under asynchronous forcing reduced the abundance of one species, consistent with increasing regional competition and general metacommunity theory. However, no effects on its stability or persistence were observed. Our work highlights the context‐dependent effects of dispersal on population dynamics in varying environments.     

On the stabilization of animal numbers. Problems of testing

Summary When testing census data of insect populations for regulation, and/or for overall density dependence in the course of numbers over years, certain conditions, which follow from the testing models, should be fulfilled. Even if the series of densities may be considered a piece of first-order Markov chain (a necessary condition) significant test results need not obviously point to regulation of numbers by dominant density-dependent processes. Such a case is presented by the pine looper population at Hoge Veluwe studied by Klomp. A drastic drop in density from 1952 to 1953, which takes 78–97% of the log-density range (LR) over all years, most probably wrongly causes significant test results. This is supported by some simulation experiments. Moreover, we cannot be sure that the population was sufficiently isolated, i.e. that dispersal of adults from surrounding populations did not importantly influence population numbers. Among 6 Panolis-populations studied by Schwerdtfeger during 17 years a single one scored significantly with all tests. This resulted, however, from such a drastic drop in density that it covered the entire log-density range (LR=9.39), which therefore is wider than in any of the other (non-significant) populations. Another Panolis-population that maintained itself during 60 years, and which also scored significantly, most probably was kept within limits by supplementation of very low densities with immigrants, on the one hand, and by restriction of high densities by defoliation caused by other species, on the other. It is discussed whether this can be considered regulation, or results from spreading of risk. It is concluded that the range stability of particular populations must be considered generally to be the result of stabilization by both internal and external processes among which both density-dependent and density-independent processes play a significant part, and from which the contribution of the density-dependent processes need not be separated. The most interesting aspect of the stabilization of animal numbers is its relationship with the expected survival time of the population.Communication No. 402 of the Biological Station, Wijster     

Effects of population size on genetic diversity and seed production in the rare <Emphasis Type="Italic">Dictamnus albus</Emphasis>(Rutaceae) in central Germany

It is widely assumed that population size significantly affects the dynamics of plant populations. Smaller populations are threatened by genetic drift and inbreeding depression, both of which may result in a decrease of genetic variation and a resulting negative impact on plant fitness. In our study we analysed the patterns of random amplified polymorphic DNA (RAPD) variation among 10 Dictamnus albuspopulations of varying size. The aim was to examine local differentiation in relation to spatial isolation resulting from limited population size and geographical distancing between populations. Significant correlations were noted between population size and both percentage of polymorphic loci (P <0.01) and genetic diversity (P<0.01). The matrix correlation between genetic and geographical distances revealed that geographical differentiation was reflected in the RAPD profile (Mantel test: r²=0.34, P<0.001). We found the highest level of molecular variance of RAPD patterns among individuals within the populations (72.6%), whereas among-population variation accounted for only 21.6% of variation. These results were highly significant in that they indicated a restricted population differentiation, as would be expected from outcrossing species. An additional analysis of seed production showed that there was significant variation among populations in terms of mean seed number per flower and mean seed mass per population which could be attributed to differences in population size as well as levels of genetic variation.     

Population synchrony in small-world networks

Network topography ranges from regular graphs (linkage between nearest neighbours only) via small-world graphs (some random connections between nodes) to completely random graphs. Small-world linkage is seen as a revolutionary architecture for a wide range of social, physical and biological networks, and has been shown to increase synchrony between oscillating subunits. We study small-world topographies in a novel context: dispersal linkage between spatially structured populations across a range of population models. Regular dispersal between population patches interacting with density-dependent renewal provides one ecological explanation for the large-scale synchrony seen in the temporal fluctuations of many species, for example, lynx populations in North America, voles in Fennoscandia and grouse in the UK. Introducing a small-world dispersal kernel leads to a clear reduction in synchrony with both increasing dispersal rate and small-world dispersal probability across a variety of biological scenarios. Synchrony is also reduced when populations are affected by globally correlated noise. We discuss ecological implications of small-world dispersal in the frame of spatial synchrony in population fluctuations.     

Effects of environmental synchrony and density-dependent dispersal on temporal and spatial slopes of Taylor's law

Taylor's law (TL) is an empirical rule that describes an approximate relationship between the variance and mean of population density: log₁₀(variance) ≈ log₁₀(a) + b × log₁₀(mean). Population synchrony is another prevailing feature observed in empirical populations. This study investigated the effects of environmental synchrony and density-dependent dispersal on the temporal (b_T) and spatial (b_S) slopes of TL, using an empirical dataset of gray-sided vole populations and simulation analyses based on the second-order autoregressive (AR) model. Eighty-five empirical populations satisfied the temporal and spatial TLs with b_T = 1.943 (±SE 0.143) and b_S = 1.579 (±SE 0.136). The pairwise synchrony of population was 0.377 ± 0.199 (mean ± SD). Most simulated populations that obeyed the AR model satisfied the form of the temporal and spatial TLs without being affected by the environmental synchrony and density-dependent dispersal; however, those simulated slopes were too steep. The incorporation of environmental synchrony resulted in reduced simulated slopes, but those slopes, too, were still unrealistically steep. By incorporating density-dependent dispersal, simulated slopes decreased and fell within a realistic range. However, the simulated populations without environmental synchrony did not exhibit an adequate degree of density synchrony. In simulations that included both environmental synchrony and density-dependent dispersal, 92.7% of the simulated datasets provided realistic values for b_T, b_S and population synchrony. Because the two slopes were more sensitive to the variation of density-dependent dispersal than that of environmental synchrony, density-dependent dispersal may be the key to the determination of b_T and b_S.