Transient synchronization following invasion: revisiting Moran’s model and a case study

Opposing Patterns of Spatial Synchrony in Lyme Disease Incidence

Incidence of Lyme disease, a tick-borne illness prevalent in the US, is increasing in endemic regions and regions with no previous history of the disease, significantly impacting public health. We examined space-time patterns of Lyme disease incidence and the influence of ecological and social factors on spatial synchrony, i.e., correlated incidence fluctuations across US counties. Specifically, we addressed these questions: Does Lyme disease incidence exhibit spatial synchrony? If so, what geographic patterns does Lyme disease synchrony exhibit? Are geographic patterns of disease synchrony related to weather, land cover, access to health care, or tick-borne disease awareness? How do effects of these variables on Lyme disease synchrony differ geographically? We used network analysis and matrix regression to examine geographical patterns of Lyme disease synchrony and their potential mechanisms in 399 counties in the eastern and Midwestern US. We found two distinct regions of synchrony in Northeast and upper Midwest regions exhibiting opposing temporal fluctuations in incidence. Spatial patterns of Lyme disease synchrony were partly explained by land cover, weather, poverty, and awareness of tick-borne illness, with significant predictive variables changing regionally. However, the two regions may have become more synchronous over time, potentially leading to higher-amplitude nation-wide fluctuations in disease incidence.

Drivers of amphibian population dynamics and asynchrony at local and regional scales

Identifying the drivers of population fluctuations in spatially distinct populations remains a significant challenge for ecologists. Whereas regional climatic factors may generate population synchrony (i.e. the Moran effect), local factors including the level of density dependence may reduce the level of synchrony. Although divergences in the scaling of population synchrony and spatial environmental variation have been observed, the regulatory factors that underlie such mismatches are poorly understood. Few previous studies have investigated how density-dependent processes and population-specific responses to weather variation influence spatial synchrony at both local and regional scales. We addressed this issue in a pond-breeding amphibian, the great crested newt Triturus cristatus. We used capture-recapture data collected through long-term surveys in five T. cristatus populations in Western Europe. In all populations-and subpopulations within metapopulations-population size, annual survival and recruitment fluctuated over time. Likewise, there was considerable variation in these demographic rates between populations and within metapopulations. These fluctuations and variations appear to be context-dependent and more related to site-specific characteristics than local or regional climatic drivers. We found a low level of demographic synchrony at both local and regional levels. Weather has weak and spatially variable effects on survival, recruitment and population growth rate. In contrast, density dependence was a common phenomenon (at least for population growth) in almost all populations and subpopulations. Our findings support the idea that the Moran effect is low in species where the population dynamics more closely depends on local factors (e.g. population density and habitat characteristics) than on large-scale environmental fluctuation (e.g. regional climatic variation). Such responses may have far-reaching consequences for the long-term viability of spatially structured populations and their ability to respond to large-scale climatic anomalies.

Sampling to elucidate the dynamics of infections in reservoir hosts

The risk of zoonotic spillover from reservoir hosts, such as wildlife or domestic livestock, to people is shaped by the spatial and temporal distribution of infection in reservoir populations. Quantifying these distributions is a key challenge in epidemiology and disease ecology that requires researchers to make trade-offs between the extent and intensity of spatial versus temporal sampling. We discuss sampling methods that strengthen the reliability and validity of inferences about the dynamics of zoonotic pathogens in wildlife hosts. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.

Temporal scale of environmental correlations affects ecological synchrony

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

Transient synchrony among populations of five foliage-feeding Lepidoptera

Studies of transient population dynamics have largely focused on temporal changes in dynamical behaviour, such as the transition between periods of stability and instability. This study explores a related dynamic pattern, namely transient synchrony during a 49-year period among populations of five sympatric species of forest insects that share host tree resources. The long time series allows a more comprehensive exploration of transient synchrony patterns than most previous studies. Considerable variation existed in the dynamics of individual species, ranging from periodic to aperiodic. We used time-averaged methods to investigate long-term patterns of synchrony and time-localized methods to detect transient synchrony. We investigated transient patterns of synchrony between species and related these to the species' varying density dependence structures; even species with very different density dependence exhibited at least temporary periods of synchrony. Observed periods of interspecific synchrony may arise from interactions with host trees (e.g., induced host defences), interactions with shared natural enemies or shared impacts of environmental stochasticity. The transient nature of synchrony observed here raises questions both about the identity of synchronizing mechanisms and how these mechanisms interact with the endogenous dynamics of each species. We conclude that these patterns are the result of interspecific interactions that act only temporarily to synchronize populations, after which differences in the endogenous population dynamics among the species acts to desynchronize their dynamics.

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.

Using multivariate cross correlations, Granger causality and graphical models to quantify spatiotemporal synchronization and causality between pest populations

Background

This work combines multivariate time series analysis and graph theory to detect synchronization and causality among certain ecological variables and to represent significant correlations via network projections. Four different statistical tools (cross-correlations, partial cross-correlations, Granger causality and partial Granger causality) utilized to quantify correlation strength and causality among biological entities. These indices correspond to different ways to estimate the relationships between different variables and to construct ecological networks using the variables as nodes and the indices as edges. Specifically, correlations and Granger causality indices introduce rules that define the associations (links) between the ecological variables (nodes). This approach is used for the first time to analyze time series of moth populations as well as temperature and relative humidity in order to detect spatiotemporal synchronization over an agricultural study area and to illustrate significant correlations and causality interactions via graphical models.

Results

The networks resulting from the different approaches are trimmed and show how the network configurations are affected by each construction technique. The Granger statistical rules provide a simple test to determine whether one series (population) is caused by another series (i.e. environmental variable or other population) even when they are not correlated. In most cases, the statistical analysis and the related graphical models, revealed intra-specific links, a fact that may be linked to similarities in pest population life cycles and synchronizations. Graph theoretic landscape projections reveal that significant associations in the populations are not subject to landscape characteristics. Populations may be linked over great distances through physical features such as rivers and not only at adjacent locations in which significant interactions are more likely to appear. In some cases, incidental connections, with no ecological explanation, were also observed; however, this was expected because some of the statistical methods used to define non trivial associations show connections that cannot be interpreted phenomenologically.

Conclusions

Incorporating multivariate causal interactions in a probabilistic sense comes closer to reality than doing per se binary theoretic constructs because the former conceptually incorporate the dynamics of all kinds of ecological variables within the network. The advantage of Granger rules over correlations is that Granger rules have dynamic features and provide an easy way to examine the dynamic causal relations of multiple time-series variables. The constructed networks may provide an intuitive, advantageous representation of multiple populations’ associations that can be realized within an agro-ecosystem. These relationships may be due to life cycle synchronizations, exposure to a shared climate or even more complicated ecological interactions such as moving behavior, dispersal patterns and host allocation. Moreover, they are useful for drawing inferences regarding pest population dynamics and their spatial management. Extending these models by including more variables should allow the exploration of intra and interspecies relationships in larger ecological systems, and the identification of specific population traits that might constrain their structures in larger areas.

Electronic supplementary material

The online version of this article (doi:10.1186/s12898-016-0087-7) contains supplementary material, which is available to authorized users.

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.

Long-term shifts in the cyclicity of outbreaks of a forest-defoliating insect

Recent collapses of population cycles in several species highlight the mutable nature of population behavior as well as the potential role of human-induced environmental change in causing population dynamics to shift. We investigate changes in the cyclicity of gypsy moth (Lymantria dispar) outbreaks by applying wavelet analysis to an 86-year time series of forest defoliation in the northeastern United States. Gypsy moth population dynamics shifted on at least four occasions during the study period (1924-2009); strongly cyclical outbreaks were observed between ca. 1943-1965 and ca. 1978-1996, with noncyclical dynamics in the intervening years. During intervals of cyclical dynamics, harmonic oscillations at cycle lengths of 4-5 and 8-10 years co-occurred. Cross-correlation analyses indicated that the intensity of suppression efforts (area treated by insecticide application) did not significantly reduce the total area of defoliation across the region in subsequent years, and no relationship was found between insecticide use and the cyclicity of outbreaks. A gypsy moth population model incorporating empirically based trophic interactions produced shifting population dynamics similar to that observed in the defoliation data. Gypsy moth cycles were the result of a high-density limit cycle driven by a specialist pathogen. Though a generalist predator did not produce an alternative stable equilibrium, cyclical fluctuations in predator density did generate extended intervals of noncyclical behavior in the gypsy moth population. These results suggest that changes in gypsy moth population behavior are driven by trophic interactions, rather than by changes in climatic conditions frequently implicated in other systems.

Spatial synchrony propagates through a forest food web via consumer-resource interactions

In many study systems, populations fluctuate synchronously across large regions. Several mechanisms have been advanced to explain this, but their importance in nature is often uncertain. Theoretical studies suggest that spatial synchrony initiated in one species through Moran effects may propagate among trophically linked species, but evidence for this in nature is lacking. By applying the nonparametric spatial correlation function to time series data, we discover that densities of the gypsy moth, the moth's chief predator (the white-footed mouse), and the mouse's winter food source (red oak acorns) fluctuate synchronously over similar distances (approximately1000 km) and with similar levels of synchrony. In addition, we investigate the importance of consumer-resource interactions in propagating synchrony among species using an empirically informed simulation model of interactions between acorns, the white-footed mouse, the gypsy moth, and a viral pathogen of the gypsy moth. Our results reveal that regional stochasticity acting directly on populations of the mouse, moth, or pathogen likely has little effect on levels of the synchrony displayed by these species. In contrast, synchrony in mast seeding can propagate across trophic levels, thus explaining observed levels of synchrony in both white-footed mouse and gypsy moth populations. This work suggests that the transfer of synchrony among trophically linked species may be a major factor causing interspecific synchrony.