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  1. Abstract

    In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE and establish the existence of travelling waves. In particular, we consider the time dependent spatial mesh adaptation method that aims to equidistribute the arclength of the solution under consideration. We assume that this equidistribution is strictly enforced, which leads to the non-local problem with infinite range interactions that we derived in Hupkes and Van Vleck (J Dyn Differ Eqn, 2021). Using the Fredholm theory developed in Hupkes and Van Vleck (J Dyn Differ Eqn, 2021) we setup a fixed point procedure that enables the travelling PDE waves to be lifted to our spatially discrete setting.

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  2. Abstract

    Spatial synchrony may be tail‐dependent, that is, stronger when populations are abundant than scarce, or vice‐versa. Here, ‘tail‐dependent’ follows from distributions having a lower tail consisting of relatively low values and an upper tail of relatively high values. We present a general theory of how the distribution and correlation structure of an environmental driver translates into tail‐dependent spatial synchrony through a non‐linear response, and examine empirical evidence for theoretical predictions in giant kelp along the California coastline. In sheltered areas, kelp declines synchronously (lower‐tail dependence) when waves are relatively intense, because waves below a certain height do little damage to kelp. Conversely, in exposed areas, kelp is synchronised primarily by periods of calmness that cause shared recovery (upper‐tail dependence). We find evidence for geographies of tail dependence in synchrony, which helps structure regional population resilience: areas where population declines are asynchronous may be more resilient to disturbance because remnant populations facilitate reestablishment.

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  3. Abstract

    Synchronous dynamics (fluctuations that occur in unison) are universal phenomena with widespread implications for ecological stability. Synchronous dynamics can amplify the destabilizing effect of environmental variability on ecosystem functions such as productivity, whereas the inverse, compensatory dynamics, can stabilize function. Here we combine simulation and empirical analyses to elucidate mechanisms that underlie patterns of synchronous versus compensatory dynamics. In both simulated and empirical communities, we show that synchronous and compensatory dynamics are not mutually exclusive but instead can vary by timescale. Our simulations identify multiple mechanisms that can generate timescale‐specific patterns, including different environmental drivers, diverse life histories, dispersal, and non‐stationary dynamics. We find that traditional metrics for quantifying synchronous dynamics are often biased toward long‐term drivers and may miss the importance of short‐term drivers. Our findings indicate key mechanisms to consider when assessing synchronous versus compensatory dynamics and our approach provides a pathway for disentangling these dynamics in natural systems.

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  4. Abstract

    Synchrony is broadly important to population and community dynamics due to its ubiquity and implications for extinction dynamics, system stability, and species diversity. Investigations of synchrony in community ecology have tended to focus on covariance in the abundances of multiple species in a single location. Yet, the importance of regional environmental variation and spatial processes in community dynamics suggests that community properties, such as species richness, could fluctuate synchronously across patches in a metacommunity, in an analog of population spatial synchrony. Here, we test the prevalence of this phenomenon and the conditions under which it may occur using theoretical simulations and empirical data from 20 marine and terrestrial metacommunities. Additionally, given the importance of biodiversity for stability of ecosystem function, we posit that spatial synchrony in species richness is strongly related to stability. Our findings show that metacommunities often exhibit spatial synchrony in species richness. We also found that richness synchrony can be driven by environmental stochasticity and dispersal, two mechanisms of population spatial synchrony. Richness synchrony also depended on community structure, including species evenness and beta diversity. Strikingly, ecosystem stability was more strongly related to richness synchrony than to species richness itself, likely because richness synchrony integrates information about community processes and environmental forcing. Our study highlights a new approach for studying spatiotemporal community dynamics and emphasizes the spatial dimensions of community dynamics and stability.

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  5. Abstract

    Population cycles are fundamentally linked with spatial synchrony, the prevailing paradigm being that populations with cyclic dynamics are easily synchronised. That is, population cycles help give rise to spatial synchrony. Here we demonstrate this process can work in reverse, with synchrony causing population cycles. We show that timescale‐specific environmental effects, by synchronising local population dynamics on certain timescales only, cause major population cycles over large areas in white‐tailed deer. An important aspect of the new mechanism is specificity of synchronising effects to certain timescales, which causes local dynamics to sum across space to a substantial cycle on those timescales. We also demonstrate, to our knowledge for the first time, that synchrony can be transmitted not only from environmental drivers to populations (deer), but also from there to human systems (deer‐vehicle collisions). Because synchrony of drivers may be altered by climate change, changes to population cycles may arise via our mechanism.

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  6. Abstract

    Fluctuations in population abundances are often correlated through time across multiple locations, a phenomenon known as spatial synchrony. Spatial synchrony can exhibit complex spatial structures, termed ‘geographies of synchrony’, that can reveal mechanisms underlying population fluctuations. However, most studies have focused on spatial extents of 10s to 100s of kilometres, making it unclear how synchrony concepts and approaches should apply to dynamics at finer spatial scales.

    We used network analyses, multiple regression on similarity matrices, and wavelet coherence analyses to examine micro‐scale synchrony and geographies of synchrony, over distances up to 30 m, in a serpentine grassland plant community.

    We found that species' populations exhibited a geography of synchrony even over such short distances. Often, well‐synchronized populations were geographically separate, a spatial structure that was shaped mainly by gopher disturbance and dispersal limitation, and to a lesser extent by relationships with other plant species. Precipitation was a significant driver of site‐ and community‐wide temporal dynamics. Gopher disturbance appeared to drive synchrony on 2‐ to 6‐year timescales, and we detected coherent fluctuations among pairs of focal plant taxa.

    Synthesis. Micro‐geographies of synchrony are an intriguing phenomenon that may also help us better understand community dynamics. Additionally, the related geographies of synchrony and coherent temporal dynamics among some species pairs indicate that incorporating interspecific interactions can improve understanding of population spatial synchrony.

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  7. Abstract

    Periodical cicadas exhibit an extraordinary capacity for self‐organizing spatially synchronous breeding behavior. The regular emergence of periodical cicada broods across the United States is a phenomenon of longstanding public and scientific interest, as the cicadas of each brood emerge in huge numbers and briefly dominate their ecosystem. During the emergence, the 17‐year periodical cicada speciesMagicicada cassiniis found to form synchronized choruses, and we investigated their chorusing behavior from the standpoint of spatial synchrony.

    Cicada choruses were observed to form in trees, calling regularly every five seconds. In order to determine the limits of this self‐organizing behavior, we set out to quantify the spatial synchronization between cicada call choruses in different trees, and how and why this varies in space and time.

    We performed 20 simultaneous recordings in Clinton State Park, Kansas, in June 2015 (Brood IV), with a team of citizen‐science volunteers using consumer equipment (smartphones). We use a wavelet approach to show in detail how spatially synchronous, self‐organized chorusing varies across the forest.

    We show how conditions that increase the strength of audio interactions between cicadas also increase the spatial synchrony of their chorusing. Higher forest canopy light levels increase cicada activity, corresponding to faster and higher‐amplitude chorus cycling and to greater synchrony of cycles across space. We implemented a relaxation‐oscillator‐ensemble model of interacting cicadas, finding that a tendency to call more often, driven by light levels, results in all these effects.

    Results demonstrate how the capacity to self‐organize in ecology depends sensitively on environmental conditions. Spatially correlated modulation of cycling rate by an external driver can also promote self‐organization of phase synchrony.

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  8. Abstract

    Extreme climatic events (ECEs) are becoming more frequent and more intense due to climate change. Furthermore, there is reason to believe ECEs may modify tail associations between distinct population vital rates, or between values of an environmental variable measured in different locations. Tail associations between two variables are associations that occur between values in the left or right tails of the distributions of the variables. Two positively associated variables can be principally left‐tail associated (i.e., more correlated when they take low values than when they take high values) or right‐tail associated (more correlated when they take high than low values), even with the same overall correlation coefficient in both cases. We tested, in the context of non‐spatial stage‐structured matrix models, whether tail associations between stage‐specific vital rates may influence extinction risk. We also tested whether the nature of spatial tail associations of environmental variables can influence metapopulation extinction risk. For instance, if low values of an environmental variable reduce the growth rates of local populations, one may expect that left‐tail associations increase metapopulation extinction risks because then environmental catastrophes are spatially synchronized, presumably reducing the potential for rescue effects. For the non‐spatial, stage‐structured models we considered, left‐tail associations between vital rates did accentuate extinction risk compared to right‐tail associations, but the effect was small. In contrast, we showed that density dependence interacts with tail associations to influence metapopulation extinction risk substantially: For population models showing undercompensatory density dependence, left‐tail associations in environmental variables often strongly accentuated and right‐tail associations mitigated extinction risk, whereas the reverse was usually true for models showing overcompensatory density dependence. Tail associations and their asymmetries are taken into account in assessing risks in finance and other fields, but to our knowledge, our study is one of the first to consider how tail associations influence population extinction risk. Our modeling results provide an initial demonstration of a new mechanism influencing extinction risks and, in our view, should help motivate more comprehensive study of the mechanism and its importance for real populations in future work.

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  9. Abstract

    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.

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  10. Abstract

    Understanding the mechanisms governing ecological stability—why a property such as primary productivity is stable in some communities and variable in others—has long been a focus of ecology. Compensatory dynamics, in which anti‐synchronous fluctuations between populations buffer against fluctuations at the community level, are a key theoretical mechanism of stability. Classically, compensatory dynamics have been quantified using a variance ratio approach that compares the ratio between community variance and aggregate population variance, such that a lower ratio indicates compensation and a higher ratio indicates synchrony among species fluctuations. However, population dynamics may be influenced by different drivers that operate on different timescales, and evidence from aquatic systems indicates that communities can be compensatory on some timescales and synchronous on others. The variance ratio and related metrics cannot reflect this timescale specificity, yet have remained popular, especially in terrestrial systems. Here, we develop a timescale‐specific variance ratio approach that formally decomposes the classical variance ratio according to the timescales of distinct contributions. The approach is implemented in a new R package, called tsvr, that accompanies this paper. We apply our approach to a long‐term, multisite grassland community dataset. Our approach demonstrates that the degree of compensation vs. synchrony in community dynamics can vary by timescale. Across sites, population variability was typically greater over longer compared to shorter timescales. At some sites, minimal timescale specificity in compensatory dynamics translated this pattern of population variability into a similar pattern of greater community variability on longer compared to shorter timescales. But at other sites, differentially stronger compensatory dynamics at longer compared to shorter timescales produced lower‐than‐expected community variability on longer timescales. Within every site, there were plots that exhibited shifts in the strength of compensation between timescales. Our results highlight that compensatory vs. synchronous dynamics are intrinsically timescale‐dependent concepts, and our timescale‐specific variance ratio provides a metric to quantify timescale specificity and relate it back to the classic variance ratio.

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