Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world ...systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions.
The concept of ecological stability occupies a prominent place in both fundamental and applied ecological research. We review decades of work on the topic and examine how our understanding has ...progressed. We show that our understanding of stability has remained fragmented and is limited largely to simple or simplified systems. There has been a profusion of metrics proposed to quantify stability, of which only a handful are used commonly. Furthermore, studies typically quantify one to two metrics of stability at a time and in response to a single perturbation, with some of the main environmental pressures of today being the least studied. We argue that we need to build on the existing consensus and strong theoretical foundation of the stability concept to better understand its multidimensionality and the interdependencies between metrics, levels of organisation and types of perturbations. Only by doing so can we make progress in the quantification of stability in theory and in practice, and eventually build a more comprehensive understanding of how ecosystems will respond to ongoing environmental change.
A rich body of knowledge links biodiversity to ecosystem functioning (BEF), but it is primarily focused on small scales. We review the current theory and identify six expectations for scale ...dependence in the BEF relationship: (1) a nonlinear change in the slope of the BEF relationship with spatial scale; (2) a scale‐dependent relationship between ecosystem stability and spatial extent; (3) coexistence within and among sites will result in a positive BEF relationship at larger scales; (4) temporal autocorrelation in environmental variability affects species turnover and thus the change in BEF slope with scale; (5) connectivity in metacommunities generates nonlinear BEF and stability relationships by affecting population synchrony at local and regional scales; (6) spatial scaling in food web structure and diversity will generate scale dependence in ecosystem functioning. We suggest directions for synthesis that combine approaches in metaecosystem and metacommunity ecology and integrate cross‐scale feedbacks. Tests of this theory may combine remote sensing with a generation of networked experiments that assess effects at multiple scales. We also show how anthropogenic land cover change may alter the scaling of the BEF relationship. New research on the role of scale in BEF will guide policy linking the goals of managing biodiversity and ecosystems.
We address the challenge of scale for biodiversity and ecosystem functioning (BEF) research. We review current theory and identify six expectations for scale dependence in the BEF relationship. We suggest directions for synthesis that combine theoretical and empirical methods and suggest their application to human transformed landscapes.
Species are linked to each other by a myriad of positive and negative interactions. This complex spectrum of interactions constitutes a network of links that mediates ecological communities' response ...to perturbations, such as exploitation and climate change. In the last decades, there have been great advances in the study of intricate ecological networks. We have, nonetheless, lacked both the data and the tools to more rigorously understand the patterning of multiple interaction types between species (i.e., "multiplex networks"), as well as their consequences for community dynamics. Using network statistical modeling applied to a comprehensive ecological network, which includes trophic and diverse non-trophic links, we provide a first glimpse at what the full "entangled bank" of species looks like. The community exhibits clear multidimensional structure, which is taxonomically coherent and broadly predictable from species traits. Moreover, dynamic simulations suggest that this non-random patterning of how diverse non-trophic interactions map onto the food web could allow for higher species persistence and higher total biomass than expected by chance and tends to promote a higher robustness to extinctions.
How multiple types of non-trophic interactions map onto trophic networks in real communities remains largely unknown. We present the first effort, to our knowledge, describing a comprehensive ...ecological network that includes all known trophic and diverse non-trophic links among >100 coexisting species for the marine rocky intertidal community of the central Chilean coast. Our results suggest that non-trophic interactions exhibit highly nonrandom structures both alone and with respect to food web structure. The occurrence of different types of interactions, relative to all possible links, was well predicted by trophic structure and simple traits of the source and target species. In this community, competition for space and positive interactions related to habitat/refuge provisioning by sessile and/or basal species were by far the most abundant non-trophic interactions. If these patterns are corroborated in other ecosystems, they may suggest potentially important dynamic constraints on the combined architecture of trophic and non-trophic interactions. The nonrandom patterning of non-trophic interactions suggests a path forward for developing a more comprehensive ecological network theory to predict the functioning and resilience of ecological communities.
A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early ...warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.
Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can ...happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called 'early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.
Facilitation occurs when one species positively impacts the fitness of another, and has predominantly been studied in free-living species like plants. Facilitation can also occur among symbiont ...(mutualistic or parasitic) species or strains, but equivalent studies are scarce. To advance an integrated view of the effect of facilitation on symbiont ecology and evolution, we review empirical evidence and their underlying mechanisms, explore the factors favouring its emergence, and discuss its consequences for virulence and transmission. We argue that the facilitation concept can improve understanding of the evolutionary forces shaping symbiont communities and their effects on hosts.
Ecosystem responses to external changes can surprise us by their abruptness and irreversibility. Models have helped identifying indicators of impending catastrophic shifts, referred to as 'generic ...early warning signals'. These indicators are linked to a phenomenon known as 'critical slowing down' which describes the fact that the recovery rate of a system after a perturbation decreases when the system approaches a bifurcation — such as the classical fold bifurcation associated to catastrophic shifts. However, contrary to what has sometimes been suggested in the literature, a decrease in recovery rate cannot be considered as specific to approaching catastrophic shifts. Here, we analyze the behavior of early warning signals based on critical slowing down in systems approaching a range of catastrophic and non-catastrophic situations. Our results show that slowing down generally happens in situations where a system is becoming increasingly sensitive to external perturbations, independently of whether the impeding change is catastrophic or not. These results highlight that indicators specific to catastrophic shifts are still lacking. More importantly, they also imply that in systems where we have no reason to expect catastrophic transitions, slowing down may still be used in a more general sense as a warning signal for a potential decrease in stability.
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