Transformation starts at the periphery of networks where pushback is less.

Complex systems ranging from societies to ecological communities and power grids may be viewed as networks of connected elements. Such systems can go through critical transitions driven by an avalanche of contagious change. Here we ask, where in a complex network such a systemic shift is most likely to start. Intuitively, a central node seems the most likely source of such change. Indeed, topological studies suggest that central nodes can be the Achilles heel for attacks. We argue that the opposite is true for the class of networks in which all nodes tend to follow the state of their neighbors, a category we call two-way pull networks. In this case, a well-connected central node is an unlikely starting point of a systemic shift due to the buffering effect of connected neighbors. As a result, change is most likely to cascade through the network if it spreads first among relatively poorly connected nodes in the periphery. The probability of such initial spread is highest when the perturbation starts from intermediately connected nodes at the periphery, or more specifically, nodes with intermediate degree and relatively low closeness centrality. Our finding is consistent with empirical observations on social innovation, and may be relevant to topics as different as the sources of originality of art, collapse of financial and ecological networks and the onset of psychiatric disorders.

Five fundamental ways in which complex food webs may spiral out of control.

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these 'delayed negative feedbacks' may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large-scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food-web patterns are sufficient to prevent abrupt, large-scale transitions under global environmental change.

Linking human impacts to community processes in terrestrial and freshwater ecosystems.

Human impacts such as habitat loss, climate change and biological invasions are radically altering biodiversity, with greater effects projected into the future. Evidence suggests human impacts may differ substantially between terrestrial and freshwater ecosystems, but the reasons for these differences are poorly understood. We propose an integrative approach to explain these differences by linking impacts to four fundamental processes that structure communities: dispersal, speciation, species-level selection and ecological drift. Our goal is to provide process-based insights into why human impacts, and responses to impacts, may differ across ecosystem types using a mechanistic, eco-evolutionary comparative framework. To enable these insights, we review and synthesise (i) how the four processes influence diversity and dynamics in terrestrial versus freshwater communities, specifically whether the relative importance of each process differs among ecosystems, and (ii) the pathways by which human impacts can produce divergent responses across ecosystems, due to differences in the strength of processes among ecosystems we identify. Finally, we highlight research gaps and next steps, and discuss how this approach can provide new insights for conservation. By focusing on the processes that shape diversity in communities, we aim to mechanistically link human impacts to ongoing and future changes in ecosystems.

Foreseeing the future of mutualistic communities beyond collapse.

Changing conditions may lead to sudden shifts in the state of ecosystems when critical thresholds are passed. Some well-studied drivers of such transitions lead to predictable outcomes such as a turbid lake or a degraded landscape. Many ecosystems are, however, complex systems of many interacting species. While detecting upcoming transitions in such systems is challenging, predicting what comes after a critical transition is terra incognita altogether. The problem is that complex ecosystems may shift to many different, alternative states. Whether an impending transition has minor, positive or catastrophic effects is thus unclear. Some systems may, however, behave more predictably than others. The dynamics of mutualistic communities can be expected to be relatively simple, because delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. Here, we address the question of whether this relative simplicity allows us to foresee a community's future state. As a case study, we use a model of a bipartite mutualistic network and show that a network's post-transition state is indicated by the way in which a system recovers from minor disturbances. Similar results obtained with a unipartite model of facilitation suggest that our results are of relevance to a wide range of mutualistic systems.

Finding the direction of lowest resilience in multivariate complex systems.

The dynamics of complex systems, such as ecosystems, financial markets and the human brain, emerge from the interactions of numerous components. We often lack the knowledge to build reliable models for the behaviour of such network systems. This makes it difficult to predict potential instabilities. We show that one could use the natural fluctuations in multivariate time series to reveal network regions with particularly slow dynamics. The multidimensional slowness points to the direction of minimal resilience, in the sense that simultaneous perturbations on this set of nodes will take longest to recover. We compare an autocorrelation-based method with a variance-based method for different time-series lengths, data resolution and different noise regimes. We show that the autocorrelation-based method is less robust for short time series or time series with a low resolution but more robust for varying noise levels. This novel approach may help to identify unstable regions of multivariate systems or to distinguish safe from unsafe perturbations.

The sudden collapse of pollinator communities.

Declines in pollinator populations may harm biodiversity and agricultural productivity. Little attention has, however, been paid to the systemic response of mutualistic communities to global environmental change. Using a modelling approach and merging network theory with theory on critical transitions, we show that the scale and nature of critical transitions is likely to be influenced by the architecture of mutualistic networks. Specifically, we show that pollinator populations may collapse suddenly once drivers of pollinator decline reach a critical point. A high connectance and/or nestedness of the mutualistic network increases the capacity of pollinator populations to persist under harsh conditions. However, once a tipping point is reached, pollinator populations collapse simultaneously. Recovering from this single community-wide collapse requires a relatively large improvement of conditions. These findings may have large implications for our view on the sustainability of pollinator communities and the services they provide.