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.

Various complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These ‘tipping points’ are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

The surge of post-truth political argumentation suggests that we are living in a special historical period when it comes to the balance between emotion and reasoning. To explore if this is indeed the case, we analyze language in millions of books covering the period from 1850 to 2019 represented in Google nGram data. We show that the use of words associated with rationality, such as “determine” and “conclusion,” rose systematically after 1850, while words related to human experience such as “feel” and “believe” declined. This pattern reversed over the past decades, paralleled by a shift from a collectivistic to an individualistic focus as reflected, among other things, by the ratio of singular to plural pronouns such as “I”/”we” and “he”/”they.” Interpreting this synchronous sea change in book language remains challenging. However, as we show, the nature of this reversal occurs in fiction as well as nonfiction. Moreover, the pattern of change in the ratio between sentiment and rationality flag words since 1850 also occurs in New York Times articles, suggesting that it is not an artifact of the book corpora we analyzed. Finally, we show that word trends in books parallel trends in corresponding Google search terms, supporting the idea that changes in book language do in part reflect changes in interest. All in all, our results suggest that over the past decades, there has been a marked shift in public interest from the collective to the individual, and from rationality toward emotion.

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.