Stability and Fluctuations in Complex Ecological Systems

From 08-12 August, 2022, 32 individuals participated in a workshop, Stability and Fluctuations in Complex Ecological Systems, at the Lorentz Center, located in Leiden, The Netherlands. An interdisciplinary dialogue between ecologists, mathematicians, and physicists provided a foundation of important problems to consider over the next 5-10 years. This paper outlines eight areas including (1) improving our understanding of the effect of scale, both temporal and spatial, for both deterministic and stochastic problems; (2) clarifying the different terminologies and definitions used in different scientific fields; (3) developing a comprehensive set of data analysis techniques arising from different fields but which can be used together to improve our understanding of existing data sets; (4) having theoreticians/computational scientists collaborate closely with empirical ecologists to determine what new data should be collected; (5) improving our knowledge of how to protect and/or restore ecosystems; (6) incorporating socio-economic effects into models of ecosystems; (7) improving our understanding of the role of deterministic and stochastic fluctuations; (8) studying the current state of biodiversity at the functional level, taxa level and genome level.Comment: 22 page

Dynamics of complex systems inferred from multivariate time series

Complex systems are systems whose behaviour arises from the interaction between different elements. The dynamics of complex systems are highly unpredictable and are characterized by interactions on different scales and nonlinear responses. In chapter 1 I describe how these properties complicate the analysis of complex systems. Additionally, I explain that the analysis of complex systems requires a range of approaches, such as simplistic models, realistic models, experiments, and time series analysis. The latter is the focus of this thesis.Two popular tools to analyze complex systems are resilience indicators and complexity indicators. In chapter 2 I address the use of these indicators, with applications to systems related to human physiology. I explore how resilience indicators can be used to infer a systems capacity to recover from small perturbations and can be used to signal upcoming `tipping points' related to some diseases, such as atrial fibrillation or depression. Complexity indicators can be used to infer when a system loses responsiveness and can be used to infer a loss of complexity which is related to old age and some diseases such as congestive heart failure. I propose that the variables that constitute `the human system' have different functions. Some variables aim for homeostasis, i.e. they seek an equilibrium. For these variables, their capacity to recover seems like a good statistic to quantify their functioning. Other variables aim for high responsiveness. For these variables, their complexity seems like a good statistic to quantify their functioning.Currently, the most popular methods to infer a system's resilience are autocorrelation and variance of a time series. As these quantification tools are based on single time series, it is not always clear how to adapt these tools to multivariate complex systems. In Chapter 3 I propose a novel usage of a known statistical tool called Min/Max Autocorrelation Factors (MAF). This tool was developed as an alternative to PCA, but instead of finding the direction of highest variance (as with PCA), it finds the direction of the highest autocorrelation. I propose that this direction of highest autocorrelation can be used to tell which perturbation in the system is most dangerous, in the sense that perturbations in this direction will lead to the slowest recovery of the system. Furthermore, if the system is subject to tipping points, this ‘dangerous direction’ will likely also be the direction where the system can most easily shift to another state.An obvious next question is what this future state might look like. This question is addressed in chapter 4. We use the fact that most complex behaviour, such as oscillations or reactivity, arise from delayed negative feedbacks. Therefore, positive feedbacks, which are at the core of mutualistic networks, are expected to give rise to relatively simple dynamics. We find that this relative simplicity allows for extrapolation of the direction of lowest resilience, found by PCA in this chapter, to predict the future state after a tipping point has passed. Therefore, this tool is a valuable addition to our toolbox to analyse complex systems as it provides a way to predict not just when something is about to happen, but also what might happen.A clear comparison between different multivariate indicators of resilience is lacking. Therefore in chapter 5 I investigate how different methods relate to one another, if there are methods that are preferred over others and under which conditions the different methods are expected to correctly predict an upcoming tipping point. I demonstrate that there is not one best indicator to warn for an upcoming transition, but that instead it depends on the scenario that the system is subject to. Furthermore, this chapter demonstrates that all methods become unreliable when not all variables can be observed. As this scenario is extremely relevant for empirical studies, where one can never be sure that all variables are included, this suggests a cautious interpretation of all work on multivariate resilience indicators.In chapters 6-7 I explore the applications of time series analysis tools for complex systems to two real world datasets. In chapter 6, I systematically analyze word-use in millions of books from 1850-2019. I demonstrate that there are two dominant modes of change. The first captures the general trends of world popularity over time. The second mode disentangles human nature related words, such as pronouns and emotions, from words related to rational decision and procedures. I demonstrate that the ‘rational’ words show a steady increase from 1850-1980, followed by a drop. The words related to humans/emotions show the opposite behaviour. We propose that the current increase of sentiment laden words, could be a reaction to several decades of rational thinking. The fact that the strong increase in sentiment laden words is accompanied by an increase in the use of facebook, suggests that this shift from rational thinking to intuitive thinking is strengthened by the increasing popularity of social media.In chapter 7 I use climate data of the past 800.000 years to infer causal links in the carbon cycle. I use sediment cores to determine Ba/Fe (a proxy for biological productivity), δ18O (a proxy for climate and ice cover), and δ13C (a proxy for ocean ventilation) and ice cores to determine dust and CO2 (a proxy for climate and alkalinity). One mystery of the glacial-interglacial cycles is their saw-tooth shape of slow cooling and rapid warming, which hints at the existence of nonlinear processes in the system, such as a feedback loop. As all possible links have been described, it is hard to pinpoint the dominant drivers. Here, I demonstrate that a causal detection method based on Taken's theorem (convergent cross-mapping) can elucidate causal links in the system and results in one dominant causal loop from ocean ventilation to biological productivity to climate back to ocean ventilation. This loop forms a potential explanation for the shape of the glacial-interglacial cycles.In chapter 8 I reflect on the findings of the previous chapters, bring up some scientific considerations that I learned about while performing the work presented here, and share ideas for future studies

The rise and fall of rationality in language

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

Anticipating the direction of symptom progression using critical slowing down: a proof-of-concept study

Background As complex dynamic systems approach a transition, their dynamics change. This process, called critical slowing down (CSD), may precede transitions in psychopathology as well. This study investigated whether CSD may also indicate the direction of future symptom transitions, i.e., whether they involve an increase or decrease in symptoms. Methods In study 1, a patient with a history of major depression monitored their mental states ten times a day for almost eight months. Study 2 used data from the TRAILS TRANS-ID study, where 122 young adults at increased risk of psychopathology (mean age 23.64±0.67 years, 56.6% males) monitored their mental states daily for six consecutive months. Symptom transitions were inferred from semi-structured diagnostic interviews. In both studies, CSD direction was estimated using moving-window principal component analyses. Results In study 1, CSD was directed towards an increase in negative mental states. In study 2, the CSD direction matched the direction of symptom shifts in 34 individuals. The accuracy of the indicator was higher in subsets of individuals with larger absolute symptom transitions. The indicator’s accuracy exceeded chance levels in sensitivity analyses (accuracy 22.92% vs. 11.76%, z=-2.04, P=.02) but not in main analyses (accuracy 27.87% vs. 20.63%, z=-1.32, P=.09). Conclusions The CSD direction may predict whether upcoming symptom transitions involve remission or worsening. However, this may only hold for specific individuals, namely those with large symptom transitions. Future research is needed to replicate these findings and to delineate for whom CSD reliably forecasts the direction of impending symptom transitions

A potential feedback loop underlying glacial-interglacial cycles

The sawtooth-patterned glacial-interglacial cycles in the Earth’s atmospheric temperature are a well-known, though poorly understood phenomenon. Pinpointing the relevant mechanisms behind these cycles will not only provide insights into past climate dynamics, but also help predict possible future responses of the Earth system to changing CO2 levels. Previous work on this phenomenon suggests that the most important underlying mechanisms are interactions between marine biological production, ocean circulation, temperature and dust. So far, interaction directions (i.e., what causes what) have remained elusive. In this paper, we apply Convergent Cross-Mapping (CCM) to analyze paleoclimatic and paleoceanographic records to elucidate which mechanisms proposed in the literature play an important role in glacial-interglacial cycles, and to test the directionality of interactions. We find causal links between ocean ventilation, biological productivity, benthic δ18O and dust, consistent with some but not all of the mechanisms proposed in the literature. Most importantly, we find evidence for a potential feedback loop from ocean ventilation to biological productivity to climate back to ocean ventilation. Here, we propose the hypothesis that this feedback loop of connected mechanisms could be the main driver for the glacial-interglacial cycles.</p

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

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