Search

The notion that small changes can have large consequences in the climate or ecosystems has become popular as the concept of tipping points. Typically, tipping points are thought to arise from a loss of stability of an equilibrium when external conditions are slowly varied. However, this appealingly simple view puts us on the wrong foot for understanding a range of abrupt transitions in the climate or ecosystems because complex environmental systems are never in equilibrium. In particular, they are forced by diurnal variations, the seasons, Milankovitch cycles and internal climate oscillations. Here we show how abrupt and sometimes even irreversible change may be evoked by even small shifts in the amplitude or time scale of such environmental oscillations. By using model simulations and reconciling evidence from previous studies we illustrate how these phenomena can be relevant for ecosystems and elements of the climate system including terrestrial ecosystems, Arctic sea ice and monsoons. Although the systems we address are very different and span a broad range of time scales, the phenomena can be understood in a common framework that can help clarify and unify the interpretation of abrupt shifts in the Earth system.

International audience

International audience; We address whether robust early warning signals can, in principle, be provided before a climate tipping point is reached, focusing on methods that seek to detect critical slowing down as a precursor of bifurcation. As a test bed, six previously analysed datasets are reconsidered, three palaeoclimate records approaching abrupt transitions at the end of the last ice age and three models of varying complexity forced through a collapse of the Atlantic thermohaline circulation. Approaches based on examining the lag-1 autocorrelation function or on detrended fluctuation analysis are applied together and compared. The effects of aggregating the data, detrending method, sliding window length and filtering bandwidth are examined. Robust indicators of critical slowing down are found prior to the abrupt warming event at the end of the Younger Dryas, but the indicators are less clear prior to the Bølling-Allerød warming, or glacial termination in Antarctica. Early warnings of thermohaline circulation collapse can be masked by inter-annual variability driven by atmospheric dynamics. However, rapidly decaying modes can be successfully filtered out by using a long bandwidth or by aggregating data. The two methods have complementary strengths and weaknesses and we recommend applying them together to improve the robustness of early warnings.

We explored how well the aggregated biovolume of groups of species can be predicted from environmental variables using three different classification approaches: morphology-based functional groups, phylogenetic groups, and functional groups proposed by Reynolds. We assessed the relationships between biovolume of each group and environmental conditions using canonical correlation analyses as well as multiple linear regressions, using data from 211 lakes worldwide ranging from subpolar to tropical regions. We compared the results of these analyses with those obtained for single species following the same protocol. While some species appear relatively predictable, a vast majority of the species showed no clear relationship to the environmental conditions we had measured. However, both the multivariate and the regression analyses indicated that morphology-based groups can be predicted better from environmental conditions than groups based on the other classification methods. This suggests that morphology captures ecological function of phytoplankton well, and that functional groups based on morphology may be the most suitable focus for predicting the composition of communities.

Although some ecosystem responses to climate change are gradual, many ecosystems react in highly nonlinear ways. They show little response until a threshold or tipping point is reached where even a small perturbation may trigger collapse into a state from which recovery is difficult (1). Increasing evidence shows that the critical climate level for such collapse may be altered by conditions that can be managed locally. These synergies between local stressors and climate change provide potential opportunities for proactive management. Although their clarity and scale make such local approaches more conducive to action than global greenhouse gas management, crises in iconic UNESCO World Heritage sites illustrate that such stewardship is at risk of failing.

The road to recovery of a deteriorated system is often different, and fraught with more barriers, than the path to the system's deterioration. This phenomenon is called hysteresis, and is inherent to systems presenting alternative stable states. In such systems, the stability of a given state is the product of positive feedback loops. A broad range of natural systems have been predicted to show hysteretic behaviour, but hysteresis has so far only been unambiguously demonstrated at cellular or metabolic levels, not yet at the population or ecosystem level. To extend our understanding of hysteresis at the population level, we performed an experiment on light-stressed cyanobacteria and found hysteresis between alternative stable states. Furthermore, during the experiment, the cyanobacteria adapted physiologically to high light levels, and deviated from their theoretically predicted pathway of hysteresis, therewith also avoiding extinction. Our experiment confirmed that a population that loses resilience due to deteriorating external conditions can show a delayed – hysteretic – recovery-response when conditions are improved. This population-level study also indicates that the slowness of these systems may obscure the true state they are in, which is important to factor into ecosystem monitoring. Additionally, we show that adaptation can drastically alter the systems’ predicted behaviour to ecosystem management. Flexibility of species and slowness should, therefore, be included in the monitoring and prediction of ecosystem responses to environmental changes.

1. The development of bream populations, water transparency, chlorophyll-a concentration, extent of submerged vegetation and densities of the zebra mussel, Dreissena polymorpha, were analysed in three shallow eutrophic lake systems subject to different fish management. 2. In Lake Veluwemeer, the bream population was reduced from c. 100 to 20 kg ha -1 after 5 years of fishing. The mortality caused by the fishery was estimated at 38% of bream >15 cm in addition to a 13% natural mortality of bream >17 cm. The decline was followed by an expansion of the Chara beds present in the shallow parts, an increase in water transparency in the open-water zone, an increase in the density of zebra mussels and a decrease in chlorophyll-a concentrations. 3. The newly created Lake Volkerak showed trends opposite to those in Lake Veluwe-meer. Bream colonised the lake in 1988 and reached a biomass of c. 140 kg ha -1 in 1998. The water transparency decreased from a maximum of 3 m to c. 1 m and the chlorophyll-a concentration increased from 5 to 45 μg L -1 . Submerged vegetation colonised up to 20% of the total lake area in the first 5 years after creation of the lake in 1987 but decreased to 10% as turbidity increased. 4. Seine fishery in the Frisian lake system did not appear to affect the bream population despite annual catches as high as 40-50 kg ha -1 . The estimated natural mortality of fish >15 cm was 15% and mortality by fishery was 26%. The high loss was apparently compensated by good recruitment and high growth rates resulting from a c. 1 °C higher water temperature during the years when bream were removed by fishing. There was only a slight decrease in chlorophyll-a concentrations and a slight increase in water transparency. 5. The results of this study suggest that the effects of bream exploitation in eutrophic lakes can vary depending on the efficiency of the fishery, recruitment success and temperature regime. In the absence of fishery, bream dominated the fish community in the study lakes and apparently prevented D. polymorpha and submerged vegetation from establishing because of physical disturbance, enhanced internal P-loading and resettling of resuspended sediments.

The shift from a turbid-water state to a clear macrophyte-dominatedstate in the shallow lake Veluwemeer (The Netherlands) has led to nuisance forrecreational navigation. The nuisance concerns the dense beds ofPotamogeton perfoliatus in particular, whereas thelow-canopy forming charophytes cause much less harm. On the other hand, theimportance of macrophyte cover for the stability of the clear-water state hasbeen recognised. To assess the potential of mechanical removal of densemacrophyte beds, several cutting regimes were simulated in a mixed vegetation ofP. perfoliatus and Chara aspera, usingthe individual-based model Charisma. These species occupy a wide range of waterdepths between 0.5 and 2.5 m, with C. asperadominating the shallower zone and P. perfoliatus dominatingthe deeper zone; intermediary is a zone where either species may dominate asalternative equilibria. Both the cutting height and timing affected the amountof biomass present in summer. The effect of cutting was more profound fortreatment later in the season. With a cutting level above theChara-canopy, the simulations showed an increased biomassof C. aspera and reduction of P.perfoliatus. In the zone of alternative equilibria, it was possibleto provoke a sustainable shift from P. perfoliatusdominance to C. aspera dominance. To achieve this, annualrepetition of cutting for a number of years was necessary. A harvesting regimeaimed at shifting the vegetation dominance from P.perfoliatus towards C. aspera could be an optionfor management of the lake, since it holds the perspective of decreasedmanagement effort after a number of years. Moreover, removing only high-canopyvegetation implies high conservation values and recreational use can becombined.

The somatic growth rate of 0+ fish of the six major species in Dutch shallow eutrophic lakes, bream (Abramis brama), roach (Rutilus rutilus), pikeperch (Stizostedion lucioperca) (planktivorous and piscivorous), perch (Perca fluviatilis), ruffe (Gymnocephalus cernuus), and smelt (Osmerus eperlanus), was analysed by using a differential equation. This equation models the instantaneous growth rate of a fish as a temperature-dependent power function of body weight. Two of the model parameters were calibrated by optimising the prediction of the growth rate of the fish. Using a new method, which included a parametric bootstrap procedure, confidence limits were estimated for these two calibrated parameters and were used to test the significance of differences between species in growth performance under natural conditions. These tests revealed four groups of species: (A) smelt, (B) roach and bream, (C) ruffe and perch, and (D) piscivorous pikeperch. Growth performance of planktivorous pikeperch mainly overlapped with roach and bream (B) but showed some overlap with ruffe and perch (C). Differences and similarities are explained from the food type (D Versus A, B, and C) and the phylogenetic constraints (A versus B versus C) of each species. [KEYWORDS: Shallow eutrophic lake; rutilus-rutilus; salmo-trutta; brown trout; body-size; tjeukemeer; patterns; bream; roach; life]

Modelling populations on an individual-by-individual basis has proven to be a fruitful approach. Many complex patterns that are observed on the population level have been shown to arise from simple interactions between individuals. However, a major problem with these models is that the typically large number of individuals needed requires impractically large computation times. The common solution, reduction of the number of individuals in the model, can lead to loss of variation, irregular dynamics, and large sensitivity to the value of random generator seeds. As a solution to these problems, we propose to add an extra variable feature to each model individual, namely the number of real individuals it actually represents. This approach allows zooming from a real individual-by-individual model to a cohort representation or ultimately an all-animals-are-equal view without changing the model formulation. Therefore, the super-individual concept offers easy possibilities to check whether the observed behaviour is an artifact of following a limited number of individuals or of lumping individuals, and also to verify whether individual variability is indeed an essential ingredient for the observed behaviour. In addition the approach offers arbitrarily large computational advantages. As an example the super-individual approach is applied to a generic model of the dynamics of a size-distributed consumer cohort as well as to an elaborate applied simulation model of the recruitment of striped bass.

In many aquatic ecosystems, free-floating plants compete with submerged plants for nutrients and light. Being on top of the water surface free-floating plants are superior competitors for light. Submerged plants can take up nutrients from the sediment and the water column, hereby reducing these levels for free-floating plants. Global warming may change chances of successful species invasion and can alter species dominance. We studied the combined effects of nutrient loading and increased temperature on the competition between the potentially invasive free-floating Salvinia natans (L.) All. and the naturalized submerged Elodea nuttallii Planch. St. John by an outdoor mesocosm experiment under temperate climate conditions (The Netherlands) over a period of 71 days. The free-floating S. natans benefited from increased temperature and increased nutrient loading and limited the chances for the submerged E. nuttallii to take advantage of these changed conditions. S. natans substantially increased temperature in the top layer, while limiting the temperature increase below the mat. Our results suggest that with global warming, invasive free-floating plants might become more successful at the expense of submerged plants.

A sharp regime shift from a brittle star Amphiura filiformis dominated state to a burrowing mud shrimp Callianassa subterranea dominated situation was observed in a region of the North Sea known as the Frisian Front in the mid-1990s. No indications exist that food levels or other relevant conditions in this part of the North Sea had changed significantly. However, the new state has persisted until the present. This could suggest that this regime shift represents a transition between alternative stable community states. We propose a potential explanation for the existence of 2 stable states, which agrees with experimental and field observations. We demonstrated experimentally that sediments inhabited by burrowing shrimps are more susceptible to sediment resuspension by tidal currents and wave forces than sediments inhabited by brittle stars. Although the burrowing shrimps apparently thrive under these conditions, successful recruitment of brittle stars may be hampered on such unstable frequently resuspended sediments. This implies a positive feedback; brittle stars promote sediment stability, which favors their persistence. We created a model to demonstrate that this feedback between the benthic community and sediment stability may cause both the shrimp dominated state and the brittle star dominated state to be stable under the same external conditions.

Dense beds of aquatic macrophytes often cause nuisance to boaters and swimmers, and may obstruct water flow. Management of aquatic vegetation is, therefore, often aimed at reducing the biomass of the plants. If the nuisance is caused by exotic invasive species, there usually is no controversy with nature conservation aims. In shallow lakes, however, the interests of recreational users may conflict with nature conservation because the promotion of indigenous submerged vegetation is considered an important tool for lake restoration. Aiming at intermediate vegetation biomass seems a good solution for this controversy at first sight. However, we argue that such a compromise is often not the best policy from a welfare economic point of view. We present preliminary results of a graphical model, showing that the overall benefit for all ecosystem users may be minimal at the intermediate vegetation biomass. Furthermore, even if there is an optimal benefit at an intermediate macrophyte biomass, we argue that it is may not always be feasible to force the vegetation biomass to the desired level. Due to ecological feedback mechanisms, the system can have two alternative stable states: one with high vegetation biomass and one with little or no vegetation. It is concluded that it will often be better to realise a management strategy aimed at keeping some lakes (or parts of lakes) free of aquatic plants, whereas allowing others to be densely vegetated.

The effects of fish stock reduction have been studied in 3 Dutch lakes (Lake Zwemlust, Lake Bleiswijkse Zoom and Lake Noorddiep) and 1 Danish lake (Lake Vaeng) during 4–5 years. A general response is described. The fish stock reduction led in general to a low fish stock, low chlorophyll-a, high Secchi-disc transparency and high abundance of macrophytes. Large Daphnia became abundant, but their density decreased, due to food limitation and predation by fish. The total nitrogen concentration became low due to N-uptake by macrophytes and enhanced denitrification. In Lake Bleiswijkse Zoom the water transparency deteriorated and the clear water state was not stable. The fish stock increased and the production of young fish in summer was high. Clear water occurred only in spring. Large daphnids were absent in summer and the macrophytes decreased.

Macroinvertebrates were studied during the first five years after closure and freshening of the lake system Volkerak-Zoom, two lakes interconnected by a channel. Before embankment, in 1987, these lakes were part of the tidal Eastern Scheldt estuary in the south-western part of The Netherlands. Four months after embankment, the first freshwater species were found. In general, the colonization process followed the same pattern as was reported for newly created reservoirs. In Lake Volkerak-Zoom differences in colonization time were observed between distinguished depth zones. Within the chironomid assemblages, dominance of Chironomus muratensis was followed by a dominance of Procladius,Glyptotendipes and Cladotanytarsus. The succession was related to changes in phytoplankton concentrations. Although in 1991 changes in macrofauna composition were less pronounced as compared to previous years, succession was still going on.

Ecosystems are complex systems which can respond to gradual changes of their conditions by a sudden shift to a contrasting regime or alternative stable state (ASS). Predicting such critical points before they are reached is extremely difficult and providing early warnings is fundamental to design management protocols for ecosystems. Here we study different spatial versions of popular ecological models which are known to exhibit ASS. The spatial heterogeneity is introduced by a local parameter varying from cell to cell in a regular lattice. Transport of biomass among cells occurs by simple diffusion. We investigate whether different quantities from statistical mechanics -like the variance, the two-point correlation function and the patchiness- may serve as early warnings of catastrophic phase transitions between the ASS. In particular, we find that the patch-size distribution follows a power law when the system is close to the catastrophic transition. We also provide links between spatial and temporal indicators and analyze how the interplay between diffusion and spatial heterogeneity may affect the earliness of each of the observables. Finally, we comment on similarities and differences between these catastrophic shifts and paradigmatic thermodynamic phase transitions like the liquid-vapor change of state for a fluid like water.

In sheltered, eutrophicated estuaries, reduced nitrogen (NH x ), and pH levels in the water layer can be greatly enhanced. In laboratory experiments, we studied the interactive effects of NH x , pH, and shoot density on the physiology and survival of eelgrass (Zostera marina). We tested long-term tolerance to NH x at pH 8 in a 5-week experiment. Short-term tolerance was tested for two shoot densities at both pH 8 and 9 in a 5-day experiment. At pH 8, eelgrass accumulated nitrogen as free amino acids when exposed to high loads of NH x , but showed no signs of necrosis. Low shoot density treatments became necrotic within days when exposed to NH x at pH 9. Increased NH3 intrusion and carbon limitation seemed to be the cause of this, as intracellular NH x could no longer be assimilated. Remarkably, experiments with high shoot densities at pH 9 showed hardly any necrosis, as the plants seemed to be able to alleviate the toxic effects of high NH x loads through joint NH x uptake. Our results suggest that NH x toxicity can be important in worldwide observed seagrass mass mortalities. We argue that the mitigating effect of high seagrass biomass on NH x toxicity is a positive feedback mechanism, potentially leading to alternative stable states in field conditions.

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.

It is common knowledge that the millions of species that inhabit the Earth have adaptations that enable them to survive in different environments. Fish have gills which allow them to breath under water, while the wings of birds allow them to fly. These adaptations are, as different as they may be, a different solution to the same problem: the problem of staying alive and reproduce in a world where species are under the constant pressure of natural selection. Perhaps less well known, but maybe not surprising when thought about carefully, is that the often complex networks of interactions between species, e.g. between plants and pollinators or between predators and prey, have certain non-random properties as well. These ‘network structural properties’, i.e. specific ways in which the interactions within networks are arranged most likely allow the often large numbers of species in ecosystems to coexist. Just like similar adaptations may be found in a wide variety of species, e.g. gills or gill-like organs in aquatic animals and wings on birds, insects, and bats, similar network structural properties may be found in a wide variety of ecosystems. Similarities that may occur simply because they are, like adaptations, a solution to the same problem: the problem of coexistence in systems where species heavily influence each other’s probability of survival.While we are beginning to understand more about the structural properties of ecological networks, i.e. the networks of interactions between species, and how they might allow large numbers of species to coexist in complex ecosystems, the Earth and its ecosystems are changing at increasingly rapid rates due to human activities. In some cases, these changes are relatively simple in the sense that they affect a large group of species similarly, e.g. the effect of pesticides on a large group of insect pollinators, while in other cases these changes may be complex, e.g. the effects of climate change on the phenology and distribution of species which in turn leads to alterations in strengths of interspecific interactions in a way that is unique for each interaction. Ecosystems may respond in various ways to such changes (regardless of whether their effects are simple or complex). When conditions change gradually, the state of some ecosystems (e.g. the size of populations) may change likewise, in a smooth, gradual manner. Other systems may respond strongly to change within a narrow range of environmental conditions, but are relatively insensitive to change outside of this range. Particularly sudden shifts may occur when ecosystems have multiple alternative states. Such systems cannot change smoothly from one state (e.g. large population sizes) to an alternative state (e.g. a state in which some or all species are extinct). Instead, a sudden shift or ‘critical transition’ occurs when environmental conditions pass a critical point. To return back to the original state after such a transition, a return to conditions prior to the transition is often not sufficient; instead, a larger change in conditions is needed until another critical point is reached at which the system shifts back to the original state, a phenomenon called ‘hysteresis’.While the outcome of critical transitions is relatively predictable when a few leading species or species groups determine the state of an ecosystem, this may not be the case when ecosystem dynamics are determined by many interacting species. The consequences of critical transitions in such complex ecosystems might be severe, for example, when leading to the extinction of a large number of species. Not all critical transitions, however, will have dramatic consequences. Complex ecosystems may potentially shift to many different, alternative states. Some of those may imply minor, harmless changes in the state of a system, or invoke positive change, whereas others may have catastrophic con- sequences. The amount and type of change needed to cause a transition and a system’s future state after an impending critical transition depends in complex and often unknown ways on how ecosystems are organized, i.e. on the feedback mechanisms within it, and thus on the structure of ecological networks and/or how this structure might be changed by changing environmental conditions. Assessing or mitigating the risks associated with critical transitions in complex ecosystems thus requires a fundamental insight in the interrelationships between the structural properties of ecological networks, the dynamics of ecosystems, and the way in which these properties and dynamics might be affected by changing environmental conditions.Despite a longstanding interest in ecological networks and more recent advances in detecting commonalities in the structure of ecological networks, the common ground between studying the structure of ecological networks and the potential causes and consequences of critical transitions in complex ecosystems remains largely unexplored. In this thesis, I hope to have provided novel ideas and insights that might help to address the question of whether changing environmental conditions are likely to lead to large-scale systemic regime shifts in complex ecosystems. An emerging property of complex ecosystems that may be referred to as ‘systemic risk’.

The backbone of this thesis is the interdisciplinary interaction between dynamic systems theory and a selection of biological problems. Each chapter focuses in one problem, namely plankton dynamics, cell development paths and sleep-wake dynamics. Despite these topics may seem disconnected, they share an important feature: all of them show cyclic behaviour under certain circumstances. In the present thesis we show that cyclic (or chaotic) behaviour is deeply related with plankton biodiversity. We also use cycles to show, in an intuitive way, that Waddington’s epigenetic landscapes (a common visual tool in stem cell research) are poorly defined, and we provide a practical solution to this. Lastly, we provide an algorithm to forecast a transition between synchronized and non-synchronized cyclic systems (such as normal sleep – insomnia, or normal hearth functioning – arrhythmia), with potential applications in medical sciences.

This thesis explores three interrelated research streams. First, I am interested in the very fundamental and ancient question about the functioning of our societies – why are some individuals or countries rich and others poor? Under this broad question, I aim to understand the drivers of inequality, that traverse the artificial boundaries between economic, social and natural sciences. Second, I study inequality, as being complex and governed by highly interconnected processes such as technology, globalization, trade and migration. These processes can be highly nonlinear causing cyclical behaviour and/or critical transitions such as tipping points. Third, using dynamic models and empirical data, I explain the flow of information between heterogeneous agents, including individuals, households or countries, and how these interactions define the emergent dynamics of inequality. Heterogeneous individuals interact not only inside economic systems but also across systems, such as with the environment and climate. Furthermore, these interactions are governed by formal and informal rules, such as institutions, social norms and agreements.

Complex systems in ecology and the climate can have tipping points. The term ‘tipping point’ is loosely defined as a threshold point in the conditions after which runaway change brings the system to a new stable state. Such a transition can have long-term dire consequences, and therefore it is of critical importance to understand why and when these transitions occur. Under the ongoing climate change, these critical transitions are projected to increase. However, little is understood about how relative timescales of the rate of environmental change and variability affect the occurrence and detectability of these critical transitions in nature and society. The aim of this thesis is to provide some insights in how differences in these timescales may affect critical transitions.This thesis starts with the analysis of bistability of marine anoxic events in the Mediterranean Sea. Reconstructed time series have been used to detect changes in resilience indicators prior to several abrupt shifts in the past climate. This is, however, only possible under a limited set of conditions. For the past marine anoxic events in the Mediterranean Sea, these conditions are met. Recent technological advances made it possible to construct high-resolution and (almost) evenly spaced time series of past widespread anoxic events in the Mediterranean Sea. In Chapter 2, we analysed whether past transitions in the Mediterranean Sea could have been predicted using the resilience indicators autocorrelation and variance. We show that the repeated shifts into marine anoxia in the Mediterranean Sea had the character of critical transitions, because there was a gradual increase in the temporal autocorrelation and variance in the deep cores (>1600 meter depth) before the onset of most events. Our results imply that future widespread anoxia in marine systems might be recognizable using an appropriate statistical approach and high-resolution records.These shifts to an anoxic state occurred relatively fast, but not all shifts to an alternative stable state unfold rapidly. Slowly responding systems show a gradual shift to the alternative state, once the tipping point has been passed. As the rate of the current environmental change is unprecedented, more system respond relatively slow to changes in the environment. The current resilience indicators are based on the theoretical finding that the system slows down close to the tipping point. But in these relatively slow systems, the recovery rates are always slow. Therefore, it is the question whether these resilience indicators flag that a relatively slow system is approaching a tipping point. In Chapter 3, we show that it is more difficult to quantify the resilience of a system that responds relatively slow. These results indicate that as the rates of environmental change keep increasing, it become more and more difficult to detect whether systems are approaching a tipping point.Another risk under current rates of environmental change is that the rate of change in the conditions triggers a shift to an alternative stable state, whereas a change of the same magnitude but at slower rates would not. Only few studies describe this so-called ‘rate-tipping’ in ecological systems, but understanding rate-tipping is needed to understand and predict ecosystem response to the ongoing rapid environmental change. Therefore, we show in Chapter 4 that there can be rate-induced tipping for a range of initial conditions in a model of cyanobacteria with realistic parameter settings. A pulse in the environmental conditions, for example as a result of an extreme event, can cause a temporary collapse, depending on both the rate and the duration of the pulse. In addition, we showed that the type of environmental variability can influence the probability of inducing rate-tipping. These results imply that we need to incorporate critical rates of change in our ecosystems assessment and management.In addition to affecting the probability of inducing rate-tipping, environmental variability itself can bring a system past a tipping point. The variability is different in different parts of the climate, but because of climate change, the climatic variability is changing systematically in different parts of the world. Therefore, we analysed in Chapter 5 what the effect of changes in the memory of the climatic variability is on the chance of undergoing a critical transition. We show that chances of invoking such critical transitions are strongly affected by the climate memory as measured for instance by temporal autocorrelation in climatic variables. We illustrate the implications of this prediction with evidence from forests, corals reefs, poverty traps, violent conflict and ice-sheet instability. In all of these examples, the duration of anomalous dry or warm events increases the chance of invoking a critical transition. Our results imply that understanding the effects of altered climate variability requires research on climate memory.In the Afterthoughts I conclude that fast rates of environmental change and changes in environmental variability can affect the detectability and predictability of critical transitions. While the exact impacts of climate change are likely system-specific, interacting timescales make it difficult to untangle system dynamics from external forcing. The relations I describe throughout this thesis, however, are relative. This means that it is impossible to make general rules about whether resilience indicators can be observed, or if the conditions can be restored. Therefore, we should not give up on a priori detecting and reversing critical transitions driven by climate change.

The core of my thesis concerns addressing the ecosystem resilience in a data-driven manner. In this direction, I have tried to make a bridge between advanced mathematical models and existing ecological data. I could come up with some quantitative measures of resilience and applied them to some ecological field and experimental data. These measures are more exact compared with the classical measures mentioned by Holling. I show that Holling measures are just two extremes of the measure I introduced and they do not necessarily capture the notion of resilience in its real sense of the word. Furthermore, I could also address the resilience of low-resolution tropical satellite data across the tropics (South America, Africa, south east Asia and, Australia). Besides, my thesis also sheds more light on the concept of ‘alternative stable states’ which is an important concept in ecology. I argue that advanced ‘system reconstruction’ approaches should be applied first, from where one can better justify weather or not an ecosystem has alternative stable states.

This thesis explores the hypothesis that tropical forest and savanna can be alternative stable states. Feedbacks of tree cover with fire across the tropics, and with rainfall in the Amazon basin, are studied by linking modelling to the analysis of broad-scale remote-sensing data. Time series of tree cover and fire observations are used to quantify the strength of the fire-tree cover feedback loop along climatic gradients. From these empirical results a spatially explicit and stochastic fire-tree cover model is developed. The model predicts that forest and savanna are fire-driven alternative stable states across rainfall conditions, but the exact rainfall range depends strongly on rainfall seasonality. Next, regional-scale effects of tree cover on rainfall in the Amazon basin are presented. Forest transpiration is estimated and the trajectories of that transpired water through the atmosphere are simulated. It is found that one-third of all rainfall in the Amazon basin originates from the basin; two-thirds of that water has been transpired by trees at least once. Forests in the southern half of the basin contribute most to the resilience of other forests, whereas forests in the south-western Amazon are most dependent on transpiration from forests elsewhere in the basin. The relative contribution of forest transpiration to rainfall is higher in drier months and in drier years. In conclusion, tree cover will not change smoothly with climate change and possible transitions between forest and savanna will likely be relatively abrupt. The main mechanism behind such tipping points is a feedback between tree cover and fire. Increasing rainfall seasonality will strengthen that feedback and in the Amazon at least, reduced forest transpiration resulting from tree-cover loss will enhance that seasonality.