Vasilis Dakos

Slowing down in spatially patterned ecosystems at the brink of collapse.

Predicting the risk of critical transitions, such as the collapse of a population, is important in order to direct management efforts. In any system that is close to a critical transition, recovery upon small perturbations becomes slow, a phenomenon known as critical slowing down. It has been suggested that such slowing down may be detected indirectly through an increase in spatial and temporal correlation and variance. Here, we tested this idea in arid ecosystems, where vegetation may collapse to desert as a result of increasing water limitation. We used three models that describe desertification but differ in the spatial vegetation patterns they produce. In all models, recovery rate upon perturbation decreased before vegetation collapsed. However, in one of the models, slowing down failed to translate into rising variance and correlation. This is caused by the regular self-organized vegetation patterns produced by this model. This finding implies an important limitation of variance and correlation as indicators of critical transitions. However, changes in such self-organized patterns themselves are a reliable indicator of an upcoming transition. Our results illustrate that while critical slowing down may be a universal phenomenon at critical transitions, its detection through indirect indicators may have limitations in particular systems.

Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness

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.

Evaluating early-warning indicators of critical transitions in natural aquatic ecosystems

Significance Early-warning indicators (EWIs), statistical metrics of system resilience, have been hypothesized to provide advance warning of sudden shifts in ecosystems, or so-called “regime shifts.” Here we tested this hypothesis for four commonly used EWIs. We used empirical time series from five freshwater ecosystems with documented sudden, persistent transitions hypothesized to represent critical transitions. EWIs were detected in several of these long-term records, and in some cases several years before the transition; however, these EWIs varied in reliability, and agreement between indicators was low. Moreover, their applicability was strongly limited by the requirement for ecosystem-specific knowledge of transition-generating mechanisms and their drivers to choose relevant state variables for analysis. Ecosystems can show sudden and persistent changes in state despite only incremental changes in drivers. Such critical transitions are difficult to predict, because the state of the system often shows little change before the transition. Early-warning indicators (EWIs) are hypothesized to signal the loss of system resilience and have been shown to precede critical transitions in theoretical models, paleo-climate time series, and in laboratory as well as whole lake experiments. The generalizability of EWIs for detecting critical transitions in empirical time series of natural aquatic ecosystems remains largely untested, however. Here we assessed four commonly used EWIs on long-term datasets of five freshwater ecosystems that have experienced sudden, persistent transitions and for which the relevant ecological mechanisms and drivers are well understood. These case studies were categorized by three mechanisms that can generate critical transitions between alternative states: competition, trophic cascade, and intraguild predation. Although EWIs could be detected in most of the case studies, agreement among the four indicators was low. In some cases, EWIs were detected considerably ahead of the transition. Nonetheless, our results show that at present, EWIs do not provide reliable and consistent signals of impending critical transitions despite using some of the best routinely monitored freshwater ecosystems. Our analysis strongly suggests that a priori knowledge of the underlying mechanisms driving ecosystem transitions is necessary to identify relevant state variables for successfully monitoring EWIs.

Resonance of Plankton Communities with Temperature Fluctuations

The interplay between intrinsic population dynamics and environmental variation is still poorly understood. It is known, however, that even mild environmental noise may induce large fluctuations in population abundances. This is due to a resonance effect that occurs in communities on the edge of stability. Here, we use a simple predator-prey model to explore the sensitivity of plankton communities to stochastic environmental fluctuations. Our results show that the magnitude of resonance depends on the timescale of intrinsic population dynamics relative to the characteristic timescale of the environmental fluctuations. Predator-prey communities with an intrinsic tendency to oscillate at a period T are particularly responsive to red noise characterized by a timescale of . We compare these theoretical predictions with the timescales of temperature fluctuations measured in lakes and oceans. This reveals that plankton communities will be highly sensitive to natural temperature fluctuations. More specifically, we demonstrate that the relatively fast temperature fluctuations in shallow lakes fall largely within the range to which rotifers and cladocerans are most sensitive, while marine copepods and krill will tend to resonate more strongly with the slower temperature variability of the open ocean.

Vegetation recovery in tidal marshes reveals critical slowing down under increased inundation

A declining rate of recovery following disturbance has been proposed as an important early warning for impending tipping points in complex systems. Despite extensive theoretical and laboratory studies, this ‘critical slowing down remains largely untested in the complex settings of real-world ecosystems. Here, we provide both observational and experimental support of critical slowing down along natural stress gradients in tidal marsh ecosystems. Time series of aerial images of European marsh development reveal a consistent lengthening of recovery time as inundation stress increases. We corroborate this finding with transplantation experiments in European and North American tidal marshes. In particular, our results emphasize the power of direct observational or experimental measures of recovery over indirect statistical signatures, such as spatial variance or autocorrelation. Our results indicate that the phenomenon of critical slowing down can provide a powerful tool to probe the resilience of natural ecosystems.

Slow Recovery from Local Disturbances as an Indicator for Loss of Ecosystem Resilience

A range of indicators have been proposed for identifying the elevated risk of critical transitions in ecosystems. Most indicators are based on the idea that critical slowing down can be inferred from changes in statistical properties of natural fluctuations and spatial patterns. However, identifying these signals in nature has remained challenging. An alternative approach is to infer changes in resilience from differences in standardized experimental perturbations. However, system-wide experimental perturbations are rarely feasible. Here we evaluate the potential to infer the risk of large-scale systemic transitions from local experimental or natural perturbations. We use models of spatially explicit landscapes to illustrate how recovery rates upon small-scale perturbations decrease as an ecosystem approaches a tipping point for a large-scale collapse. We show that the recovery trajectory depends on: (1) the resilience of the ecosystem at large scale, (2) the dispersal rate of organisms, and (3) the scale of the perturbation. In addition, we show that recovery of natural disturbances in a heterogeneous environment can potentially function as an indicator of resilience of a large-scale ecosystem. Our analyses reveal fundamental differences between large-scale weak and local-scale strong perturbations, leading to an overview of opportunities and limitations of the use of local disturbance-recovery experiments.

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom–bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress.

Climate models predict increasing temperature variability in poor countries

Temperature variability will increase in poor countries and decrease in rich countries, creating a new climate injustice. Extreme events such as heat waves are among the most challenging aspects of climate change for societies. We show that climate models consistently project increases in temperature variability in tropical countries over the coming decades, with the Amazon as a particular hotspot of concern. During the season with maximum insolation, temperature variability increases by ~15% per degree of global warming in Amazonia and Southern Africa and by up to 10%°C−1 in the Sahel, India, and Southeast Asia. Mechanisms include drying soils and shifts in atmospheric structure. Outside the tropics, temperature variability is projected to decrease on average because of a reduced meridional temperature gradient and sea-ice loss. The countries that have contributed least to climate change, and are most vulnerable to extreme events, are projected to experience the strongest increase in variability. These changes would therefore amplify the inequality associated with the impacts of a changing climate.

Detecting the Collapse of Cooperation in Evolving Networks.

The sustainability of biological, social, economic and ecological communities is often determined by the outcome of social conflicts between cooperative and selfish individuals (cheaters). Cheaters avoid the cost of contributing to the community and can occasionally spread in the population leading to the complete collapse of cooperation. Although such collapse often unfolds unexpectedly, it is unclear whether one can detect the risk of cheater’s invasions and loss of cooperation in an evolving community. Here, we combine dynamical networks and evolutionary game theory to study the abrupt loss of cooperation with tools for studying critical transitions. We estimate the risk of cooperation collapse following the introduction of a single cheater under gradually changing conditions. We observe an increase in the average time it takes for cheaters to be eliminated from the community as the risk of collapse increases. We argue that such slow system response resembles slowing down in recovery rates prior to a critical transition. In addition, we show how changes in community structure reflect the risk of cooperation collapse. We find that these changes strongly depend on the mechanism that governs how cheaters evolve in the community. Our results highlight novel directions for detecting abrupt transitions in evolving networks.

Observed trends in the magnitude and persistence of monthly temperature variability

Climate variability is critically important for nature and society, especially if it increases in amplitude and/or fluctuations become more persistent. However, the issues of whether climate variability is changing, and if so, whether this is due to anthropogenic forcing, are subjects of ongoing debate. Increases in the amplitude and persistence of temperature fluctuations have been detected in some regions, e.g. the North Pacific, but there is no agreed global signal. Here we systematically scan monthly surface temperature indices and spatial datasets to look for trends in variance and autocorrelation (persistence). We show that monthly temperature variability and autocorrelation increased over 1957–2002 across large parts of the North Pacific, North Atlantic, North America and the Mediterranean. Furthermore, (multi)decadal internal climate variability appears to influence trends in monthly temperature variability and autocorrelation. Historically-forced climate models do not reproduce the observed trends in temperature variance and autocorrelation, consistent with the models poorly capturing (multi)decadal internal climate variability. Based on a review of established spatial correlations and corresponding mechanistic ‘teleconnections’ we hypothesise that observed slowing down of sea surface temperature variability contributed to observed increases in land temperature variability and autocorrelation, which in turn contributed to persistent droughts in North America and the Mediterranean.