Ecosystems off track: rate-induced critical transitions in ecological models

Adaptive foraging of pollinators fosters gradual tipping under resource competition and rapid environmental change

Plant and pollinator communities are vital for transnational food chains. Like many natural systems, they are affected by global change: rapidly deteriorating conditions threaten their numbers. Previous theoretical studies identified the potential for community-wide collapse above critical levels of environmental stressors-so-called bifurcation-induced tipping points. Fortunately, even as conditions deteriorate, individuals have some adaptive capacity, potentially increasing the boundary for a safe operating space where changes in ecological processes are reversible. Our study considers this adaptive capacity of pollinators to resource availability and identifies a new threat to disturbed pollinator communities. We model the adaptive foraging of pollinators in changing environments. Pollinator's adaptive foraging alters the dynamical responses of species, to the advantage of some-typically generalists-and the disadvantage of others, with systematic non-linear and non-monotonic effects on the abundance of particular species. We show that, in addition to the extent of environmental stress, the pace of change of environmental stress can also lead to the early collapse of both adaptive and nonadaptive pollinator communities. Specifically, perturbed communities exhibit rate-induced tipping points at stress levels within the safe boundary defined for constant stressors. With adaptive foraging, tipping is a more asynchronous collapse of species compared to nonadaptive pollinator communities, meaning that not all pollinator species reach a tipping event simultaneously. These results suggest that it is essential to consider the adaptive capacity of pollinator communities for monitoring and conservation. Both the extent and the rate of stress change relative to the ability of communities to recover are critical environmental boundaries.

Life-history speed, population disappearances and noise-induced ratchet effects

Nature is replete with variation in the body sizes, reproductive output and generation times of species that produce life-history responses known to vary from small and fast to large and slow. Although researchers recognize that life-history speed likely dictates fundamental processes in consumer-resource interactions like productivity and stability, theoretical work remains incomplete in this critical area. Here, we examine the role of life-history speed on consumer-resource interactions by using a well-used mathematical approach that manipulates the speed of the consumer's growth rate in a consumer-resource interaction. Importantly, this approach holds the isocline geometry intact, allowing us to assess the impacts of altered life-history speed on stability (coefficient of variation, CV) without changing the underlying qualitative dynamics. Although slowing life history can be initially stabilizing, we find that in stochastic settings slowing ultimately drives highly destabilizing population disappearances, especially under reddened noise. Our results suggest that human-driven reddening of noise may decrease species stability because the autocorrelation of red noise enlarges the period and magnitude of perturbations, overwhelming a species' natural compensatory responses via a ratchet-like effect. This ratchet-like effect then pushes species' population dynamics far away from equilibria, which can lead to precipitous local extinction.

Global analysis and prediction scenario of infectious outbreaks by recurrent dynamic model and machine learning models: A case study on COVID-19

It is essential to evaluate patient outcomes at an early stage when dealing with a pandemic to provide optimal clinical care and resource management. Many methods have been proposed to provide a roadmap against different pandemics, including the recent pandemic disease COVID-19. Due to recurrent epidemic waves of COVID-19, which have been observed in many countries, mathematical modeling and forecasting of COVID-19 are still necessary as long as the world continues to battle against the pandemic. Modeling may aid in determining which interventions to try or predict future growth patterns. In this article, we design a combined approach for analyzing any pandemic in two separate parts. In the first part of the paper, we develop a recurrent SEIRS compartmental model to predict recurrent outbreak patterns of diseases. Due to its time-varying parameters, our model is able to reflect the dynamics of infectious diseases, and to measure the effectiveness of the restrictive measures. We discuss the stable solutions of the corresponding autonomous system with frozen parameters. We focus on the regime shifts and tipping points; then we investigate tipping phenomena due to parameter drifts in our time-varying parameters model that exhibits a bifurcation in the frozen-in case. Furthermore, we propose an optimal numerical design for estimating the system’s parameters. In the second part, we introduce machine learning models to strengthen the methodology of our paper in data analysis, particularly for prediction scenarios. We use MLP, RBF, LSTM, ANFIS, and GRNN for training and evaluation of COVID-19. Then, we compare the results with the recurrent dynamical system in the fitting process and prediction scenario. We also confirm results by implementing our methods on the released data on COVID-19 by WHO for Italy, Germany, Iran, and South Africa between 1/22/2020 and 7/24/2021, when people were engaged with different variants including Alpha, Beta, Gamma, and Delta. The results of this article show that the dynamic model is adequate for long-term analysis and data fitting, as well as obtaining parameters affecting the epidemic. However, it is ineffective in providing a long-term forecast. In contrast machine learning methods effectively provide disease prediction, although they do not provide analysis such as dynamic models. Finally, some metrics, including RMSE, R-Squared, and accuracy, are used to evaluate the machine learning models. These metrics confirm that ANFIS and RBF perform better than other methods in training and testing zones.

Extreme drought disrupts plant phenology: Insights from 35 years of cloud forest data in Venezuela

The potential effects of climate change on plant reproductive phenology include asynchronies with pollinators and reductions in plant fitness, leading to extinction and loss of ecosystem function. In particular, plant phenology is sensitive to extreme weather events, which are occurring with increasing severity and frequency in recent decades and are linked to anthropogenic climate change and shifts in atmospheric circulation. For 15 plant species in a Venezuelan cloud forest, we documented dramatic changes in monthly flower and fruit community composition over a 35-year time series, from 1983 to 2017, and these changes were linked directly to higher temperatures, lower precipitation, and decreased soil water availability. The patterns documented here do not mirror trends in temperate zones but corroborate results from the Asian tropics. More intense droughts are predicted to occur in the region, which will cause dramatic changes in flower and fruit availability.

Continental flood basalts drive Phanerozoic extinctions

Refinements of the geological timescale driven by the increasing precision and accuracy of radiometric dating have revealed an apparent correlation between large igneous provinces (LIPs) and intervals of Phanerozoic faunal turnover that has been much discussed at a qualitative level. However, the extent to which such correlations are likely to occur by chance has yet to be quantitatively tested, and other kill mechanisms have been suggested for many mass extinctions. Here, we show that the degree of temporal correlation between continental LIPs and faunal turnover in the Phanerozoic is unlikely to occur by chance, suggesting a causal relationship linking extinctions and continental flood basalts. The relationship is stronger for LIPs with higher estimated eruptive rates and for stage boundaries with higher extinction magnitudes. This suggests LIP magma degassing as a primary kill mechanism for mass extinctions and other intervals of faunal turnover, which may be related to [Formula: see text], Cl, and F release. Our results suggest continental LIPs as a major, direct driver of extinctions throughout the Phanerozoic.

Critical rates of climate warming and abrupt collapse of ecosystems

In the age of climate warming, comprehension of ecosystems’ future is one of the pressing challenges to humanity. While most studies on climate warming focus on the ‘magnitude of change’ of the Earth’s temperature, the ‘rate’ at which it is increasing cannot be ruled out. Rapid warming has already caused sudden ecosystem transitions at numerous biodiversity hot spots; a mechanistic understanding of such transitions is crucial. Here, we study a slow–fast consumer–resource ecosystem interacting in rapid warming scenarios. Employing geometric singular perturbation theory, we find that while a gradual change in mean temperature may accord population persistence, a critical warming rate can drive the resource’s sudden collapse, termed a warming-induced abrupt transition. This further triggers the bottom-up effect, resulting in the extinction of the consumer. The difference between the optimum temperature of the resource’s growth rate and the habitat temperature is crucial in deciding the critical rate of warming. Consequently, species inhabiting extreme temperature regions are more susceptible to warming-induced collapse than those within intermediate temperature ranges. We find that stochastic fluctuations in the system can advance warming-induced transitions, and the efficacy of generic early warning signals to anticipate sudden transitions is challenged.

Evolutionary rescue can prevent rate-induced tipping

The transformation of ecosystems proceeds at unprecedented rates. Recent studies suggest that high rates of environmental change can cause rate-induced tipping. In ecological models, the associated rate-induced critical transition manifests during transient dynamics in which populations drop to dangerously low densities. In this work, we study how indirect evolutionary rescue—due to the rapid evolution of a predator’s trait—can save a prey population from the rate-induced collapse. Therefore, we explicitly include the time-dependent dynamics of environmental change and evolutionary adaptation in an eco-evolutionary system. We then examine how fast the evolutionary adaptation needs to be to counteract the response to environmental degradation and express this relationship by means of a critical rate. Based on this critical rate, we conclude that indirect evolutionary rescue is more probable if the predator population possesses a high genetic variation and, simultaneously, the environmental change is slow. Hence, our results strongly emphasize that the maintenance of biodiversity requires a deceleration of the anthropogenic degradation of natural habitats.

Fungal response to abruptly or gradually delivered antifungal agent amphotericin B is growth stage dependent

Anthropogenic disturbances pose a multitude of novel challenges to ecosystems. While many experiments have tested effects using abrupt treatment applications, most environmental changes in fact are gradual. Since ecosystem responses might be highly dependent on the temporal nature of stressors, it is crucial to differentiate the effects of abrupt vs gradual treatment application. Antifungal agents, which are widely used in disease control both for humans and in agriculture, are becoming a new class of environmental contaminants. In this study, we examined the effect of a sub-lethal application of one antifungal agent, amphotericin B. We applied different rates of delivery, e.g. gradual and abrupt, and monitored biomass and sporulation of the model fungus Neurospora crassa in a batch culture. Our results demonstrate that: (i) the effect size difference between abrupt and gradual treatments is fungal growth stage dependent and (ii) the gradual treatment clearly had a higher sporulation level compared with all types of abrupt treatments. Our findings highlight the importance of considering the rate of change in environmental change research and point to a new research direction for future global change studies. Furthermore, our results also have important implications for avoiding treatment-induced spore production in agriculture and medical practise.

Metacommunity persistence to environmental change: Stabilizing and destabilizing effects of individual species dispersal

Ecological communities face a high risk of extinction to climate change which can destabilize ecological systems. In the face of accelerating environmental change, understanding the factors and the mechanisms that stabilize the ecological communities is a central focus in ecology. Although dispersal has been widely used as an important stabilizing process, it remains unclear how individual species dispersal affects the stability and persistence of an ecological community. In this study, using a spatially coupled predator-prey community, we address the effects of individual species dispersal and nutrient enrichment on metacommunity stability in constant and varying environments. We show two contrasting effects of dispersal on metacommunity persistence in temporally constant and varying environments. Specifically, predator dispersal in constant environments shows stronger stability through inhomogeneous (asynchronized) states, whereas prey dispersal shows an increasing extinction risk through a homogeneous (synchronized) state. On the contrary, the metacommunity dynamics in temporally varying environments reveal that predator dispersal causes a local extinction through tracking unstable states and also a delayed shift between dynamical states. Moreover, our results emphasize that metacommunity persistence depends on individual species dispersal and environmental variations. Thus, our findings of the individual species dispersal can help to develop conservation measures that are tailored to varying environmental conditions.

Oscillations and Pattern Formation in a Slow-Fast Prey-Predator System

We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of the prey-predator system is apparent rather than real and there are still many of its hidden properties that have been poorly studied or overlooked altogether. We further focus on the case where, in the slow-fast system, the prey growth is affected by a weak Allee effect. We first consider this system in the non-spatial case and make its comprehensive study using a variety of mathematical techniques. In particular, we show that the interplay between the Allee effect and the existence of multiple timescales may lead to a regime shift where small-amplitude oscillations in the population abundances abruptly change to large-amplitude oscillations. We then consider the spatially explicit slow-fast prey-predator system and reveal the effect of different timescales on the pattern formation. We show that a decrease in the timescale ratio may lead to another regime shift where the spatiotemporal pattern becomes spatially correlated, leading to large-amplitude oscillations in spatially average population densities and potential species extinction.

Understanding the critical rate of environmental change for ecosystems, cyanobacteria as an example

Recently it has been show that in some ecosystems fast rates of change of environmental drivers may trigger a critical transition, whereas change of the same magnitude but at slower rates would not. So far, few studies describe this phenomenon of rate-induced tipping, while it is important to understand this phenomenon in the light of the ongoing rapid environmental change. Here, we demonstrate rate-induced tipping in a simple model of cyanobacteria with realistic parameter settings. We explain graphically that there is a range of initial conditions at which a gradual increase in environmental conditions can cause a collapse of the population, but only if the change is fast enough. In addition, we show that a pulse in the environmental conditions can cause a temporary collapse, but that is dependent on both the rate and the duration of the pulse. Furthermore, we study whether the autocorrelation of stochastic environmental conditions can influence the probability of inducing rate-tipping. As both the rate of environmental change, and autocorrelation of the environmental variability are increasing in parts of the climate, the probability for rate-induced tipping to occur is likely to increase. Our results imply that, even though the identification of rate sensitive ecosystems in the real world will be challenging, we should incorporate critical rates of change in our ecosystem assessments and management.

Rethinking the definition of rate-induced tipping

The current definition of rate-induced tipping is tied to the idea of a pullback attractor limiting in forward and backward time to a stable quasi-static equilibrium. Here, we propose a new definition that encompasses the standard definition in the literature for certain scalar systems and includes previously excluded N-dimensional systems that exhibit rate-dependent critical transitions.

A resilience concept based on system functioning: A dynamical systems perspective

We introduce a new framework for resilience, which is traditionally understood as the ability of a system to absorb disturbances and maintain its state, by proposing a shift from a state-based to a system functioning-based approach to resilience, which takes into account that several different coexisting stable states could fulfill the same functioning. As a consequence, not every regime shift, i.e., transition from one stable state to another, is associated with a lack or loss of resilience. We emphasize the importance of flexibility-the ability of a system to shift between different stable states while still maintaining system functioning. Furthermore, we provide a classification of system responses based on the phenomenological properties of possible disturbances, including the role of their timescales. Therefore, we discern fluctuations, shocks, press disturbances, and trends as possible disturbances. We distinguish between two types of mechanisms of resilience: (i) tolerance and flexibility, which are properties of the system, and (ii) adaptation and transformation, which are processes that alter the system's tolerance and flexibility. Furthermore, we discuss quantitative methods to investigate resilience in model systems based on approaches developed in dynamical systems theory.

Early Warning Signals for Rate-induced Critical Transitions in Salt Marsh Ecosystems

Intertidal ecosystems are important because of their function as coastal protection and ecological value. Sea level rise may lead to submergence of salt marshes worldwide. Salt marshes can exhibit critical transitions if the rate of sea level rise exceeds salt marsh sedimentation, leading to a positive feedback between reduced sedimentation and vegetation loss, drowning the marshes. However, a general framework to recognize such rate-induced critical transitions and predict salt marsh collapse through early warning signals is lacking. Therefore, we apply the novel concept of rate-induced critical transitions to salt marsh ecosystems. We reveal rate-induced critical transitions and new geomorphic early warning signals for upcoming salt marsh collapse in a spatial model. These include a decrease in marsh height, the ratio of marsh area to creek area, and creek cliff steepness, as well as an increase in creek depth. Furthermore, this research predicts that increasing sediment capture ability by vegetation would be an effective measure to increase the critical rate of sea level rise at which salt marshes collapse. The generic spatial model also applies to other intertidal ecosystems with similar dynamics, such as tidal flats and mangroves. Our findings facilitate better resilience assessment of intertidal ecosystems globally and identifying measures to protect these ecosystems.

Rate of environmental change across scales in ecology

The rate of change (RoC) of environmental drivers matters: biotic and abiotic components respond differently when faced with a fast or slow change in their environment. This phenomenon occurs across spatial scales and thus levels of ecological organization. We investigated the RoC of environmental drivers in the ecological literature and examined publication trends across ecological levels, including prevalent types of evidence and drivers. Research interest in environmental driver RoC has increased over time (particularly in the last decade), however, the amount of research and type of studies were not equally distributed across levels of organization and different subfields of ecology use temporal terminology (e.g. 'abrupt' and 'gradual') differently, making it difficult to compare studies. At the level of individual organisms, evidence indicates that responses and underlying mechanisms are different when environmental driver treatments are applied at different rates, thus we propose including a time dimension into reaction norms. There is much less experimental evidence at higher levels of ecological organization (i.e. population, community, ecosystem), although theoretical work at the population level indicates the importance of RoC for evolutionary responses. We identified very few studies at the community and ecosystem levels, although existing evidence indicates that driver RoC is important at these scales and potentially could be particularly important for some processes, such as community stability and cascade effects. We recommend shifting from a categorical (e.g. abrupt versus gradual) to a quantitative and continuous (e.g. °C/h) RoC framework and explicit reporting of RoC parameters, including magnitude, duration and start and end points to ease cross-scale synthesis and alleviate ambiguity. Understanding how driver RoC affects individuals, populations, communities and ecosystems, and furthermore how these effects can feed back between levels is critical to making improved predictions about ecological responses to global change drivers. The application of a unified quantitative RoC framework for ecological studies investigating environmental driver RoC will both allow cross-scale synthesis to be accomplished more easily and has the potential for the generation of novel hypotheses.

Soil Saprobic Fungi Differ in Their Response to Gradually and Abruptly Delivered Copper

The overwhelming majority of studies examining environmental change deliver treatments abruptly, although, in fact, many important changes are gradual. One example of a gradually increasing environmental stressor is heavy metal contamination. Essential heavy metals, such as copper, play an important role within cells of living organisms but are toxic at higher concentrations. In our study, we focus on the effects of copper pollution on filamentous soil fungi, key players in terrestrial ecosystem functioning. We hypothesize that fungi exposed to gradually increasing copper concentrations have higher chances for physiological acclimation and will maintain biomass production and accumulate less copper, compared to fungi abruptly exposed to the highest copper concentration. To test this hypothesis, we conducted an experiment with 17 fungal isolates exposed to gradual and abrupt copper addition. Contrary to our hypothesis, we find diverse idiosyncratic responses, such that for many fungi gradually increasing copper concentrations have more severe effects (stronger growth inhibition and higher copper accumulation) than an abrupt increase. While a number of environmental change studies have accumulated evidence based on the magnitude of changes, the results of our study imply that the rate of change can be an important factor to consider in future studies in ecology, environmental science, and environmental management.

The effect of climate change on the resilience of ecosystems with adaptive spatial pattern formation

In a rapidly changing world, quantifying ecosystem resilience is an important challenge. Historically, resilience has been defined via models that do not take spatial effects into account. These systems can only adapt via uniform adjustments. In reality, however, the response is not necessarily uniform, and can lead to the formation of (self-organised) spatial patterns - typically localised vegetation patches. Classical measures of resilience cannot capture the emerging dynamics in spatially self-organised systems, including transitions between patterned states that have limited impact on ecosystem structure and productivity. We present a framework of interlinked phase portraits that appropriately quantifies the resilience of patterned states, which depends on the number of patches, the distances between them and environmental conditions. We show how classical resilience concepts fail to distinguish between small and large pattern transitions, and find that the variance in interpatch distances provides a suitable indicator for the type of imminent transition. Subsequently, we describe the dependency of ecosystem degradation based on the rate of climatic change: slow change leads to sporadic, large transitions, whereas fast change causes a rapid sequence of smaller transitions. Finally, we discuss how pre-emptive removal of patches can minimise productivity losses during pattern transitions, constituting a viable conservation strategy.

Tipping phenomena in typical dynamical systems subjected to parameter drift

Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics. Based on the example of a paradigmatic low-dimensional dissipative system subjected to different scenarios of parameter drifts of non-negligible rates, we show that a number of novel types of tippings can be observed due to the topological complexity underlying general systems. Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. Tipping from or through an extended chaotic attractor might lead to random tipping into coexisting regular attractors, and rate-induced tippings appear not abruptly as phase transitions, rather they show up gradually when the rate of the parameter drift is increased. Since chaotic systems of arbitrary time-dependence call for ensemble methods, we argue for a probabilistic approach and propose the use of tipping probabilities as a measure of tipping. We numerically determine these quantities and their parameter dependence for all tipping forms discussed.

Multistability of model and real dryland ecosystems through spatial self-organization

Spatial self-organization of dryland vegetation constitutes one of the most promising indicators for an ecosystem's proximity to desertification. This insight is based on studies of reaction-diffusion models that reproduce visual characteristics of vegetation patterns observed on aerial photographs. However, until now, the development of reliable early warning systems has been hampered by the lack of more in-depth comparisons between model predictions and real ecosystem patterns. In this paper, we combined topographical data, (remotely sensed) optical data, and in situ biomass measurements from two sites in Somalia to generate a multilevel description of dryland vegetation patterns. We performed an in-depth comparison between these observed vegetation pattern characteristics and predictions made by the extended-Klausmeier model for dryland vegetation patterning. Consistent with model predictions, we found that for a given topography, there is multistability of ecosystem states with different pattern wavenumbers. Furthermore, observations corroborated model predictions regarding the relationships between pattern wavenumber, total biomass, and maximum biomass. In contrast, model predictions regarding the role of slope angles were not corroborated by the empirical data, suggesting that inclusion of small-scale topographical heterogeneity is a promising avenue for future model development. Our findings suggest that patterned dryland ecosystems may be more resilient to environmental change than previously anticipated, but this enhanced resilience crucially depends on the adaptive capacity of vegetation patterns.

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.