It is necessary to predict the critical transition of lake ecosystems due to their abrupt, non-linear effects on social-economic systems. Given the promising application of paleolimnological archives to tracking the historical changes of lake ecosystems, it is speculated that they can also record the lake\'s critical transition. We studied Lake Dali-Nor in the arid region of Inner Mongolia because of the profound shrinking the lake experienced between the 1300 s and the 1600 s. We reconstructed the succession of bacterial communities from a 140-cm-long sediment core at 4-cm intervals and detected the critical transition. Our results showed that the historical trajectory of bacterial communities from the 1200 s to the 2010s was divided into two alternative states: state1 from 1200 to 1300 s and state2 from 1400 to 2010s. Furthermore, in the late 1300 s, the appearance of a tipping point and critical slowing down implied the existence of a critical transition. By using a multi-decadal time series from the sedimentary core, with general Lotka-Volterra model simulations, local stability analysis found that bacterial communities were the most unstable as they approached the critical transition, suggesting that the collapse of stability triggers the community shift from an equilibrium state to another state. Furthermore, the most unstable community harbored the strongest antagonistic and mutualistic interactions, which may imply the detrimental role of interaction strength on community stability. Collectively, our study showed that sediment DNA can be used to detect the critical transition of lake ecosystems.

Understanding the transient dynamics of interlinked social-ecological systems (SES) is imperative for assessing sustainability in the Anthropocene. However, how to identify critical transitions in real-world SES remains a formidable challenge. In this study, we present an evolutionary framework to characterize these dynamics over an extended historical timeline. Our approach leverages multidecadal rates of change in socioeconomic data, paleoenvironmental, and cutting-edge sedimentary ancient DNA records from China\'s Yangtze River Delta, one of the most densely populated and intensively modified landscapes on Earth. Our analysis reveals two significant social-ecological transitions characterized by contrasting interactions and feedback spanning several centuries. Initially, the regional SES exhibited a loosely connected and ecologically sustainable regime. Nevertheless, starting in the 1950s, an increasingly interconnected regime emerged, ultimately resulting in the crossing of tipping points and an unprecedented acceleration in soil erosion, water eutrophication, and ecosystem degradation. Remarkably, the second transition occurring around the 2000s, featured a notable decoupling of socioeconomic development from ecoenvironmental degradation. This decoupling phenomenon signifies a more desirable reconfiguration of the regional SES, furnishing essential insights not only for the Yangtze River Basin but also for regions worldwide grappling with similar sustainability challenges. Our extensive multidecadal empirical investigation underscores the value of coevolutionary approaches in understanding and addressing social-ecological system dynamics.

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as \"critical transitions,\" by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Epithelial-mesenchymal transition (EMT) is a trans-differentiating and reversible process that leads to dramatic cell phenotypic changes, enabling epithelial cells in acquiring mesenchymal phenotypes and behaviors. EMT plays a crucial role during embryogenesis, and occurs in several para-physiologic and pathological conditions, as during fibrosis or cancer development. EMT displays some hallmarks of critical transitions, as a sudden change in the overall configuration of a system in correspondence of specific tipping point around which a \"catastrophic bifurcation\" happens. The transition occurs when external conditions breach specific thresholds. This definition helps in highlighting two main aspects: (1) the change involves the overall system, rather than single, discrete components; (2) cues from the microenvironment play an irreplaceable role in triggering the transition. This evidence implies that critical transition should be ascertained focusing the investigation at the system level (rather than investigating only molecular parameters) in a well-defined context, as the transition is strictly dependent on the microenvironment in which it occurs. Therefore, we need a systems biology approach to investigate EMT across the Waddington-like epigenetic landscape wherein the participation of both internal and external cues can be studied to follow the extent and the main characteristics of the phenotypic transition. Herein, we suggest a set of systems parameters (motility, invasiveness) altogether with specific molecular/histological markers to identify those critical observables, which can be integrated into a comprehensive mechanistic model.

The critical point or pivotal threshold of cell transition occurs in early embryonic development when cell differentiation culminates in its transition to specific cell fates, at which the cell population undergoes an abrupt and qualitative shift. Revealing such critical points of cell transitions can track cellular heterogeneity and shed light on the molecular mechanisms of cell differentiation. However, precise detection of critical state transitions proves challenging when relying on single-cell RNA sequencing data due to their inherent sparsity, noise, and heterogeneity. In this study, diverging from conventional methods like differential gene analysis or static techniques that emphasize classification of cell types, an innovative computational approach, single-cell gene association entropy (SGAE), is designed for the analysis of single-cell RNA-seq data and utilizes gene association information to reveal critical states of cell transitions. More specifically, through the translation of gene expression data into local SGAE scores, the proposed SGAE can serve as an index to quantitatively assess the resilience and critical properties of genetic regulatory networks, consequently detecting the signal of cell transitions. Analyses of five single-cell datasets for embryonic development demonstrate that the SGAE method achieves better performance in facilitating the characterization of a critical phase transition compared with other existing methods. Moreover, the SGAE value can effectively discriminate cellular heterogeneity over time and performs well in the temporal clustering of cells. Besides, biological functional analysis also indicates the effectiveness of the proposed approach.

The progression of complex diseases sometimes undergoes a drastic critical transition, at which the biological system abruptly shifts from a relatively healthy state (before-transition stage) to a disease state (after-transition stage). Searching for such a critical transition or critical state is crucial to provide timely and effective scientific treatment to patients. However, in most conditions where only a small sample size of clinical data is available, resulting in failure when detecting the critical states of complex diseases, particularly only single-sample data.
In this study, different from traditional methods that require multiple samples at each time, a model-free computational method, single-sample Markov flow entropy (sMFE), provides a solution to the identification problem of critical states/pre-disease states of complex diseases, solely based on a single-sample. Our proposed method was employed to characterize the dynamic changes of complex diseases from the perspective of network entropy.
The proposed approach was verified by unmistakably identifying the critical state just before the occurrence of disease deterioration for four tumor datasets from The Cancer Genome Atlas (TCGA) database. In addition, two new prognostic biomarkers, optimistic sMFE (O-sMFE) and pessimistic sMFE (P-sMFE) biomarkers, were identified by our method and enable the prognosis evaluation of tumors.
The proposed method has shown its capability to accurately detect pre-disease states of four cancers and provide two novel prognostic biomarkers, O-sMFE and P-sMFE biomarkers, to facilitate the personalized prognosis of patients. This is a remarkable achievement that could have a major impact on the diagnosis and treatment of complex diseases.

Harmful algal blooms (HABs) producing toxic metabolites are increasingly threatening environmental and human health worldwide. Unfortunately, long-term process and mechanism triggering HABs remain largely unclear due to the scarcity of temporal monitoring. Retrospective analysis of sedimentary biomarkers using up-to-date chromatography and mass spectrometry techniques provide a potential means to reconstruct the past occurrence of HABs. By combining aliphatic hydrocarbons, photosynthetic pigments, and cyanotoxins, we quantified herein century-long changes in abundance, composition, and variability of phototrophs, particularly toxigenic algal blooms, in China\'s third largest freshwater Lake Taihu. Our multi-proxy limnological reconstruction revealed an abrupt ecological shift in the 1980s characterized by elevated primary production, Microcystis-dominated cyanobacterial blooms, and exponential microcystin production, in response to nutrient enrichment, climate change, and trophic cascades. The empirical results from ordination analysis and generalized additive models support climate warming and eutrophication synergy through nutrient recycling and their feedback through buoyant cyanobacterial proliferation, which sustain bloom-forming potential and further promote the occurrence of increasingly-toxic cyanotoxins (e.g., microcystin-LR) in Lake Taihu. Moreover, temporal variability of the lake ecosystem quantified using variance and rate of change metrics rose continuously after state change, indicating increased ecological vulnerability and declined resilience following blooms and warming. With the persistent legacy effects of lake eutrophication, nutrient reduction efforts mitigating toxic HABs probably be overwhelmed by climate change effects, emphasizing the need for more aggressive and integrated environmental strategies.

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.

Tipping points or critical transitions widely exist during the progression of many biological processes. It is of great importance to detect the tipping point with the measured omics data, which may be a key to achieving predictive or preventive medicine. We present the tipping point detector (TPD), a web tool for the detection of the tipping point during the dynamic process of biological systems, and further its leading molecules or network, based on the input high-dimensional time series or stage course data. With the solid theoretical background of dynamic network biomarker (DNB) and a series of computational methods for DNB detection, TPD detects the potential tipping point/critical state from the input omics data and outputs multifarious visualized results, including a suggested tipping point with a statistically significant P value, the identified key genes and their functional biological information, the dynamic change in the DNB/leading network that may drive the critical transition and the survival analysis based on DNB scores that may help to identify \'dark\' genes (nondifferential in terms of expression but differential in terms of DNB scores). TPD fits all current browsers, such as Chrome, Firefox, Edge, Opera, Safari and Internet Explorer. TPD is freely accessible at http://www.rpcomputationalbiology.cn/TPD.

The progression of complex diseases generally involves a pre-deterioration stage that occurs during the transition from a healthy state to disease deterioration, at which a drastic and qualitative shift occurs. The development of an effective approach is urgently needed to identify such a pre-deterioration stage or critical state just before disease deterioration, which allows the timely implementation of appropriate measures to prevent a catastrophic transition. However, identifying the pre-deterioration stage is a challenging task in clinical medicine, especially when only a single sample is available for most patients, which is responsible for the failure of most statistical methods. In this study, a novel computational method, called single-sample network module biomarkers (sNMB), is presented to predict the pre-deterioration stage or critical point using only a single sample. Specifically, the proposed single-sample index effectively quantifies the disturbance caused by a single sample against a group of given reference samples. Our method successfully detected the early warning signal of the critical transitions when applied to both a numerical simulation and four real datasets, including acute lung injury, stomach adenocarcinoma, esophageal carcinoma, and rectum adenocarcinoma. In addition, it provides signaling biomarkers for further practical application, which helps to discover prognostic indicators and reveal the underlying molecular mechanisms of disease progression.