Distinguishing time-delayed causal interactions using convergent cross mapping

A framework for identifying factors controlling cyanobacterium Microcystis flos-aquae blooms by coupled CCM-ECCM Bayesian networks

Cyanobacterial blooms in freshwater sources are a global concern, and gaining insight into their causes is crucial for effective resource management and control. In this study, we present a novel computational framework for the causal analysis of cyanobacterial harmful algal blooms (cyanoHABs) in Lake Kinneret. Our framework integrates Convergent Cross Mapping (CCM) and Extended CCM (ECCM) causal networks with Bayesian Network (BN) models. The constructed CCM-ECCM causal networks and BN models unveil significant interactions among factors influencing cyanoHAB formation. These interactions have been validated by domain experts and supported by evidence from peer-reviewed publications. Our findings suggest that Microcystis flos-aquae levels are influenced not only by community structure but also by ammonium, phosphate, oxygen, and temperature levels in the weeks preceding bloom occurrences. We demonstrated a non-parametric computational framework for causal analysis of a multivariate ecosystem. Our framework offers a more comprehensive understanding of the underlying mechanisms driving M. flos-aquae blooms in Lake Kinneret. It captures complex interactions and provides an explainable prediction model. By considering causal relationships, temporal dynamics, and joint probabilities of environmental factors, the proposed framework enhances our understanding of cyanoHABs in Lake Kinneret.

Using empirical dynamic modeling to identify the impact of meteorological factors on hemorrhagic fever with renal syndrome in Weifang, Northeastern China, from 2011 to 2020

BACKGROUND

Hemorrhagic Fever with Renal Syndrome (HFRS) continues to pose a significant public health threat to the well-being of the population. Given that the spread of HFRS is susceptible to meteorological factors, we aim to probe into the meteorological drivers of HFRS. Thus, novel techniques that can discern time-delayed non-linear relationships from nonlinear dynamical systems are compulsory.

METHODS

We analyze the epidemiological features of HFRS in Weifang City, 2011-2020, via the employment of the Empirical Dynamic Modeling (EDM) method. Our analysis delves into the intricate web of time-delayed non-linear associations between meteorological factors and HFRS. Additionally, we investigate the repercussions of minor perturbations in meteorological variables on future HFRS incidence.

RESULTS

A total of 2515 HFRS cases were reported in Weifang from 2011 to 2020. The number of cases per week was 4.81, and the average weekly incidence was 0.52 per 1,000,000. The propagation of HFRS is significantly impacted by the mean weekly temperature, relative humidity, cumulative rainfall, and wind speed, and the ρCCM converges to 0.55,0.48,0.38 and 0.39, respectively. The graphical representation of the relationship between temperature (lagged by 2 weeks) and the incidence of HFRS exhibits an inverted U-shaped curve, whereby the incidence of HFRS culminates as the temperature reaches 10 °C. Moreover, temperature, relative humidity, cumulative rainfall, and wind speed exhibit a positive correlation with HFRS incidence, with a time lag of 4-6 months.

CONCLUSIONS

Our discoveries suggest that meteorological factors can drive the transmission of HFRS both at a macroscopic and microscopic scale. Prospective alterations in meteorological conditions, for instance, elevations in temperature, relative humidity, and precipitation will instigate an upsurge in the incidence of HFRS after 4-6 months, and thus, timely public health measures should be taken to mitigate these changes.

Hierarchy between forelimb premotor and primary motor cortices and its manifestation in their firing patterns

Though hierarchy is commonly invoked in descriptions of motor cortical function, its presence and manifestation in firing patterns remain poorly resolved. Here we use optogenetic inactivation to demonstrate that short-latency influence between forelimb premotor and primary motor cortices is asymmetric during reaching in mice, demonstrating a partial hierarchy between the endogenous activity in each region. Multi-region recordings revealed that some activity is captured by similar but delayed patterns where either region's activity leads, with premotor activity leading more. Yet firing in each region is dominated by patterns shared between regions and is equally predictive of firing in the other region at the single-neuron level. In dual-region network models fit to data, regions differed in their dependence on across-region input, rather than the amount of such input they received. Our results indicate that motor cortical hierarchy, while present, may not be exposed when inferring interactions between populations from firing patterns alone.

Revealing causality in the associations between meteorological variables and air pollutant concentrations

Understanding the role of meteorology in determining air pollutant concentrations is an important goal for better comprehension of air pollution dispersion and fate. It requires estimating the strength of the causal associations between all the relevant meteorological variables and the pollutant concentrations. Unfortunately, many of the meteorological variables are not routinely observed. Furthermore, the common analysis methods cannot establish causality. Here we use the output of a numerical weather prediction model as a proxy for real meteorological data, and study the causal relationships between a large suite of its meteorological variables, including some rarely observed ones, and the corresponding nitrogen dioxide (NO2) concentrations at multiple observation locations. Time-lagged convergent cross mapping analysis is used to ascertain causality and its strength, and the Pearson and Spearman correlations are used to study the direction of the associations. The solar radiation, temperature lapse rate, boundary layer height, horizontal wind speed and wind shear were found to be causally associated with the NO2 concentrations, with mean time lags of their maximal impact at -3, -1, -2 and -3 hours, respectively. The nature of the association with the vertical wind speed was found to be uncertain and region-dependent. No causal association was found with relative humidity, temperature and precipitation.

Causal effect of air pollution and meteorology on the COVID-19 pandemic: A convergent cross mapping approach

Environmental factors have been suspected to influence the propagation and lethality of COVID-19 in the global population. However, most of the studies have been limited to correlation analyses and did not use specific methods to address the dynamic of the causal relationship between the virus and its external drivers. This work focuses on inferring and understanding the causal effect of critical air pollutants and meteorological parameters on COVID-19 by using an Empirical Dynamic Modeling approach called Convergent Cross Mapping. This technique allowed us to identify the time-delayed causation and the sign of interactions. Considering its remarkable urban environment and mortality rate during the pandemic, Quito, Ecuador, was chosen as a case study. Our results show that both urban air pollution and meteorology have a causal impact on COVID-19. Even if the strength and the sign of the causality vary over time, a general trend can be drawn. NO2, SO2, CO and PM2.5 have a positive causation for COVID-19 infections (ρ > 0.35 and ∂ > 9.1). Contrary to current knowledge, this study shows a rapid effect of pollution on COVID-19 cases (1 < lag days <24) and a negative impact of O3 on COVID-19-related deaths (ρ = 0.53 and ∂ = -0.3). Regarding the meteorology, temperature (ρ = 0.24 and ∂ = -0.4) and wind speed (ρ = 0.34 and ∂ = -3.9) tend to mitigate the epidemiological consequences of SARS-CoV-2, whereas relative humidity seems to increase the excess deaths (ρ = 0.4 and ∂ = 0.05). A causal network is proposed to synthesize the interactions between the studied variables and to provide a simple model to support the management of coronavirus outbreaks.

Empirical dynamic modelling and enhanced causal analysis of short-length Culex abundance timeseries with vector correlation metrics

Employing Empirical Dynamic Modelling we investigate whether model free methods could be applied in the study of Culex mosquitoes in Northern Greece. Applying Simplex Projection and S-Map algorithms on yearly timeseries of maximum abundances from 2011 to 2020 we successfully predict the decreasing trend in the maximum number of mosquitoes which was observed in the rural area of Thessaloniki during 2021. Leveraging the use of vector correlation metrics we were able to deduce the main environmental factors driving mosquito abundance such as temperature, rain and wind during 2012 and study the causal interaction between neighbouring populations in the industrial area of Thessaloniki between 2019 and 2020. In all three cases a chaotic and non-linear behaviour of the underlying system was observed. Given the health risk associated with the presence of mosquitoes as vectors of viral diseases these results hint to the usefulness of EDM methods in entomological studies as guides for the construction of more accurate and realistic mechanistic models which are indispensable to public health authorities for the design of targeted control strategies and health prevention measures.

Land use/cover and land degradation across the Eurasian steppe: Dynamics, patterns and driving factors

Despite the ecological and socio-economic importance of Eurasian steppe, the land use/cover change, land degradation and the threats facing this precious ecosystem still have not been comprehensively understood. Taking advantages of the land use/cover change monitoring platform (FROM-GLC Plus), this study developed the annual land use/cover maps during 2000-2022, and the land use/cover change, especially the change of grassland, was further analyzed. The grassland area exhibited a net increase, predominantly transformed from cropland, forest, and bareland, accounting for 17.64 %, 31.91 %, and 45.60 %, respectively. To monitor land degradation, we adopted the framework suggested by the United Nations Convention to Combat Desertification (UNCCD). According to the monitoring result, grassland constituted the highest proportion of degraded land (39.82 %). This may due to its dominance in the Eurasian steppe's land use/cover, as the extent of grassland degradation (1.92 %) was lower than the overall land degradation level (2.83 %) across the region. To offer tailored and sustainable development recommendations, we quantified the driving factors behind land dynamics using the geographical detector model and convergent cross mapping (CCM), considering both spatial and temporal dimensions. Environmental and socio-economic factors, such as precipitation, temperature, urbanization, mining and grazing intensity, etc., were integrated into the analysis. We found that urbanization, cropland and moisture distribution emerged as key drivers influencing land degradation's spatial distribution in the Eurasian steppe, while temperature variations between years impacted vegetation changes. This research thus provides a deeper understanding of the region's land dynamics, enhancing comprehensive monitoring of the Eurasian steppe's land dynamics. Moreover, it serves as a foundation for policymakers and land managers to devise conservation strategies and sustainable development initiatives for this critical ecosystem.

Agent-based simulation and child protection systems: Rationale, implementation, and verification

BACKGROUND AND OBJECTIVE

Simulation models are an important tool used in health care and other disciplines to support operational research and decision-making. In the child protection literature, simulation models are an under-utilized source of research evidence.

PARTICIPANTS AND SETTING

In this paper, we describe the rationale for and the development of an agent-based simulation of a child protection system in the US. Using the investigation, prevention service, and placement histories of 600,000 children served in an urban child welfare system, we walk the reader through the development of a prototype known as OSPEDALE.

METHODS

The governing equations built into OSPEDALE probabilistically simulate the onset of investigations. Then, drawing from empirical survival distributions, the governing equations trace the probability of subsequent interactions with the system (recurrence of maltreatment, service referrals, and placement) conditional on the characteristics of children, their assessed risk level, and prior child protection system involvement.

RESULTS

As an initial test of OSPEDALE's utility, we compare empirical admission counts with counts generated from OSPEDALE. Though the verification step is admittedly simple, the comparison shows that OSPEDALE replicates the empirical count of new admissions closely enough to justify further investment in OSPEDALE.

CONCLUSIONS

Management of public child protection systems is increasingly research evidence-dependent. The emphasis on research evidence as a decision-support tool has elevated evidence acquired through randomized clinical trials. Though important, the evidence from clinical trials represents only one type of research evidence. Properly specified, simulation models are another source of evidence with real-world relevance.

Causalized convergent cross-mapping and its approximate equivalence with directed information in causality analysis

Convergent cross-mapping (CCM) has attracted increased attention recently due to its capability to detect causality in nonseparable systems under deterministic settings, which may not be covered by the traditional Granger causality. From an information-theoretic perspective, causality is often characterized as the directed information (DI) flowing from one side to the other. As information is essentially nondeterministic, a natural question is: does CCM measure DI flow? Here, we first causalize CCM so that it aligns with the presumption in causality analysis-the future values of one process cannot influence the past of the other, and then establish and validate the approximate equivalence of causalized CCM (cCCM) and DI under Gaussian variables through both theoretical derivations and fMRI-based brain network causality analysis. Our simulation result indicates that, in general, cCCM tends to be more robust than DI in causality detection. The underlying argument is that DI relies heavily on probability estimation, which is sensitive to data size as well as digitization procedures; cCCM, on the other hand, gets around this problem through geometric cross-mapping between the manifolds involved. Overall, our analysis demonstrates that cross-mapping provides an alternative way to evaluate DI and is potentially an effective technique for identifying both linear and nonlinear causal coupling in brain neural networks and other settings, either random or deterministic, or both.

Kernel-Based Independence Tests for Causal Structure Learning on Functional Data

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert-Schmidt independence criterion (hsic) and its d-variate version (d-hsic), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (cpt) based on the Hilbert-Schmidt conditional independence criterion (hscic), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socioeconomic data.

Detecting causal relationship of non-floodplain wetland hydrologic connectivity using convergent cross mapping

The hydrologic connectivity of non-floodplain wetlands (NFWs) with downstream water (DW) has gained increased importance, but connectivity via groundwater (GW) is largely unknown owing to the high complexity of hydrological processes and climatic seasonality. In this study, a causal inference method, convergent cross mapping (CCM), was applied to detect the hydrologic causality between upland NFW and DW through GW. CCM is a nonlinear inference method for detecting causal relationships among environmental variables with weak or moderate coupling in nonlinear dynamical systems. We assumed that causation would exist when the following conditions were observed: (1) the presence of two direct causal (NFW → GW and GW → DW) and one indirect causal (NFW → DW) relationship; (2) a nonexistent opposite causal relationship (DW → NFW); (3) the two direct causations with shorter lag times relative to indirect causation; and (4) similar patterns not observed with pseudo DW. The water levels monitored by a well and piezometer represented NFW and GW measurements, respectively, and the DW was indicated by the baseflow at the outlet of the drainage area, including NFW. To elucidate causality, the DW taken at the adjacent drainage area with similar climatic seasonality was also tested as pseudo DW. The CCM results showed that the water flow from NFW to GW and then DW was only present, and any opposite flows did not exist. In addition, direct causations had shorter lag time than indirect causation, and 3-day lag time was shown between NFW and DW. Interestingly, the results with pseudo DW did not show any lagged interactions, indicating non-causation. These results provide the signals for the hydrologic connectivity of NFW and DW with GW. Therefore, this study would support the importance of NFW protection and management.

Dryland sensitivity to climate change and variability using nonlinear dynamics

Primary productivity response to climatic drivers varies temporally, indicating state-dependent interactions between climate and productivity. Previous studies primarily employed equation-based approaches to clarify this relationship, ignoring the state-dependent nature of ecological dynamics. Here, using 40 y of climate and productivity data from 48 grassland sites across Mongolia, we applied an equation-free, nonlinear time-series analysis to reveal sensitivity patterns of productivity to climate change and variability and clarify underlying mechanisms. We showed that productivity responded positively to annual precipitation in mesic regions but negatively in arid regions, with the opposite pattern observed for annual mean temperature. Furthermore, productivity responded negatively to decreasing annual aridity that integrated precipitation and temperature across Mongolia. Productivity responded negatively to interannual variability in precipitation and aridity in mesic regions but positively in arid regions. Overall, interannual temperature variability enhanced productivity. These response patterns are largely unrecognized; however, two mechanisms are inferable. First, time-delayed climate effects modify annual productivity responses to annual climate conditions. Notably, our results suggest that the sensitivity of annual productivity to increasing annual precipitation and decreasing annual aridity can even be negative when the negative time-delayed effects of annual precipitation and aridity on productivity prevail across time. Second, the proportion of plant species resistant to water and temperature stresses at a site determines the sensitivity of productivity to climate variability. Thus, we highlight the importance of nonlinear, state-dependent sensitivity of productivity to climate change and variability, accurately forecasting potential biosphere feedback to the climate system.

A general model-based causal inference method overcomes the curse of synchrony and indirect effect

To identify causation, model-free inference methods, such as Granger Causality, have been widely used due to their flexibility. However, they have difficulty distinguishing synchrony and indirect effects from direct causation, leading to false predictions. To overcome this, model-based inference methods that test the reproducibility of data with a specific mechanistic model to infer causality were developed. However, they can only be applied to systems described by a specific model, greatly limiting their applicability. Here, we address this limitation by deriving an easily testable condition for a general monotonic ODE model to reproduce time-series data. We built a user-friendly computational package, General ODE-Based Inference (GOBI), which is applicable to nearly any monotonic system with positive and negative regulations described by ODE. GOBI successfully inferred positive and negative regulations in various networks at both the molecular and population levels, unlike existing model-free methods. Thus, this accurate and broadly applicable inference method is a powerful tool for understanding complex dynamical systems.

Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series

Causality detection methods are valuable tools for detecting causal links in complex systems. The efficiency of continuity scaling (CS) and the convergent cross sorting (CSS) methods to detect causality was analysed. Usefulness and limitations of both methods in their application to simulated and real-world time series was explored under different scenarios. We find that CS is more robust and efficient than the CSS method for all simulated systems, even when increasing noise levels were considered. Both methods were not able to infer causality when time series with a marked difference in their main frequencies were analysed. Minimum time-series length required for the detection of a causal link depends on intrinsic system dynamics and on the method selected to detect it. Using simulated time series, only the CS method was capable to detect bidirectional causality. Causality detection, using the CS method, should at least include: (i) causality strength convergence analysis, (ii) statistical tests of significance, (iii) time-series standardization, and (iv) causality strength ratios as a strength indicator of relative causality between systems. Causality cannot be detected by either method in simulated time series that exhibit generalized synchronization.

Distinct life history strategies underpin clear patterns of succession in microparasite communities infecting a wild mammalian host

Individual animals in natural populations tend to host diverse parasite species concurrently over their lifetimes. In free-living ecological communities, organismal life histories shape interactions with their environment, which ultimately forms the basis of ecological succession. However, the structure and dynamics of mammalian parasite communities have not been contextualized in terms of primary ecological succession, in part because few datasets track occupancy and abundance of multiple parasites in wild hosts starting at birth. Here, we studied community dynamics of 12 subtypes of protozoan microparasites (Theileria spp.) in a herd of African buffalo. We show that Theileria communities followed predictable patterns of succession underpinned by four different parasite life history strategies. However, in contrast to many free-living communities, network complexity decreased with host age. Examining parasite communities through the lens of succession may better inform the effect of complex within host eco-evolutionary dynamics on infection outcomes, including parasite co-existence through the lifetime of the host.

Relationships of temperature and biodiversity with stability of natural aquatic food webs

Temperature and biodiversity changes occur in concert, but their joint effects on ecological stability of natural food webs are unknown. Here, we assess these relationships in 19 planktonic food webs. We estimate stability as structural stability (using the volume contraction rate) and temporal stability (using the temporal variation of species abundances). Warmer temperatures were associated with lower structural and temporal stability, while biodiversity had no consistent effects on either stability property. While species richness was associated with lower structural stability and higher temporal stability, Simpson diversity was associated with higher temporal stability. The responses of structural stability were linked to disproportionate contributions from two trophic groups (predators and consumers), while the responses of temporal stability were linked both to synchrony of all species within the food web and distinctive contributions from three trophic groups (predators, consumers, and producers). Our results suggest that, in natural ecosystems, warmer temperatures can erode ecosystem stability, while biodiversity changes may not have consistent effects.

Inferring a Causal Relationship between Environmental Factors and Respiratory Infections Using Convergent Cross-Mapping

The incidence of respiratory infections in the population is related to many factors, among which environmental factors such as air quality, temperature, and humidity have attracted much attention. In particular, air pollution has caused widespread discomfort and concern in developing countries. Although the correlation between respiratory infections and air pollution is well known, establishing causality between them remains elusive. In this study, by conducting theoretical analysis, we updated the procedure of performing the extended convergent cross-mapping (CCM, a method of causal inference) to infer the causality between periodic variables. Consistently, we validated this new procedure on the synthetic data generated by a mathematical model. For real data in Shaanxi province of China in the period of 1 January 2010 to 15 November 2016, we first confirmed that the refined method is applicable by investigating the periodicity of influenza-like illness cases, an air quality index, temperature, and humidity through wavelet analysis. We next illustrated that air quality (quantified by AQI), temperature, and humidity affect the daily influenza-like illness cases, and, in particular, the respiratory infection cases increased progressively with increased AQI with a time delay of 11 days.

Wavelet clustering analysis as a tool for characterizing community structure in the human microbiome

Human microbiome research is helped by the characterization of microbial networks, as these may reveal key microbes that can be targeted for beneficial health effects. Prevailing methods of microbial network characterization are based on measures of association, often applied to limited sampling points in time. Here, we demonstrate the potential of wavelet clustering, a technique that clusters time series based on similarities in their spectral characteristics. We illustrate this technique with synthetic time series and apply wavelet clustering to densely sampled human gut microbiome time series. We compare our results with hierarchical clustering based on temporal correlations in abundance, within and across individuals, and show that the cluster trees obtained by using either method are significantly different in terms of elements clustered together, branching structure and total branch length. By capitalizing on the dynamic nature of the human microbiome, wavelet clustering reveals community structures that remain obscured in correlation-based methods.

Mitochondrial and metabolic features of salugenesis and the healing cycle

Pathogenesis and salugenesis are the first and second stages of the two-stage problem of disease production and health recovery. Salugenesis is the automatic, evolutionarily conserved, ontogenetic sequence of molecular, cellular, organ system, and behavioral changes that is used by living systems to heal. It is a whole-body process that begins with mitochondria and the cell. The stages of salugenesis define a circle that is energy- and resource-consuming, genetically programmed, and environmentally responsive. Energy and metabolic resources are provided by mitochondrial and metabolic transformations that drive the cell danger response (CDR) and create the three phases of the healing cycle: Phase 1-Inflammation, Phase 2-Proliferation, and Phase 3-Differentiation. Each phase requires a different mitochondrial phenotype. Without different mitochondria there can be no healing. The rise and fall of extracellular ATP (eATP) signaling is a key driver of the mitochondrial and metabolic reprogramming required to progress through the healing cycle. Sphingolipid and cholesterol-enriched membrane lipid rafts act as rheostats for tuning cellular sensitivity to purinergic signaling. Abnormal persistence of any phase of the CDR inhibits the healing cycle, creates dysfunctional cellular mosaics, causes the symptoms of chronic disease, and accelerates the process of aging. New research reframes the rising tide of chronic disease around the world as a systems problem caused by the combined action of pathogenic triggers and anthropogenic factors that interfere with the mitochondrial functions needed for healing. Once chronic pain, disability, or disease is established, salugenesis-based therapies will start where pathogenesis-based therapies end.

Loss of Earth system resilience during early Eocene transient global warming events

Superimposed on long-term late Paleocene-early Eocene warming (~59 to 52 million years ago), Earth's climate experienced a series of abrupt perturbations, characterized by massive carbon input into the ocean-atmosphere system and global warming. Here, we examine the three most punctuated events of this period, the Paleocene-Eocene Thermal Maximum and Eocene Thermal Maximum 2 and 3, to probe whether they were initiated by climate-driven carbon cycle tipping points. Specifically, we analyze the dynamics of climate and carbon cycle indicators acquired from marine sediments to detect changes in Earth system resilience and to identify positive feedbacks. Our analyses suggest a loss of Earth system resilience toward all three events. Moreover, dynamic convergent cross mapping reveals intensifying coupling between the carbon cycle and climate during the long-term warming trend, supporting increasingly dominant climate forcing of carbon cycle dynamics during the Early Eocene Climatic Optimum when these recurrent global warming events became more frequent.

Loss of Earth system resilience during early Eocene transient global warming events

Superimposed on long-term late Paleocene-early Eocene warming (~59 to 52 million years ago), Earth's climate experienced a series of abrupt perturbations, characterized by massive carbon input into the ocean-atmosphere system and global warming. Here, we examine the three most punctuated events of this period, the Paleocene-Eocene Thermal Maximum and Eocene Thermal Maximum 2 and 3, to probe whether they were initiated by climate-driven carbon cycle tipping points. Specifically, we analyze the dynamics of climate and carbon cycle indicators acquired from marine sediments to detect changes in Earth system resilience and to identify positive feedbacks. Our analyses suggest a loss of Earth system resilience toward all three events. Moreover, dynamic convergent cross mapping reveals intensifying coupling between the carbon cycle and climate during the long-term warming trend, supporting increasingly dominant climate forcing of carbon cycle dynamics during the Early Eocene Climatic Optimum when these recurrent global warming events became more frequent.

Directional coupling detection through cross-distance vectors

Inferring the coupling direction from measured time series of complex systems is challenging. We propose a state-space-based causality measure obtained from cross-distance vectors for quantifying interaction strength. It is a model-free noise-robust approach that requires only a few parameters. The approach is applicable to bivariate time series and is resilient to artefacts and missing values. The result is two coupling indices that quantify coupling strength in each direction more accurately than the already established state-space measures. We test the proposed method on different dynamical systems and analyze numerical stability. As a result, a procedure for optimal parameter selection is proposed, circumventing the challenge of determining the optimal embedding parameters. We show it is robust to noise and reliable in shorter time series. Moreover, we show that it can detect cardiorespiratory interaction in measured data. A numerically efficient implementation is available at https://repo.ijs.si/e2pub/cd-vec.

Atmospheric CO2 forcing on Mediterranean biomes during the past 500 kyrs

There is growing concern on the survival of Mediterranean forests under the projected near-future droughts as a result of anthropogenic climate change. Here we determine the resilience of Mediterranean forests across the entire range of climatic boundary conditions realized during the past 500 kyrs based on continuous pollen and geochemical records of (sub)centennial-scale resolution from drillcores from Tenaghi Philippon, Greece. Using convergent cross-mapping we provide empirical confirmation that global atmospheric carbon dioxide (CO₂) may affect Mediterranean vegetation through forcing on moisture availability. Our analysis documents two stable vegetation regimes across the wide range of CO₂ and moisture levels realized during the past four glacial-interglacial cycles, with abrupt shifts from forest to steppe biomes occurring when a threshold in precipitation is crossed. Our approach highlights that a CO₂-driven moisture decrease in the near future may bear an impending risk for abrupt vegetation regime shifts prompting forest loss in the Mediterranean region.

Sentiment analysis and causal learning of COVID-19 tweets prior to the rollout of vaccines

While the impact of the COVID-19 pandemic has been widely studied, relatively fewer discussions about the sentimental reaction of the public are available. In this article, we scrape COVID-19 related tweets on the microblogging platform, Twitter, and examine the tweets from February 24, 2020 to October 14, 2020 in four Canadian cities (Toronto, Montreal, Vancouver, and Calgary) and four U.S. cities (New York, Los Angeles, Chicago, and Seattle). Applying the RoBERTa, Vader and NRC approaches, we evaluate sentiment intensity scores and visualize the results over different periods of the pandemic. Sentiment scores for the tweets concerning three anti-epidemic measures, "masks", "vaccine", and "lockdown", are computed for comparison. We explore possible causal relationships among the variables concerning tweet activities and sentiment scores of COVID-19 related tweets by integrating the echo state network method with convergent cross-mapping. Our analyses show that public sentiments about COVID-19 vary from time to time and from place to place, and are different with respect to anti-epidemic measures of "masks", "vaccines", and "lockdown". Evidence of the causal relationship is revealed for the examined variables, assuming the suggested model is feasible.

Planktonic functional diversity changes in synchrony with lake ecosystem state

Managing ecosystems to effectively preserve function and services requires reliable tools that can infer changes in the stability and dynamics of a system. Conceptually, functional diversity (FD) appears as a sensitive and viable monitoring metric stemming from suggestions that FD is a universally important measure of biodiversity and has a mechanistic influence on ecological processes. It is however unclear whether changes in FD consistently occur prior to state responses or vice versa, with no current work on the temporal relationship between FD and state to support a transition towards trait-based indicators. There is consequently a knowledge gap regarding when functioning changes relative to biodiversity change and where FD change falls in that sequence. We therefore examine the lagged relationship between planktonic FD and abundance-based metrics of system state (e.g. biomass) across five highly monitored lake communities using both correlation and cutting edge non-linear empirical dynamic modelling approaches. Overall, phytoplankton and zooplankton FD display synchrony with lake state but each lake is idiosyncratic in the strength of relationship. It is therefore unlikely that changes in plankton FD are identifiable before changes in more easily collected abundance metrics. These results highlight the power of empirical dynamic modelling in disentangling time lagged relationships in complex multivariate ecosystems, but suggest that FD cannot be generically viable as an early indicator. Individual lakes therefore require consideration of their specific context and any interpretation of FD across systems requires caution. However, FD still retains value as an alternative state measure or a trait representation of biodiversity when considered at the system level.

Granger causality using Jacobian in neural networks

Granger causality is a commonly used method for uncovering information flow and dependencies in a time series. Here, we introduce JGC (Jacobian Granger causality), a neural network-based approach to Granger causality using the Jacobian as a measure of variable importance, and propose a variable selection procedure for inferring Granger causal variables with this measure, using criteria of significance and consistency. The resulting approach performs consistently well compared to other approaches in identifying Granger causal variables, the associated time lags, as well as interaction signs. In addition, we also discuss the need for contemporaneous variables in Granger causal modeling as well as how these neural network-based approaches reduce the impact of nonseparability in dynamical systems, a problem where predictive information on a target variable is not unique to its causes, but also contained in the history of the target variable itself.

Causality analysis in type 1 diabetes mellitus with application to blood glucose level prediction

Effective control of blood glucose level (BGL) is the key factor in the management of type 1 diabetes mellitus (T1D). BGL prediction is an important tool to help maximise the time BGL is in the target range and thus minimise both acute and chronic diabetes-related complications. To predict future BGL, histories of variables known to affect BGL, such as carbohydrate intake, injected bolus insulin, and physical activity, are utilised. Due to these identified cause and effect relationships, T1D management can be examined via the causality context. In this respect, this work initially investigates these relations and quantifies the causality strengths of each variable with BGL using the convergent cross mapping method (CCM). Then, considering the extended CCM, the causality strengths of each variable for different lags are quantified. After that, the optimal time lag for each variable is determined according to the quantified causality effects. Subsequently, the feasibility of leveraging causality information as prior knowledge for BGL prediction is investigated by proposing two approaches. In the first approach, causality strengths are used as weights for relevant affecting variables. In the second approach, the optimal causal lags and the corresponding causality strengths are considered the shifts and weights for the variables, respectively. Overall, the evaluation criteria and statistical analysis used for comparing results show the effectiveness of using causality analysis in T1D management.

Cardiotocography analysis by empirical dynamic modeling and Gaussian processes

Introduction: During labor, fetal heart rate (FHR) and uterine activity (UA) can be continuously monitored using Cardiotocography (CTG). This is the most widely adopted approach for electronic fetal monitoring in hospitals. Both FHR and UA recordings are evaluated by obstetricians for assessing fetal well-being. Due to the complex and noisy nature of these recordings, the evaluation by obstetricians suffers from high interobserver and intraobserver variability. Machine learning is a field that has seen unprecedented advances in the past two decades and many efforts have been made in computerized analysis of CTG using machine learning methods. However, in the literature, the focus is often only on FHR signals unlike in evaluations performed by obstetricians where the UA signals are also taken into account. Methods: Machine learning is a field that has seen unprecedented advances in the past two decades and many efforts have been made in computerized analysis of CTG using machine learning methods. However, in the literature, the focus is often only on FHR signals unlike in evaluations performed by obstetricians where the UA signals are also taken into account. In this paper, we propose to model intrapartum CTG recordings from a dynamical system perspective using empirical dynamic modeling with Gaussian processes, which is a Bayesian nonparametric approach for estimation of functions. Results and Discussion: In the context of our paper, Gaussian processes are capable for simultaneous estimation of the dimensionality of attractor manifolds and reconstructing of attractor manifolds from time series data. This capacity of Gaussian processes allows for revealing causal relationships between the studied time series. Experimental results on real CTG recordings show that FHR and UA signals are causally related. More importantly, this causal relationship and estimated attractor manifolds can be exploited for several important applications in computerized analysis of CTG recordings including estimating missing FHR samples, recovering burst errors in FHR tracings and characterizing the interactions between FHR and UA signals.

Rapid eco-phenotypic feedback and the temperature response of biomass dynamics

Biomass dynamics capture information on population dynamics and ecosystem-level processes (e.g., changes in production over time). Understanding how rising temperatures associated with global climate change influence biomass dynamics is thus a pressing issue in ecology. The total biomass of a species depends on its density and its average mass. Consequently, disentangling how biomass dynamics responds to increasingly warm and variable temperatures ultimately depends on understanding how temperature influences both density and mass dynamics. Here, we address this issue by keeping track of experimental microbial populations growing to carrying capacity for 15 days at two different temperatures, and in the presence and absence of temperature variability. We develop a simple mathematical expression to partition the contribution of changes in density and mass to changes in biomass and assess how temperature responses in either one influence biomass shifts. Moreover, we use time-series analysis (Convergent Cross Mapping) to address how temperature and temperature variability influence reciprocal effects of density on mass and vice versa. We show that temperature influences biomass through its effects on density and mass dynamics, which have opposite effects on biomass and can offset each other. We also show that temperature variability influences biomass, but that effect is independent of any effects on density or mass dynamics. Last, we show that reciprocal effects of density and mass shift significantly across temperature regimes, suggesting that rapid and environment-dependent eco-phenotypic dynamics underlie biomass responses. Overall, our results connect temperature effects on population and phenotypic dynamics to explain how biomass responds to temperature regimes, thus shedding light on processes at play in cosmopolitan and abundant microbes as the world experiences increasingly warm and variable temperatures.

Diversity dependence is a ubiquitous phenomenon across Phanerozoic oceans

Biodiversity on Earth is shaped by abiotic perturbations and rapid diversifications. At the same time, there are arguments that biodiversity is bounded and regulated via biotic interactions. Evaluating the role and relative strength of diversity regulation is crucial for interpreting the ongoing biodiversity changes. We have analyzed Phanerozoic fossil record using public databases and new approaches for identifying the causal dependence of origination and extinction rates on environmental variables and standing diversity. While the effect of environmental factors on origination and extinction rates is variable and taxon specific, the diversity dependence of the rates is almost universal across the studied taxa. Origination rates are dependent on instantaneous diversity levels, while extinction rates reveal delayed diversity dependence. Although precise mechanisms of diversity dependence may be complex and difficult to recover, global regulation of diversity via negative diversity dependence of lineage diversification seems to be a common feature of the biosphere, with profound consequences for understanding current biodiversity crisis.

Decomposing predictability to identify dominant causal drivers in complex ecosystems

Ecosystems are complex systems of various physical, biological, and chemical processes. Since ecosystem dynamics are composed of a mixture of different levels of stochasticity and nonlinearity, handling these data is a challenge for existing methods of time series-based causal inferences. Here, we show that, by harnessing contemporary machine learning approaches, the concept of Granger causality can be effectively extended to the analysis of complex ecosystem time series and bridge the gap between dynamical and statistical approaches. The central idea is to use an ensemble of fast and highly predictive artificial neural networks to select a minimal set of variables that maximizes the prediction of a given variable. It enables decomposition of the relationship among variables through quantifying the contribution of an individual variable to the overall predictive performance. We show how our approach, EcohNet, can improve interaction network inference for a mesocosm experiment and simulated ecosystems. The application of the method to a long-term lake monitoring dataset yielded interpretable results on the drivers causing cyanobacteria blooms, which is a serious threat to ecological integrity and ecosystem services. Since performance of EcohNet is enhanced by its predictive capabilities, it also provides an optimized forecasting of overall components in ecosystems. EcohNet could be used to analyze complex and hybrid multivariate time series in many scientific areas not limited to ecosystems.

Historical declines in parrotfish on Belizean coral reefs linked to shifts in reef exploitation following European colonization

Humans have utilized the Mesoamerican Reef (MAR) for millennia but the effects of prehistorical and historical fishing on this ecosystem remain understudied. To assess the long-term coupling of reef ecosystem and human dynamics in this region, we tracked trends in the structure and functioning of lagoonal reefs within the Belizean portion of the MAR using fish teeth fossils and sediment accumulation rates within reef sediment cores. We then paired this with a timeline of demographic and cultural changes in this region’s human populations. The ∼1,300-year timeline encompassed in the core record shows that declines in the relative abundance and accumulation rate of teeth from parrotfish, a key reef herbivore, occurred at all three reef sites and began between ∼1500 and 1800 AD depending on site and metric of abundance. A causality analysis showed that parrotfish relative abundance had a positive causal effect on reef accretion rates, a proxy of coral growth, reconfirming the important role of these fish in reef ecosystem functioning. The timing of initial declines in parrotfish teeth occurred during a time of relatively low human population density in Belize. However, declines were synchronous with cultural and demographic upheaval resulting from European colonization of the New World. The more recent declines at these sites (∼1800 AD) occurred in tandem with increased subsistence fishing on reefs by multiple immigrant groups, a pattern that was likely necessitated by the establishment of an import economy controlled by a small group of land-owning European elites. These long-term trends from the paleoecological record reveal that current parrotfish abundances in central Belize are well below their pre-European contact peaks and that increased fishing pressure on parrotfish post-contact has likely caused a decline in reef accretion rates. The origins of reef degradation in the Belizean portion of the MAR began hundreds of years before the onset of modern declines resulting from the combined effects of local human disturbances and climate change.

Environmental context dependency in species interactions

Ecological interactions are not uniform across time and can vary with environmental conditions. Yet, interactions among species are often measured with short-term controlled experiments whose outcomes can depend greatly on the particular environmental conditions under which they are performed. As an alternative, we use empirical dynamic modeling to estimate species interactions across a wide range of environmental conditions directly from existing long-term monitoring data. In our case study from a southern California kelp forest, we test whether interactions between multiple kelp and sea urchin species can be reliably reconstructed from time-series data and whether those interactions vary predictably in strength and direction across observed fluctuations in temperature, disturbance, and low-frequency oceanographic regimes. We show that environmental context greatly alters the strength and direction of species interactions. In particular, the state of the North Pacific Gyre Oscillation seems to drive the competitive balance between kelp species, asserting bottom-up control on kelp ecosystem dynamics. We show the importance of specifically studying variation in interaction strength, rather than mean interaction outcomes, when trying to understand the dynamics of complex ecosystems. The significant context dependency in species interactions found in this study argues for a greater utilization of long-term data and empirical dynamic modeling in studies of the dynamics of other ecosystems.

Data-driven causal analysis of observational biological time series

Complex systems are challenging to understand, especially when they defy manipulative experiments for practical or ethical reasons. Several fields have developed parallel approaches to infer causal relations from observational time series. Yet, these methods are easy to misunderstand and often controversial. Here, we provide an accessible and critical review of three statistical causal discovery approaches (pairwise correlation, Granger causality, and state space reconstruction), using examples inspired by ecological processes. For each approach, we ask what it tests for, what causal statement it might imply, and when it could lead us astray. We devise new ways of visualizing key concepts, describe some novel pathologies of existing methods, and point out how so-called ‘model-free’ causality tests are not assumption-free. We hope that our synthesis will facilitate thoughtful application of methods, promote communication across different fields, and encourage explicit statements of assumptions. A video walkthrough is available (Video 1 or https://youtu.be/AlV0ttQrjK8).

Quantifying the Influences of Driving Factors on Land Surface Temperature during 2003–2018 in China Using Convergent Cross Mapping Method

The relationship between land surface temperature (LST) and environmental factors is complex and nonlinear. To determine these relationships for China, this study analyzed the driving effects of air temperature, vegetation index, soil moisture, net surface radiation, precipitation, aerosols, evapotranspiration, and water vapor on LST based on remote-sensing and reanalysis data from 2003–2018, using a convergent cross-mapping method. During the study period, air temperature and net surface radiation were the dominant drivers of LST with a cross-mapping skill above 0.9. Vegetation index and evapotranspiration were the secondary drivers of LST with a cross-mapping skill that was higher than 0.5. Except for air temperature and net surface radiation, the direction and strength of the effects of the driving factors on LST were related to the climate type. The effects of air temperature and net radiation on LST diminished from north to south, indicating that LST was more sensitive to air temperature and net radiation in energy-limited regions. However, the effects of vegetation index and evapotranspiration on LST varied significantly across climate zones; that is, positive effects were mostly in non-monsoonal zones and negative effects were primarily in monsoonal zones. Our results quantified the driving role of environmental factors on LST and provided a comprehensive understanding of LST dynamics.

A hybrid empirical and parametric approach for managing ecosystem complexity: Water quality in Lake Geneva under nonstationary futures

This paper develops a hybrid approach to account for the complex interactions affecting lake water quality and its management in a nonlinear, changing world. The approach uses data to leverage our first-principles understanding of the mechanisms operating on dissolved oxygen in the lake. This yields a manageable, but more complete systems perspective for environmental management of the lake under climate change, where our analysis suggests that multiple modes of intervention may be necessary to achieve a healthy lake.

Severe deterioration of water quality in lakes, characterized by overabundance of algae and declining dissolved oxygen in the deep lake (DO_B), was one of the ecological crises of the 20th century. Even with large reductions in phosphorus loading, termed “reoligotrophication,” DO_B and chlorophyll (CHL) have often not returned to their expected pre–20th-century levels. Concurrently, management of lake health has been confounded by possible consequences of climate change, particularly since the effects of climate are not neatly separable from the effects of eutrophication. Here, using Lake Geneva as an iconic example, we demonstrate a complementary alternative to parametric models for understanding and managing lake systems. This involves establishing an empirically-driven baseline that uses supervised machine learning to capture the changing interdependencies among biogeochemical variables and then combining the empirical model with a more conventional equation-based model of lake physics to predict DO_B over decadal time-scales. The hybrid model not only leads to substantially better forecasts, but also to a more actionable description of the emergent rates and processes (biogeochemical, ecological, etc.) that drive water quality. Notably, the hybrid model suggests that the impact of a moderate 3°C air temperature increase on water quality would be on the same order as the eutrophication of the previous century. The study provides a template and a practical path forward to cope with shifts in ecology to manage environmental systems for non-analogue futures.

Community-level ambient fine particulate matter and seasonal influenza among children in Guangzhou, China: A Bayesian spatiotemporal analysis

BACKGROUND

Influenza is a major preventable infectious respiratory disease. However, there is little detailed long-term evidence of its associations with PM_2.5 among children. We examined the community-level associations between exposure to ambient PM_2.5 and incident influenza in Guangzhou, China.

METHODS

We used data from the city-wide influenza surveillance system collected by Guangzhou Centre for Disease Control and Prevention (GZCDC) over the period 2013 and 2019. Incident influenza was defined as daily new influenza (both clinically diagnosed and laboratory confirmed) cases as per standard diagnostic criteria. A 200-meter city-wide grid of daily ambient PM_2.5 exposure was generated using a random forest model. We developed spatiotemporal Bayesian hierarchical models to examine the community-level associations between PM_2.5 and the influenza adjusting for meteorological and socioeconomic variables and accounting for spatial autocorrelation. We also calculated community-wide influenza cases attributable to PM_2.5 levels exceeding the China Grade 1 and World Health Organization (WHO) regulatory thresholds.

RESULTS

Our study comprised N = 191,846 children from Guangzhou aged ≤19 years and diagnosed with influenza between January 1, 2013 and December 31, 2019. Each 10 μg/m³ increment in community-level PM_2.5 measured on the day of case confirmation (lag 0) and over a 6-day moving average (lag 0-5 days) was associated with higher risks of influenza (RR = 1.05, 95% CI: 1.05-1.06 for lag 0 and RR = 1.15, 95% CI: 1.14-1.16 for lag 05). We estimated that 8.10% (95%CI: 7.23%-8.57%) and 20.11% (95%CI: 17.64%-21.48%) influenza cases respectively were attributable to daily PM_2.5 exposure exceeding the China Grade I (35 μg/m³) and the WHO limits (25 μg/m³). The risks associated with PM_2.5 exposures were more pronounced among children of the age-group 10-14 compared to other age groups.

CONCLUSIONS

More targeted non-pharmaceutical interventions aimed at reducing PM_2.5 exposures at home, school and during commutes among children may constitute additional influenza prevention and control polices.

Causal Analysis of Activity in Social Brain Areas During Human-Agent Conversation

This article investigates the differences in cognitive and neural mechanisms between human-human and human-virtual agent interaction using a dataset recorded in an ecologically realistic environment. We use Convergent Cross Mapping (CCM) to investigate functional connectivity between pairs of regions involved in the framework of social cognitive neuroscience, namely the fusiform gyrus, superior temporal sulcus (STS), temporoparietal junction (TPJ), and the dorsolateral prefrontal cortex (DLPFC)-taken as prefrontal asymmetry. Our approach is a compromise between investigating local activation in specific regions and investigating connectivity networks that may form part of larger networks. In addition to concording with previous studies, our results suggest that the right TPJ is one of the most reliable areas for assessing processes occurring during human-virtual agent interactions, both in a static and dynamic sense.

Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

A novel nonlinear analysis of blood flow dynamics applied to the human lung

The spatial/temporal dynamics of blood flow in the human lung can be measured noninvasively with magnetic resonance imaging (MRI) using arterial spin labeling (ASL). We report a novel data analysis method using nonlinear prediction to identify dynamic interactions between blood flow units (image voxels), potentially providing a probe of underlying vascular control mechanisms. The approach first estimates the linear relationship (predictability) of one voxel time series with another using correlation analysis, and after removing the linear component estimates the nonlinear relationship with a numerical mutual information approach. Dimensionless global metrics for linear prediction (F_L) and nonlinear prediction (F_NL) represent the average amplitude of fluctuations in one voxel estimated by another voxel, as a percentage of the global average voxel flow. A proof-of-principle test of this approach analyzed experimental data from a study of high-altitude pulmonary edema (HAPE), providing two groups exhibiting known differences in vascular reactivity. Subjects were mountaineers divided into HAPE-susceptible (S, n=4) and HAPE-resistant (R, n=5) groups based on prior history at high altitude. Dynamic ASL measurements in the lung in normoxia (N, FIO₂=0.21) and hypoxia (H, FIO₂=0.13±0.01) were compared. The nonlinear prediction metric F_NL decreased with hypoxia (7.4±1.3(N) vs. 6.3±0.7(H), P=0.03) and was significantly different between groups (7.4±1.2 (R) vs. 6.2±14.1 (S), P=0.03). This proof-of-principle test demonstrates that this nonlinear analysis approach applied to ASL data is sensitive to physiological effects even in small subject cohorts, and potentially can be used in a wide range of studies in health and disease in the lung and other organs.

Causality in Control Systems Based on Data-Driven Oscillation Identification

This paper addresses the subject of causality analysis using simulation data and data collected from a real control system. Simulated data includes Gaussian and Cauchy noise signals. Real-time series include various, mostly unknown distortions, like trends, oscillations, and noises. Presented research focuses on the oscillatory component in data and its propagation in multi-loop control systems. Oscillation identification is based on a deep decomposition process for control error time series. Identified periodic signals are used for further causality processing. The analysis uses the Transfer Entropy approach. This method belongs to the group of model-free methods. The determination of information pathways is conducted without any model or a priori process knowledge. The research investigates the impact of the oscillation time-series component on the Transfer Entropy causality analysis. The summary shows the observations obtained for given simulated datasets and those collected from real processes. The obtained results show that simulated analysis works properly. On the contrary, the direct application of the oscillation decomposition in real industrial cases may be misleading. Large datasets demand modification in the methodology. Different variants are tested. They show that oscillation propagation is biased in real systems and, therefore, the decomposition should be applied with caution. Furthermore, it is important to remember that the algorithm transition from simulated data to real industrial ones is demanding and should be done with the utmost care.

Robot Assisted Treatment of Hand Functional Rehabilitation Based on Visual Motor Imagination

This pilot study implements a hybrid brain computer interface paradigm based on motor imagery (MI) and steady-state visual evoked potential (SSVEP), in order to explore the neural mechanism and clinical effect of MI-SSVEP intervention paradigm on upper limb functional rehabilitation. In this study, EEG data of 12 healthy participants were collected, and the activation regions of MI-SSVEP paradigm were identified by power spectral density (PSD). By analyzing the inter trial phase consistency (ITPC) of characteristic regions and the causal relationship of brain network, the motor cognitive process including high-level somatosensory joint cortex in the intervention process of MI-SSVEP was studied. Subsequently, this study verified the clinical effect of MI-SSVEP intervention paradigm for 61 stroke patients. The results show that the robot assisted therapy using MI-SSVEP intervention paradigm can more effectively improve the rehabilitation effect of patients.

Embedding entropy: a nonlinear measure of dynamical causality

Research on concepts and computational methods of causality has a long history, and there are various concepts of causality as well as corresponding computing algorithms based on measured data. Here, by considering causes and effects from a dynamical perspective, we present a unified mathematical framework for the so-called dynamical causality (DC), which can detect causal interactions over time; notably, this framework covers Granger causality, transfer entropy, embedding causality and their conditional versions. Based on this framework, we further propose a causality criterion called embedding entropy (EE) to measure the DC between two variables. Moreover, its conditional version, conditional embedding entropy (cEE), is also derived for detecting conditional/direct causality. The significant advantages of EE and cEE are that they can be employed for solving not only nonlinear causal inference but also the non-separability problem, and they can reduce the scale bias in numerical calculation. The performance and robustness of EE and cEE were demonstrated through numerical simulations, and causal inference on various real-world datasets validated their effectiveness.

Beyond Experiments

It is often claimed that only experiments can support strong causal inferences and therefore they should be privileged in the behavioral sciences. We disagree. Overvaluing experiments results in their overuse both by researchers and decision makers and in an underappreciation of their shortcomings. Neglect of other methods often follows. Experiments can suggest whether X causes Y in a specific experimental setting; however, they often fail to elucidate either the mechanisms responsible for an effect or the strength of an effect in everyday natural settings. In this article, we consider two overarching issues. First, experiments have important limitations. We highlight problems with external, construct, statistical-conclusion, and internal validity; replicability; and conceptual issues associated with simple X causes Y thinking. Second, quasi-experimental and nonexperimental methods are absolutely essential. As well as themselves estimating causal effects, these other methods can provide information and understanding that goes beyond that provided by experiments. A research program progresses best when experiments are not treated as privileged but instead are combined with these other methods.