Distinguishing time-delayed causal interactions using convergent cross mapping

Does past evolutionary history under different mating regimes influence the demographic dynamics of interspecific competition?

Interspecific interactions are contingent upon organism phenotypes, and thus phenotypic evolution can modify interspecific interactions and affect ecological dynamics. Recent studies have suggested that male-male competition within a species selects for capability to reproductively interfere with a closely related species. Here, we examine the effect of past evolutionary history under different mating regimes on the demographic dynamics of interspecific competition in Callosobruchus seed beetles. We used previously established experimental evolution lines of Callosobruchus chinensis that evolved under either forced lifelong monogamy or polygamy for 17 generations, and examined the demographic dynamics of competition between these C. chinensis lines and a congener, Callosobruchus maculatus. Callosobruchus chinensis was competitively excluded by C. maculatus in all trials. Time series data analyses suggested that reproductive interference from C. chinensis was relatively more important in the trials involving polygamous C. chinensis than those involving monogamous C. chinensis, in accordance with the potentially higher reproductive interference capability of polygamous C. chinensis. However, the estimated signs and magnitudes of interspecific interactions were not fully consistent with this explanation, implying the evolution of not only reproductive interference but also other interaction mechanisms. Our study thus suggests multifaceted effects of sexually selected traits on interspecific competitive dynamics.

Climate drivers of malaria at its southern fringe in the Americas

In this work we analyze potential environmental drivers of malaria cases in Northwestern Argentina. We inspect causal links between malaria and climatic variables by means of the convergent cross mapping technique, which provides a causality criterion from the theory of dynamic systems. Analysis is based on 12 years of weekly malaria P. vivax cases in Tartagal, Salta, Argentina-at the southern fringe of malaria incidence in the Americas-together with humidity and temperature time-series spanning the same period. Our results show that there are causal links between malaria cases and both maximum temperature, with a delay of five weeks, and minimum temperature, with delays of zero and twenty two weeks. Humidity is also a driver of malaria cases, with thirteen weeks delay between cause and effect. Furthermore we also determined the sign and strength of the effects. Temperature has always a positive non-linear effect on cases, with maximum temperature effects more pronounced above 25°C and minimum above 17°C, while effects of humidity are more intricate: maximum humidity above 85% has a negative effect, whereas minimum humidity has a positive effect on cases. These results might be signaling processes operating at short (below 5 weeks) and long (over 12 weeks) time delays, corresponding to effects related to parasite cycle and mosquito population dynamics respectively. The non-linearities found for the strength of the effect of temperature on malaria cases make warmer areas more prone to higher increases in the disease incidence. Moreover, our results indicate that an increase of extreme weather events could enhance the risks of malaria spreading and re-emergence beyond the current distribution. Both situations, warmer climate and increase of extreme events, will be remarkably increased by the end of the century in this hot spot of climate change.

Improving The Performance of Motor Imagery Based Brain-Computer Interface Using Phase Space Reconstruction

In recent decades, motor imagery (MI) based brain-computer interface (BCI) is served as a control system or rehabilitation tool for motor disabled people. But it has limited applications because of its lower classification performance (classification accuracy, Cohen's kappa coefficient and etc.). The performance depends on the feature extraction techniques and extraction of relevant features from the brain is challenging task. The existing techniques have low classification performance and are computationally inefficient. This paper introduces phase space reconstruction (PSR) to detect various MI activities and improve the performance of the system. First, raw signals were decomposed into multiple frequency sub-bands using filter bank technique. Second, PSR was applied to each sub-band and dynamical behavior of the brain activities has been analyzed. The optimal parameters (time delay and embedding dimension) of PSR were calculated by average mutual information (AMI) and false nearest neighbors (FNN) methods. The time delay and embedding dimension extracted significant features related to MI activities. The significant features were fed into multi-class support vector machine (SVM) and performance of the classifier was evaluated. The performance of the system is based on classification accuracy (%CA) and Cohen's kappa coefficient (K). The proposed algorithm and classifier were tested on BCI competition-2005, MI dataset-III-a. The results show that the proposed technique increases the classification accuracy by 3.7% and achieved higher performance (%CA = 89.20% and K= 0.85).

Temporal Effects of Groundwater on Physical and Biotic Components of a Karst Stream

Although most lotic ecosystems are groundwater dependent, our knowledge on the relatively long-term ecological effects of groundwater discharge on downstream reaches remains limited. We surveyed four connected reaches of a Chinese karst stream network for 72 consecutive months, with one reach, named Hong Shi Zi (HSZ), evidently affected by groundwater. We tested whether, compared with other reaches, HSZ had (1) milder water temperature and flow regimes, and (2) weaker influences of water temperature and flow on benthic algal biomass represented by chlorophyll a (Chl. a) concentrations. We found that the maximum monthly mean water temperature in HSZ was 0.6 °C lower than of the adjacent upstream reach, and the minimum monthly mean water temperature was 1.0 °C higher than of the adjacent downstream reach. HSZ had the smallest coefficient of variation (CV) for water temperature but the largest CV for discharge. Water temperature and discharge displayed a significant 12-month periodicity in all reaches not directly groundwater influenced. Only water temperature displayed such periodicity in HSZ. Water temperature was an important predictor of temporal variation in Chl. a in all reaches, but its influence was weakest in HSZ. Our findings demonstrate that longer survey data can provide insight into groundwater–surface water interactions.

Inferring causation from time series in Earth system sciences

The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.

Causal relationship between local field potential and intrinsic optical signal in epileptiform activity in vitro

The directed causal relationship were examined between the local field potential (LFP) and the intrinsic optical signal (IOS) during induced epileptiform activity in in vitro cortical slices by the convergent cross-mapping causality analysis method. Two components of the IOS signal have been distinguished: a faster, activity dependent component (IOSh) which changes its sign between transmitted and reflected measurement, thus it is related to the reflectance or the scattering of the tissue and a slower component (IOSl), which is negative in both cases, thus it is resulted by the increase of the absorption of the tissue. We have found a strong, unidirectional, delayed causal effect from LFP to IOSh with 0.5-1s delay, without signs of feedback from the IOSh to the LFP, while the correlation was small and the peaks of the cross correlation function did not reflect the actual causal dependency. Based on these observations, a model has been set up to describe the dependency of the IOSh on the LFP power and IOSh was reconstructed, based on the LFP signal. This study demonstrates that causality analysis can lead to better understanding the physiological interactions, even in case of two data series with drastically different time scales.

Economic Complexity: Correlations between Gross Domestic Product and Fitness

In this paper we study the causal relation between country Economic Fitness Fc and its Gross Domestic Product per capita (GDP). Using the Takens’ theorem, as first suggested in (Sugihara, G. et al. 2012), we show that there exists a reasonable evidence of causal correlation between GDP and Fc for relatively rich countries. This is not the case for relatively poor countries where Fc and GDP do not show any significant causal relation. We also present some preliminary results to understand whether GDP or Fc are driving factor for economic growth.

Causal decomposition in the mutual causation system

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may underestimate the simultaneous and reciprocal nature of causal interactions observed in real-world phenomena. Here, we present a causal-decomposition approach that is not based on prediction, but based on the covariation of cause and effect: cause is that which put, the effect follows; and removed, the effect is removed. Using empirical mode decomposition, we show that causal interaction is encoded in instantaneous phase dependency at a specific time scale, and this phase dependency is diminished when the causal-related intrinsic component is removed from the effect. Furthermore, we demonstrate the generic applicability of our method to both stochastic and deterministic systems, and show the consistency of causal-decomposition method compared to existing methods, and finally uncover the key mode of causal interactions in both modelled and actual predator–prey systems.

Causality inference in time series analysis based on temporal precedence principle between cause and effect fails to detect mutual causal interactions. Here, Yang et al. introduce a causal decomposition approach based on the covariation principle of cause and effect that overcomes this limitation.

Detecting the Causal Effect of Soil Moisture on Precipitation Using Convergent Cross Mapping

As a vital land surface parameter, soil moisture influences climate through its impact on water and energy cycles. However, the effect of soil moisture on precipitation has been strongly debated. In this study, a new causal detection method, convergent cross mapping (CCM), was applied to explore the causality between soil moisture and precipitation over low- and mid- latitude regions in the Northern Hemisphere. CCM method generally identified a strong effect of soil moisture on precipitation. Specifically, the optimal effect of soil moisture on precipitation occurred with a lag of one month and clearly decreased after four months, suggesting that soil moisture has potentials to improve the accuracy of precipitation forecast at a sub-seasonal scale. In addition, as climate (i.e., aridity index) changed from dry to wet, the effect of soil moisture on precipitation first increased and then decreased with peaks in semi-arid and semi-humid areas. These findings statistically support the hypothesis that soil moisture impacts precipitation and also provide a reference for the design of climate prediction systems.

Forcing of late Pleistocene ice volume by spatially variable summer energy

Changes in Earth’s orbit set the pace of glacial cycles, but the role of spatial variability in the insolation forcing of global ice volume remains unknown. Here, we leverage the intrinsic dynamical information in empirical records to show that ice volume responded to summer energy at high northern latitudes, as predicted by Milankovitch theory. However, the external forcing of ice volume encompasses insolation signals with a wide range of orbital frequency content, and cannot be fully accounted for by a unique time series. Southern mid-latitude insolation forcing coincides with the position of the subtropical front and the westerlies, which have been implicated in Quaternary climate changes. Dominant forcing modes at northern mid-latitudes are anti-phased with the canonical Milankovitch forcing, consistent with ice volume sensitivity to latitudinal insolation gradients.

Anatomy of leadership in collective behaviour

Understanding the mechanics behind the coordinated movement of mobile animal groups (collective motion) provides key insights into their biology and ecology, while also yielding algorithms for bio-inspired technologies and autonomous systems. It is becoming increasingly clear that many mobile animal groups are composed of heterogeneous individuals with differential levels and types of influence over group behaviors. The ability to infer this differential influence, or leadership, is critical to understanding group functioning in these collective animal systems. Due to the broad interpretation of leadership, many different measures and mathematical tools are used to describe and infer "leadership," e.g., position, causality, influence, and information flow. But a key question remains: which, if any, of these concepts actually describes leadership? We argue that instead of asserting a single definition or notion of leadership, the complex interaction rules and dynamics typical of a group imply that leadership itself is not merely a binary classification (leader or follower), but rather, a complex combination of many different components. In this paper, we develop an anatomy of leadership, identify several principal components, and provide a general mathematical framework for discussing leadership. With the intricacies of this taxonomy in mind, we present a set of leadership-oriented toy models that should be used as a proving ground for leadership inference methods going forward. We believe this multifaceted approach to leadership will enable a broader understanding of leadership and its inference from data in mobile animal groups and beyond.

A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis.

Comparison of six methods for the detection of causality in a bivariate time series

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Common species link global ecosystems to climate change: dynamical evidence in the planktonic fossil record

Common species shape the world around us, and changes in their commonness signify large-scale shifts in ecosystem structure and function. However, our understanding of long-term ecosystem response to environmental forcing in the deep past is centred on species richness, neglecting the disproportional impact of common species. Here, we use common and widespread species of planktonic foraminifera in deep-sea sediments to track changes in observed global occupancy (proportion of sampled sites at which a species is present and observed) through the turbulent climatic history of the last 65 Myr. Our approach is sensitive to relative changes in global abundance of the species set and robust to factors that bias richness estimators. Using three independent methods for detecting causality, we show that the observed global occupancy of planktonic foraminifera has been dynamically coupled to past oceanographic changes captured in deep-ocean temperature reconstructions. The causal inference does not imply a direct mechanism, but is consistent with an indirect, time-delayed causal linkage. Given the strong quantitative evidence that a dynamical coupling exists, we hypothesize that mixotrophy (symbiont hosting) may be an ecological factor linking the global abundance of planktonic foraminifera to long-term climate changes via the relative extent of oligotrophic oceans.

Detecting reciprocity at a global scale

Reciprocity stabilizes cooperation from the level of microbes all the way up to humans interacting in small groups, but does reciprocity also underlie stable cooperation between larger human agglomerations, such as nation states? Famously, evolutionary models show that reciprocity could emerge as a widespread strategy for achieving international cooperation. However, existing studies have only detected reciprocity-driven cooperation in a small number of country pairs. We apply a new method for detecting mutual influence in dynamical systems to a new large-scale data set that records state interactions with high temporal resolution. Doing so, we detect reciprocity between many country pairs in the international system and find that these reciprocating country pairs exhibit qualitatively different cooperative dynamics when compared to nonreciprocating pairs. Consistent with evolutionary theories of cooperation, reciprocating country pairs exhibit higher levels of stable cooperation and are more likely to punish instances of noncooperation. However, countries in reciprocity-based relationships are also quicker to forgive single acts of noncooperation by eventually returning to previous levels of mutual cooperation. By contrast, nonreciprocating pairs are more likely to exploit each other's cooperation via higher rates of defection. Together, these findings provide the strongest evidence to date that reciprocity is a widespread mechanism for achieving international cooperation.

Non-linear Heart Rate and Blood Pressure Interaction in Response to Lower-Body Negative Pressure

Early detection of hemorrhage remains an open problem. In this regard, blood pressure has been an ineffective measure of blood loss due to numerous compensatory mechanisms sustaining arterial blood pressure homeostasis. Here, we investigate the feasibility of causality detection in the heart rate and blood pressure interaction, a closed-loop control system, for early detection of hemorrhage. The hemorrhage was simulated via graded lower-body negative pressure (LBNP) from 0 to -40 mmHg. The research hypothesis was that a significant elevation of causal control in the direction of blood pressure to heart rate (i.e., baroreflex response) is an early indicator of central hypovolemia. Five minutes of continuous blood pressure and electrocardiogram (ECG) signals were acquired simultaneously from young, healthy participants (27 ± 1 years, N = 27) during each LBNP stage, from which heart rate (represented by RR interval), systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean arterial pressure (MAP) were derived. The heart rate and blood pressure causal interaction (RR↔SBP and RR↔MAP) was studied during the last 3 min of each LBNP stage. At supine rest, the non-baroreflex arm (RR→SBP and RR→MAP) showed a significantly (p < 0.001) higher causal drive toward blood pressure regulation compared to the baroreflex arm (SBP→RR and MAP→RR). In response to moderate category hemorrhage (-30 mmHg LBNP), no change was observed in the traditional marker of blood loss i.e., pulse pressure (p = 0.10) along with the RR→SBP (p = 0.76), RR→MAP (p = 0.60), and SBP→RR (p = 0.07) causality compared to the resting stage. Contrarily, a significant elevation in the MAP→RR (p = 0.004) causality was observed. In accordance with our hypothesis, the outcomes of the research underscored the potential of compensatory baroreflex arm (MAP→RR) of the heart rate and blood pressure interaction toward differentiating a simulated moderate category hemorrhage from the resting stage. Therefore, monitoring baroreflex causality can have a clinical utility in making triage decisions to impede hemorrhage progression.

Locally embedded presages of global network bursts

Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially nonbursting network state is not fully understood. In this study, we develop a state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during nonbursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean-field activity for predicting future global bursts. Moreover, the intercell variability in the burst predictability is found to reflect the network structure realized in the nonbursting periods. These findings suggest that deterministic local dynamics can predict seemingly stochastic global events in self-organized networks, implying the potential applications of the present methodology to detecting locally concentrated early warnings of spontaneous seizure occurrence in the brain.

Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series

In order to explore the characteristics of the evolution behavior of the time-varying relationships between multivariate time series, this paper proposes an algorithm to transfer this evolution process to a complex network. We take the causality patterns as nodes and the succeeding sequence relations between patterns as edges. We used four time series as sample data. The results of the analysis reveal some statistical evidences that the causalities between time series is in a dynamic process. It implicates that stationary long-term causalities are not suitable for some special situations. Some short-term causalities that our model recognized can be referenced to the dynamic adjustment of the decisions. The results also show that weighted degree of the nodes obeys power law distribution. This implies that a few types of causality patterns play a major role in the process of the transition and that international crude oil market is statistically significantly not random. The clustering effect appears in the transition process and different clusters have different transition characteristics which provide probability information for predicting the evolution of the causality. The approach presents a potential to analyze multivariate time series and provides important information for investors and decision makers.

Detection of coupling delay: A problem not yet solved

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed-the method based on conditional mutual information-the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping-the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved.

Detection of time delays and directional interactions based on time series from complex dynamical systems

Data-based and model-free accurate identification of intrinsic time delays and directional interactions is an extremely challenging problem in complex dynamical systems and their networks reconstruction. A model-free method with new scores is proposed to be generally capable of detecting single, multiple, and distributed time delays. The method is applicable not only to mutually interacting dynamical variables but also to self-interacting variables in a time-delayed feedback loop. Validation of the method is carried out using physical, biological, and ecological models and real data sets. Especially, applying the method to air pollution data and hospital admission records of cardiovascular diseases in Hong Kong reveals the major air pollutants as a cause of the diseases and, more importantly, it uncovers a hidden time delay (about 30-40 days) in the causal influence that previous studies failed to detect. The proposed method is expected to be universally applicable to ascertaining and quantifying subtle interactions (e.g., causation) in complex systems arising from a broad range of disciplines.

Skeletal Muscle Pump Drives Control of Cardiovascular and Postural Systems

The causal interaction between cardio-postural-musculoskeletal systems is critical in maintaining postural stability under orthostatic challenge. The absence or reduction of such interactions could lead to fainting and falls often experienced by elderly individuals. The causal relationship between systolic blood pressure (SBP), calf electromyography (EMG), and resultant center of pressure (COPr) can quantify the behavior of cardio-postural control loop. Convergent cross mapping (CCM) is a non-linear approach to establish causality, thus, expected to decipher nonlinear causal cardio-postural-musculoskeletal interactions. Data were acquired simultaneously from young participants (25 ± 2 years, n = 18) during a 10-minute sit-to-stand test. In the young population, skeletal muscle pump was found to drive blood pressure control (EMG → SBP) as well as control the postural sway (EMG → COPr) through the significantly higher causal drive in the direction towards SBP and COPr. Furthermore, the effect of aging on muscle pump activation associated with blood pressure regulation was explored. Simultaneous EMG and SBP were acquired from elderly group (69 ± 4 years, n = 14). A significant (p = 0.002) decline in EMG → SBP causality was observed in the elderly group, compared to the young group. The results highlight the potential of causality to detect alteration in blood pressure regulation with age, thus, a potential clinical utility towards detection of fall proneness.

Causality analysis detects the regulatory role of maternal effect genes in the early Drosophila embryo

In developmental studies, inferring regulatory interactions of segmentation genetic network play a vital role in unveiling the mechanism of pattern formation. As such, there exists an opportune demand for theoretical developments and new mathematical models which can result in a more accurate illustration of this genetic network. Accordingly, this paper seeks to extract the meaningful regulatory role of the maternal effect genes using a variety of causality detection techniques and to explore whether these methods can suggest a new analytical view to the gene regulatory networks. We evaluate the use of three different powerful and widely-used models representing time and frequency domain Granger causality and convergent cross mapping technique with the results being thoroughly evaluated for statistical significance. Our findings show that the regulatory role of maternal effect genes is detectable in different time classes and thereby the method is applicable to infer the possible regulatory interactions present among the other genes of this network.

Prehistorical and historical declines in Caribbean coral reef accretion rates driven by loss of parrotfish

Caribbean coral reefs have transformed into algal-dominated habitats over recent decades, but the mechanisms of change are unresolved due to a lack of quantitative ecological data before large-scale human impacts. To understand the role of reduced herbivory in recent coral declines, we produce a high-resolution 3,000 year record of reef accretion rate and herbivore (parrotfish and urchin) abundance from the analysis of sediments and fish, coral and urchin subfossils within cores from Caribbean Panama. At each site, declines in accretion rates and parrotfish abundance were initiated in the prehistorical or historical period. Statistical tests of direct cause and effect relationships using convergent cross mapping reveal that accretion rates are driven by parrotfish abundance (but not vice versa) but are not affected by total urchin abundance. These results confirm the critical role of parrotfish in maintaining coral-dominated reef habitat and the urgent need for restoration of parrotfish populations to enable reef persistence.

Limits to Causal Inference with State-Space Reconstruction for Infectious Disease

Infectious diseases are notorious for their complex dynamics, which make it difficult to fit models to test hypotheses. Methods based on state-space reconstruction have been proposed to infer causal interactions in noisy, nonlinear dynamical systems. These “model-free” methods are collectively known as convergent cross-mapping (CCM). Although CCM has theoretical support, natural systems routinely violate its assumptions. To identify the practical limits of causal inference under CCM, we simulated the dynamics of two pathogen strains with varying interaction strengths. The original method of CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies. This sensitivity vanishes with alternative criteria for inferring causality. However, CCM remains sensitive to high levels of process noise and changes to the deterministic attractor. This sensitivity is problematic because it remains challenging to gauge noise and dynamical changes in natural systems, including the quality of reconstructed attractors that underlie cross-mapping. We illustrate these challenges by analyzing time series of reportable childhood infections in New York City and Chicago during the pre-vaccine era. We comment on the statistical and conceptual challenges that currently limit the use of state-space reconstruction in causal inference.