Causal inference from cross-sectional earth system data with geographical convergent cross mapping.

Causal inference in complex systems has been largely promoted by the proposal of some advanced temporal causation models. However, temporal models have serious limitations when time series data are not available or present insignificant variations, which causes a common challenge for earth system science. Meanwhile, there are few spatial causation models for fully exploring the rich spatial cross-sectional data in Earth systems. The generalized embedding theorem proves that observations can be combined together to construct the state space of the dynamic system, and if two variables are from the same dynamic system, they are causally linked. Inspired by this, here we show a Geographical Convergent Cross Mapping (GCCM) model for spatial causal inference with spatial cross-sectional data-based cross-mapping prediction in reconstructed state space. Three typical cases, where clearly existing causations cannot be measured through temporal models, demonstrate that GCCM could detect weak-moderate causations when the correlation is not significant. When the coupling between two variables is significant and strong, GCCM is advantageous in identifying the primary causation direction and better revealing the bidirectional asymmetric causation, overcoming the mirroring effect.

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.

Disruption of ecological networks in lakes by climate change and nutrient fluctuations.

Climate change interacts with local processes to threaten biodiversity by disrupting the complex network of ecological interactions. While changes in network interactions drastically affect ecosystems, how ecological networks respond to climate change, in particular warming and nutrient supply fluctuations, is largely unknown. Here, using an equation-free modelling approach on monthly plankton community data in ten Swiss lakes, we show that the number and strength of plankton community interactions fluctuate and respond nonlinearly to water temperature and phosphorus. While lakes show system-specific responses, warming generally reduces network interactions, particularly under high phosphate levels. This network reorganization shifts trophic control of food webs, leading to consumers being controlled by resources. Small grazers and cyanobacteria emerge as sensitive indicators of changes in plankton networks. By exposing the outcomes of a complex interplay between environmental drivers, our results provide tools for studying and advancing our understanding of how climate change impacts entire ecological communities.

Ranking species based on sensitivity to perturbations under non-equilibrium community dynamics.

Managing ecological communities requires fast detection of species that are sensitive to perturbations. Yet, the focus on recovery to equilibrium has prevented us from assessing species responses to perturbations when abundances fluctuate over time. Here, we introduce two data-driven approaches (expected sensitivity and eigenvector rankings) based on the time-varying Jacobian matrix to rank species over time according to their sensitivity to perturbations on abundances. Using several population dynamics models, we demonstrate that we can infer these rankings from time-series data to predict the order of species sensitivities. We find that the most sensitive species are not always the ones with the most rapidly changing or lowest abundance, which are typical criteria used to monitor populations. Finally, using two empirical time series, we show that sensitive species tend to be harder to forecast. Our results suggest that incorporating information on species interactions can improve how we manage communities out of equilibrium.

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

Severe deterioration of water quality in lakes, characterized by overabundance of algae and declining dissolved oxygen in the deep lake (DOB), was one of the ecological crises of the 20th century. Even with large reductions in phosphorus loading, termed "reoligotrophication," DOB 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 DOB 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.

Causation inference in complicated atmospheric environment.

Reliable attribution is crucial for understanding various climate change issues. However, complicated inner-interactions between various factors make causation inference in atmospheric environment highly challenging. Taking PM2.5-Meteorology causation, which involves a large number of non-Linear and uncertain interactions between many meteorological factors and PM2.5, as a case, we examined the performance of a series of mainstream statistical models, including Correlation Analysis (CA), Partial Correlation Analysis (PCA), Structural Equation Model (SEM), Convergent Cross Mapping (CCM), Partial Cross Mapping (PCM) and Geographical Detector (GD). From a coarse perspective, the Top 3 major meteorological factors for PM2.5 in 190 cities across China extracted using different models were generally consistent. From a strict perspective, the extracted dominant meteorological factor for PM2.5 demonstrated large model variations and shared a limited consistence. Such models as SEM and PCM, which are capable of further separating direct and indirect causation in simple systems, performed poorly to identify the direct and indirect PM2.5-Meteorology causation. The notable inconsistence denied the feasibility of employing multiple models for better causation inference in atmospheric environment. Instead, the sole use of CCM, which is advantageous in dealing with non-linear causation and removing disturbing factors, is a preferable strategy for causation inference in complicated ecosystems. Meanwhile, given the multi-direction, uncertain interactions between many variables, we should be more cautious and less ambitious on the separation of direct and indirect causation. For better causation inference in the complicated atmospheric environment, the combination of statistical models and atmospheric models, and the further exploration of Deep Neural Network can be promising strategies.

Networks of Causal Linkage Between Eigenmodes Characterize Behavioral Dynamics of Caenorhabditis elegans.

Behavioral phenotyping of model organisms has played an important role in unravelling the complexities of animal behavior. Techniques for classifying behavior often rely on easily identified changes in posture and motion. However, such approaches are likely to miss complex behaviors that cannot be readily distinguished by eye (e.g., behaviors produced by high dimensional dynamics). To explore this issue, we focus on the model organism Caenorhabditis elegans, where behaviors have been extensively recorded and classified. Using a dynamical systems lens, we identify high dimensional, nonlinear causal relationships between four basic shapes that describe worm motion (eigenmodes, also called "eigenworms"). We find relationships between all pairs of eigenmodes, but the timescales of the interactions vary between pairs and across individuals. Using these varying timescales, we create "interaction profiles" to represent an individual's behavioral dynamics. As desired, these profiles are able to distinguish well-known behavioral states: i.e., the profiles for foraging individuals are distinct from those of individuals exhibiting an escape response. More importantly, we find that interaction profiles can distinguish high dimensional behaviors among divergent mutant strains that were previously classified as phenotypically similar. Specifically, we find it is able to detect phenotypic behavioral differences not previously identified in strains related to dysfunction of hermaphrodite-specific neurons.

Dynamics of Florida milk production and total phosphate in Lake Okeechobee.

A central tenant of the Comprehensive Everglades Restoration Plan (CERP) is nutrient reduction to levels supportive of ecosystem health. A particular focus is phosphorus. We examine links between agricultural production and phosphorus concentration in the Everglades headwaters: Kissimmee River basin and Lake Okeechobee, considered an important source of water for restoration efforts. Over a span of 47 years we find strong correspondence between milk production in Florida and total phosphate in the lake, and, over the last decade, evidence that phosphorus concentrations in the lake water column may have initiated a long-anticipated decline.

Tracking changes in behavioural dynamics using prediction error.

Automated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterise behavioural dynamics. For the model roundworm Caenorhabditis elegans, body pose can be accurately quantified from video as coordinates in a single low-dimensional space. We focus on this well-established case as an illustrative example and propose a method to reveal subtle variations in behaviour at high time resolution. Our data-driven method, based on empirical dynamic modeling, quantifies behavioural change as prediction error with respect to a time-delay-embedded 'attractor' of behavioural dynamics. Because this attractor is constructed from a user-specified reference data set, the approach can be tailored to specific behaviours of interest at the individual or group level. We validate the approach by detecting small changes in the movement dynamics of C. elegans at the initiation and completion of delta turns. We then examine an escape response initiated by an aversive stimulus and find that the method can track return to baseline behaviour in individual worms and reveal variations in the escape response between worms. We suggest that this general approach-defining dynamic behaviours using reference attractors and quantifying dynamic changes using prediction error-may be of broad interest and relevance to behavioural researchers working with video-derived time series.

Susceptible host availability modulates climate effects on dengue dynamics.

Experiments and models suggest that climate affects mosquito-borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analysing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modelling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects respectively. By capturing mechanistic, nonlinear and context-dependent effects of population susceptibility, temperature and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state-of-the-art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drives dengue dynamics in a nonlinear and complex, yet predictable way.

A Visual Analytics Approach for Ecosystem Dynamics based on Empirical Dynamic Modeling.

An important approach for scientific inquiry across many disciplines involves using observational time series data to understand the relationships between key variables to gain mechanistic insights into the underlying rules that govern the given system. In real systems, such as those found in ecology, the relationships between time series variables are generally not static; instead, these relationships are dynamical and change in a nonlinear or state-dependent manner. To further understand such systems, we investigate integrating methods that appropriately characterize these dynamics (i.e., methods that measure interactions as they change with time-varying system states) with visualization techniques that can help analyze the behavior of the system. Here, we focus on empirical dynamic modeling (EDM) as a state-of-the-art method that specifically identifies causal variables and measures changing state-dependent relationships between time series variables. Instead of using approaches centered on parametric equations, EDM is an equation-free approach that studies systems based on their dynamic attractors. We propose a visual analytics system to support the identification and mechanistic interpretation of system states using an EDM-constructed dynamic graph. This work, as detailed in four analysis tasks and demonstrated with a GUI, provides a novel synthesis of EDM and visualization techniques such as brush-link visualization and visual summarization to interpret dynamic graphs representing ecosystem dynamics. We applied our proposed system to ecological simulation data and real data from a marine mesocosm study as two key use cases. Our case studies show that our visual analytics tools support the identification and interpretation of the system state by the user, and enable us to discover both confirmatory and new findings in ecosystem dynamics. Overall, we demonstrated that our system can facilitate an understanding of how systems function beyond the intuitive analysis of high-dimensional information based on specific domain knowledge.

The importance of making testable predictions: A cautionary tale.

We found a startling correlation (Pearson ρ > 0.97) between a single event in daily sea surface temperatures each spring, and peak fish egg abundance measurements the following summer, in 7 years of approximately weekly fish egg abundance data collected at Scripps Pier in La Jolla California. Even more surprising was that this event-based result persisted despite the large and variable number of fish species involved (up to 46), and the large and variable time interval between trigger and response (up to ~3 months). To mitigate potential over-fitting, we made an out-of-sample prediction beyond the publication process for the peak summer egg abundance observed at Scripps Pier in 2020 (available on bioRxiv). During peer-review, the prediction failed, and while it would be tempting to explain this away as a result of the record-breaking toxic algal bloom that occurred during the spring (9x higher concentration of dinoflagellates than ever previously recorded), a re-examination of our methodology revealed a potential source of over-fitting that had not been evaluated for robustness. This cautionary tale highlights the importance of testable true out-of-sample predictions of future values that cannot (even accidentally) be used in model fitting, and that can therefore catch model assumptions that may otherwise escape notice. We believe that this example can benefit the current push towards ecology as a predictive science and support the notion that predictions should live and die in the public domain, along with the models that made them.

Long-term warming destabilizes aquatic ecosystems through weakening biodiversity-mediated causal networks.

Understanding how ecosystems will respond to climate changes requires unravelling the network of functional responses and feedbacks among biodiversity, physicochemical environments, and productivity. These ecosystem components not only change over time but also interact with each other. Therefore, investigation of individual relationships may give limited insights into their interdependencies and limit ability to predict future ecosystem states. We address this problem by analyzing long-term (16-39 years) time series data from 10 aquatic ecosystems and using convergent cross mapping (CCM) to quantify the causal networks linking phytoplankton species richness, biomass, and physicochemical factors. We determined that individual quantities (e.g., total species richness or nutrients) were not significant predictors of ecosystem stability (quantified as long-term fluctuation of phytoplankton biomass); rather, the integrated causal pathway in the ecosystem network, composed of the interactions among species richness, nutrient cycling, and phytoplankton biomass, was the best predictor of stability. Furthermore, systems that experienced stronger warming over time had both weakened causal interactions and larger fluctuations. Thus, rather than thinking in terms of separate factors, a more holistic network view, that causally links species richness and the other ecosystem components, is required to understand and predict climate impacts on the temporal stability of aquatic ecosystems.

Circularity in fisheries data weakens real world prediction.

The systematic substitution of direct observational data with synthesized data derived from models during the stock assessment process has emerged as a low-cost alternative to direct data collection efforts. What is not widely appreciated, however, is how the use of such synthesized data can overestimate predictive skill when forecasting recruitment is part of the assessment process. Using a global database of stock assessments, we show that Standard Fisheries Models (SFMs) can successfully predict synthesized data based on presumed stock-recruitment relationships, however, they are generally less skillful at predicting observational data that are either raw or minimally filtered (denoised without using explicit stock-recruitment models). Additionally, we find that an equation-free approach that does not presume a specific stock-recruitment relationship is better than SFMs at predicting synthesized data, and moreover it can also predict observational recruitment data very well. Thus, while synthesized datasets are cheaper in the short term, they carry costs that can limit their utility in predicting real world recruitment.

Assessing the predictability of nonlinear dynamics under smooth parameter changes.

Short-term forecasts of nonlinear dynamics are important for risk-assessment studies and to inform sustainable decision-making for physical, biological and financial problems, among others. Generally, the accuracy of short-term forecasts depends upon two main factors: the capacity of learning algorithms to generalize well on unseen data and the intrinsic predictability of the dynamics. While generalization skills of learning algorithms can be assessed with well-established methods, estimating the predictability of the underlying nonlinear generating process from empirical time series remains a big challenge. Here, we show that, in changing environments, the predictability of nonlinear dynamics can be associated with the time-varying stability of the system with respect to smooth changes in model parameters, i.e. its local structural stability. Using synthetic data, we demonstrate that forecasts from locally structurally unstable states in smoothly changing environments can produce significantly large prediction errors, and we provide a systematic methodology to identify these states from data. Finally, we illustrate the practical applicability of our results using an empirical dataset. Overall, this study provides a framework to associate an uncertainty level with short-term forecasts made in smoothly changing environments.

Short-term effects of multiple outdoor environmental factors on risk of asthma exacerbations: Age-stratified time-series analysis.

BACKGROUND: Although the different age groups had differences in sensitivity of asthma exacerbations (AEs) to environmental factors, no comprehensive study has examined the age-stratified effects of environmental factors on AEs. OBJECTIVE: We sought to examine the short-term effects in age-stratified groups (infants, preschool children, school-aged children, adults, and the elderly) of outdoor environmental factors (air pollutants, weather conditions, aeroallergens, and respiratory viral epidemics) on AEs. METHODS: We performed an age-stratified analysis of the short-term effects of 4 groups of outdoor environmental factors on AEs in Seoul Metropolitan City (Korea) from 2008 and 2012. The statistical analysis used a Poisson generalized linear regression model, with a distributed lag nonlinear model for identification of lagged and nonlinear effects and convergent cross-mapping for identification of causal associations. RESULTS: Analysis of the total population (n = 10,233,519) indicated there were 28,824 AE events requiring admission to an emergency department during the study period. Diurnal temperature range had significant effects in pediatric (infants, preschool children, and school-aged children) and elderly (relative risk [RR], 1.056-1.078 and 1.016, respectively) subjects. Tree and weed pollen, human rhinovirus, and influenza virus had significant effects in school-aged children (RR, 1.014, 1.040, 1.042, and 1.038, respectively). Tree pollen and influenza virus had significant effects in adults (RR, 1.026 and 1.044, respectively). Outdoor air pollutants (particulate matter of ≤10 µm in diameter, nitrogen dioxide, ozone, carbon monoxide, and sulfur dioxide) had significant short-term effects in all age groups (except for carbon monoxide and sulfur dioxide in infants). CONCLUSION: These findings provide a need for the development of tailored strategies to prevent AE events in different age groups.

Inter-outbreak stability reflects the size of the susceptible pool and forecasts magnitudes of seasonal epidemics.

For dengue fever and other seasonal epidemics we show how the stability of the preceding inter-outbreak period can predict subsequent total outbreak magnitude, and that a feasible stability metric can be computed from incidence data alone. As an observable of a dynamical system, incidence data contains information about the underlying mechanisms: climatic drivers, changing serotype pools, the ecology of the vector populations, and evolving viral strains. We present mathematical arguments to suggest a connection between stability measured in incidence data during the inter-outbreak period and the size of the effective susceptible population. The method is illustrated with an analysis of dengue incidence in San Juan, Puerto Rico, where forecasts can be made as early as three to four months ahead of an outbreak. These results have immediate significance for public health planning, and can be used in combination with existing forecasting methods and more comprehensive dengue models.

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.