Causality Analysis: Identifying the Leading Element in a Coupled Dynamical System

Causal networks of phytoplankton diversity and biomass are modulated by environmental context

Untangling causal links and feedbacks among biodiversity, ecosystem functioning, and environmental factors is challenging due to their complex and context-dependent interactions (e.g., a nutrient-dependent relationship between diversity and biomass). Consequently, studies that only consider separable, unidirectional effects can produce divergent conclusions and equivocal ecological implications. To address this complexity, we use empirical dynamic modeling to assemble causal networks for 19 natural aquatic ecosystems (N24^◦~N58^◦) and quantified strengths of feedbacks among phytoplankton diversity, phytoplankton biomass, and environmental factors. Through a cross-system comparison, we identify macroecological patterns; in more diverse, oligotrophic ecosystems, biodiversity effects are more important than environmental effects (nutrients and temperature) as drivers of biomass. Furthermore, feedback strengths vary with productivity. In warm, productive systems, strong nitrate-mediated feedbacks usually prevail, whereas there are strong, phosphate-mediated feedbacks in cold, less productive systems. Our findings, based on recovered feedbacks, highlight the importance of a network view in future ecosystem management.

Disentangling causal interactions among biodiversity, ecosystem functioning and environmental factors is key to understanding how ecosystems respond to changing environment. This study presents a global scale analysis quantifying causal interactions and feedbacks among phytoplankton diversity, biomass and nutrients along environmental gradients of aquatic ecosystems.

Bidirectional causal control in the dynamics of handstand balance

The aim of this study was to identify motor control solutions associated with the ability to maintain handstand balance. Using a novel approach, we investigated the dynamical interactions between centre of pressure (CoP) and centre of mass (CoM) motion. A gymnastics cohort was divided into a ‘less skilled’ group, who held handstands for 4–6 s, and a ‘more skilled’ group, who held handstands in excess of 10 s. CoP–CoM causality was investigated in anterior–posterior (AP) and medio-lateral (ML) directions, in addition to time–space, time–frequency and Hurst Exponent (H) analyses. Lower AP CoP to CoM causal drive and lower H values (> 0.6) indicated the more skilled gymnasts were less reliant on CoP mechanics to drive CoM motion. More skilled performance demonstrated greater adaptability through use of reactive, as opposed to anticipatory, control strategies. Skilled performers additionally exploited mechanical advantages in ML (e.g. a wider base of support), compared to the less skilled athletes. A multiple regression analysis revealed H and frequency domain measures to be better predictors of handstand balance duration than time–space domain measures. The study findings highlight the advantage of an adaptable motor control system with a directional profile, and provide new insight into the clear, measurable footprint of CoP on the dynamics of CoM.

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.

Repressive chromatin modification underpins the long-term expression trend of a perennial flowering gene in nature

Natural environments require organisms to possess robust mechanisms allowing responses to seasonal trends. In Arabidopsis halleri, the flowering regulator AhgFLC shows upregulation and downregulation phases along with long-term past temperature, but the underlying machinery remains elusive. Here, we investigate the seasonal dynamics of histone modifications, H3K27me3 and H3K4me3, at AhgFLC in a natural population. Our advanced modelling and transplant experiments reveal that H3K27me3-mediated chromatin regulation at AhgFLC provides two essential properties. One is the ability to respond to the long-term temperature trends via bidirectional interactions between H3K27me3 and H3K4me3; the other is the ratchet-like character of the AhgFLC system, i.e. reversible in the entire perennial life cycle but irreversible during the upregulation phase. Furthermore, we show that the long-term temperature trends are locally indexed at AhgFLC in the form of histone modifications. Our study provides a more comprehensive understanding of H3K27me3 function at AhgFLC in a complex natural environment.

The flowering regulator FLC shows upregulation and downregulation phases along with long-term past temperature in Arabidopsishalleri. Here, the authors reveal that H3K27me3-mediated chromatin regulation at AhgFLC provides the ability to respond to both the seasonal temperature trends and the perennial life cycle.

Causality analysis and prediction of 2-methylisoborneol production in a reservoir using empirical dynamic modeling

2-Methylisobornel (MIB) is one of the most widespread and problematic biogenic compounds causing taste-and-odor problems in freshwater. To investigate the causes of MIB production and develop models to predict the MIB concentration, we have applied empirical dynamic modeling (EDM), a nonlinear approach based on Chaos theory, to the long-term water quality dataset of Kamafusa Reservoir in Japan. The study revealed the dynamic nature of MIB production in the reservoir, and determined causal variables for MIB production, including water temperature, pH, transparency, light intensity, and Green Phormidium. Moreover, EDM established that the system is three-dimensional, and the approach found elevated nonlinearity (from 1.5 to 3) across the whole study period (1996-2015). By taking only one or two candidate predictors with varying time lags, multivariate models for predicting MIB production (best model: r = 0.83, p < 0.001, root mean squared error = 3.1 ng/L) were successfully established. The modeling approach used in this study is a powerful tool for causality identification and odor prediction, thus making important contributions to reservoir management.

Analysis of causal cardio-postural interaction under orthostatic stress using convergent cross mapping

Knowledge of a cause-and-effect relationship between different physiological systems is helpful in predicting their performance under perturbations, such as orthostatic challenge. The causal coupling between representative signals of the cardiovascular and postural systems under orthostatic challenge remains unknown. Understanding the causal relationship between these two systems is critical, as their interplay is vital to maintain stable upright posture of the human body during quiet standing. In this research, convergent cross mapping (CCM) method was applied to study the causal relationship between the cardiovascular and postural systems previously shown to have coherent activity during quiet standing. Causality was studied between Systolic blood pressure (SBP)-EMG (calf muscles), EMG-COPr (resultant center of pressure), and COPr-SBP signal pairs. These signals were simultaneously recorded in a 5-minute sit-to-stand test from five young healthy participants. Strength of causality was obtained between the signal pairs in a 30-second time segments. The results from this study indicate that there exists a bidirectional causal relationship between the cardio-postural signal pairs, indicating a system level interaction to counter perturbation due to orthostatic challenge. Skeletal muscle pump was found to be driving control of SBP and COPr as the value of EMG→SBP (0.54±0.09) and EMG→COPr (0.52±0.07) were higher than the reverse causality of SBP→EMG (0.19±0.16) and COPr→EMG (0.29±0.16).