Empirical dynamic modeling for beginners

Natural systems are often complex and dynamic (i.e. nonlinear), making them difficult to understand using linear statistical approaches. Linear approaches are fundamentally based on correlation. Thus, they are ill-posed for dynamical systems, where correlation can occur without causation, and causation may also occur in the absence of correlation. “Mirage correlation” (i.e., the sign and magnitude of the correlation change with time) is a hallmark of nonlinear systems that results from state dependency. State dependency means that the relationships among interacting variables change with different states of the system. In recent decades, nonlinear methods that acknowledge state dependence have been developed. These nonlinear statistical methods are rooted in state space reconstruction, i.e. lagged coordinate embedding of time series data. These methods do not assume any set of equations governing the system but recover the dynamics from time series data, thus called empirical dynamic modeling (EDM). EDM bears a variety of utilities to investigating dynamical systems. Here, we provide a step-by-step tutorial for EDM applications with rEDM, a free software package written in the R language. Using model examples, we aim to guide users through several basic applications of EDM, including (1) determining the complexity (dimensionality) of a system, (2) distinguishing nonlinear dynamical systems from linear stochastic systems, and quantifying the nonlinearity (i.e. state dependence), (3) determining causal variables, (4) forecasting, (5) tracking the strength and sign of interaction, and (6) exploring the scenario of external perturbation. These methods and applications can be used to provide a mechanistic understanding of dynamical systems

Influence of potential grazers on picocyanobacterial abundance in Lake Biwa revealed with empirical dynamic modeling

Picocyanobacteria in lakes generally occur as single cells (single-celled picocyanobacteria; SPcy) or colonies (colonial picocyanobacteria; CPcy), and the latter form has been considered an adaptation to grazing pressure. In addition to direct effects of grazing, grazers may also have important indirect effects on picocyanobacteria, such as those from nutrient regeneration and trophic cascades. Interactions between picocyanobacteria and their grazers in lakes can thus be complex and difficult to predict. To evaluate the influence of various grazers on SPcy and CPcy in Lake Biwa, Japan, we followed seasonal changes in their abundances and potential grazers at 2-week intervals over 2 years. The data collected were analyzed using empirical dynamic modeling (EDM), a model-free, nonlinear time-series method. We found that heterotrophic nanoflagellates (HNF), rotifers (Keratella, Polyarthra, and Trichocerca), cladocerans, and copepods played important and differing roles in controlling the abundances of SPcy and CPcy. Notably, HNF had an apparent positive influence on SPcy abundance, despite being considered major consumers of SPcy. This result suggested that the enhancement of SPcy growth due to nutrient regeneration by HNF might exceed losses from mortality due to grazing by HNF. EDM also suggested that colony formation by picocyanobacteria may be unidirectional, with SPcy tending to form CPcy. Our findings show that the seasonal dynamics of SPcy and CPcy in Lake Biwa are influenced by a variety of grazers, which may play differing ecological roles in the aquatic food web

Geographically weighted temporally correlated logistic regression model

Abstract Detecting the temporally and spatially varying correlations is important to understand the biological and disease systems. Here we proposed a geographically weighted temporally correlated logistic regression (GWTCLR) model to identify such dynamic correlation of predictors on binomial outcome data, by incorporating spatial and temporal information for joint inference. The local likelihood method is adopted to estimate the spatial relationship, while the smoothing method is employed to estimate the temporal variation. We present the construction and implementation of GWTCLR and the study of the asymptotic properties of the proposed estimator. Simulation studies were conducted to evaluate the robustness of the proposed model. GWTCLR was applied on real epidemiologic data to study the climatic determinants of human seasonal influenza epidemics. Our method obtained results largely consistent with previous studies but also revealed certain spatial and temporal varying patterns that were unobservable by previous models and methods

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

植物が春の「暖かさ」を感じて「寒さ」を無視して花を咲かせるしくみを解明. 京都大学プレスリリース. 2020-05-29.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