MotivationThe BioTIME database contains raw data on species identities and abundances in ecological assemblages through time. These data enable users to calculate temporal trends in biodiversity within and amongst assemblages using a broad range of metrics. BioTIME is being developed as a community‐led open‐source database of biodiversity time series. Our goal is to accelerate and facilitate quantitative analysis of temporal patterns of biodiversity in the Anthropocene.Main types of variables includedThe database contains 8,777,413 species abundance records, from assemblages consistently sampled for a minimum of 2 years, which need not necessarily be consecutive. In addition, the database contains metadata relating to sampling methodology and contextual information about each record.Spatial location and grainBioTIME is a global database of 547,161 unique sampling locations spanning the marine, freshwater and terrestrial realms. Grain size varies across datasets from 0.0000000158 km2 (158 cm2) to 100 km2 (1,000,000,000,000 cm2).Time period and grainBioTIME records span from 1874 to 2016. The minimal temporal grain across all datasets in BioTIME is a year.Major taxa and level of measurementBioTIME includes data from 44,440 species across the plant and animal kingdoms, ranging from plants, plankton and terrestrial invertebrates to small and large vertebrates.Software format.csv and .SQL.

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 illposed 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.

Reconstructing interactions from observational data is a critical need for investigating natural biological networks, wherein network dimensionality is usually high. However, these pose a challenge to existing methods that can quantify only small interaction networks. Here, we proposed a novel approach to reconstruct high‐dimensional interaction Jacobian networks using empirical time series without specific model assumptions. This method, named “multiview distance regularised S‐map,” generalised the state space reconstruction to accommodate high dimensionality and overcome difficulties in quantifying massive interactions with limited data. When evaluating this method using time series generated from theoretical models involving hundreds of interacting species, estimated strengths of interaction Jacobians were in good agreement with theoretical expectations. Applying this method to a natural bacterial community helped identify important species from the interaction network and revealed mechanisms governing the dynamical stability of a bacterial community. The proposed method overcame the challenge of high dimensionality in large natural dynamical systems.