**Summary:** Much of the work from this lab involves inductive theoretical approaches to understanding nature from observational data. Our study systems are diverse, ranging from ecological, to epidemiological, to genetic, to geoscience and atmospheric science, to finance and economics. The general approach is different from that in most theory-heavy research groups and involves what we describe as Minimalist Inductive Theory (MIT) – Inductive data-driven explorations of nature using minimal assumptions. Our aim is to avoid inevitable assumptions of deductive first-principle models, and develop an understanding that passes validation by out-of-sample prediction.

**Resources:** Empirical Dynamic Modeling tools can be implemented using rEDM or pyEDM.

**Key Words:** Equation-Free Mathematics, Empirical Dynamics, Detecting Causation, Out-of-Sample Prediction, Non-Equilibrium Nonlinear Dynamics, Topological Studies of Food Webs, Niche Hierarchy, Niche Theory and Species Abundance, Minimalist Inductive Theory.

**Outlook:** Science in the 21st century is being driven and enabled by the explosion of data and data-driven analysis techniques in all fields of science and engineering. These developments allow researchers to address ever more complex and ambitious problems, and to validate results by real world prediction. However, the solutions to such problems require holistic, systematic frameworks and interdisciplinary collaboration. While the last century made great strides with reductionist and specialized discipline-specific approaches, the emerging hallmark of the current century involves addressing complex problems that cannot be completely abstracted to first principles and that require interdisciplinary convergence.

Our lab attempts to provide a particular perspective that should be useful as we move away from a 20th century reductionist paradigm characterized by single factor experiments and simple toy models, toward trying to understand how messy natural systems actually behave. Thus, while it is simple to write down an accurate equation for diffusion of gases in a test tube where all other variables are held constant, modeling oxygen concentrations at depth in a large lake where biology, ecological interactions, complex chemistry and physical currents intervene is impractical with explicit equations. Empirical models, which infer patterns and associations from the data (instead of using hypothesized equations), represent an alternative and highly flexible approach. The resonance that can be achieved with a deeper understanding of the implications of simple standard assumptions like equilibrium, linearity etc. can be significant.

**Current Insights:**

- Nonlinearity and instability are ubiquitous.
- Lack of correlation between variables does not imply lack of causation.
- Viewing nature though the usual statistical lens (linear, equilibrium, constant, reductionist) will miss critical causal links.
- Causation without correlation is commonplace. “We have demonstrated that causes can be uncorrelated from their effects, and this makes deciphering mechanisms even harder.”

- Interactions in nature are episodic. Ecosystems are structured by ephemeral bottlenecks. This was hypothesized by John A. Wiens decades ago (1977).
- As such, ecological dynamics cannot be reasonably represented as having time-averaged or constant interactions/transitions such as in classical Volterra and Logistic models, or in typical Markov models.

- Gene expression is a nonlinear dynamic process.
- As such, bioinformatics with its statistical approach is fraught with difficulty.