Ecological Dynamics: Integrating Empirical, Statistical, and Analytical Methods.

Understanding ecological processes and predicting long-term dynamics are ongoing challenges in ecology. To address these challenges, we suggest an approach combining mathematical analyses and Bayesian hierarchical statistical modeling with diverse data sources. Novel mathematical analysis of ecological dynamics permits a process-based understanding of conditions under which systems approach equilibrium, experience large oscillations, or persist in transient states. This understanding is improved by combining ecological models with empirical observations from a variety of sources. Bayesian hierarchical models explicitly couple process-based models and data, yielding probabilistic quantification of model parameters, system characteristics, and associated uncertainties. We outline relevant tools from dynamical analysis and hierarchical modeling and argue for their integration, demonstrating the value of this synthetic approach through a simple predator-prey example.