University of Wisconsin–Madison
photo of a time-series

Concepts and Theory

The literature on mathematical techniques to understand abrupt nonlinear changes in ecological systems is growing. These techniques can be divided into two camps: (i) simple metrics of system dynamics that give insights into changing dynamics (e.g., autocorrelation that measures the dependence of changes in a system on the past), and (ii) complex models built from biological first principles that attempt to explain the system dynamics from known causes and effects. Each of these approaches has limitations. Simple metrics often do not have very much statistical power to identify abrupt changes before they occur, and they cannot be used to make future predictions of ecosystem dynamics. Complex system-specific models often require more information about an ecosystem than is known, and their complexity presents a significant challenge when attempting to fit them to data.

We will focus on models for analyzing and predicting abrupt changes that lie at the Goldilocks “just right” position between simple metrics and system-specific models. Our initial Goldilocks models will be multivariate time-varying autoregressive models and their statistical relatives, although we will quickly expand to explore other approaches. Our initial work will focus on four cases: lakesagricultural systems, eastern deciduous forests, and the western coniferous forests. We aim to develop simple models that describe system dynamics without forcing a priori assumptions about ecosystem processes thereby increasing our ability to generalize among multiple systems.