Collaborative Research: Scaling Properties of Ecological Variation in Complex Dynamical Systems

Ecologists forecast future animal populations to manage harvested populations and assess extinction risks of populations of conservation concern. A critical component of these forecasts is understanding how variation in limiting environmental factors such as food, water, or shelter drive population fluctuations. In the absence of specific data on these factors, ecologists must use the properties of the observed variation in the data to make projections about future risk.

In ecology, these forecasts often make simplifying assumptions about the underlying biology that may impact their accuracy. The project will integrate new mathematical ideas and models with empirical field observations to study the properties of populations that experience large fluctuations, allowing the PIs to test fundamental assumptions about how populations are structured.

This work will focus on populations that experience regular cycles, a common phenomenon arising through factors such as competition for resources among individuals or predator-prey interactions. This work will improve both the tools used in the management and conservation of wildlife and the understanding of how external factors drive variation in nonlinear dynamical systems.

The mathematical ideas and models developed in this project will use techniques similar to those that economists use to project stock market fluctuations or meteorologists use to predict paths of hurricanes; thus, the results may have important implications for many areas of general societal interest.

Emerging work has shown that universal laws describe the fluctuations of biological systems, regardless of the biological scale at which these processes operate. A key prediction of these laws is that the fluctuations of many biological systems will increase monotonically in response to increases in extrinsic variability, often termed “environmental noise”.

However, this scaling has only been studied in linearized models that are valid when fluctuations are small. When populations exhibit larger fluctuations, the assumptions underlying this theory break down. This project will develop the mathematics needed to study the variance scaling properties in nonlinear biological systems subject to increased environmental variation.

In particular, the PIs will study the scaling properties of extrinsic noise in nonlinear biological systems focusing on how increases in the magnitude of external perturbations may drive declines in total system variance. The goal is to understand how nonlinearities in ecological systems may lead to robust or sublinear responses to environmental noise.

The research scope includes developing mathematical theory to model how environmental variation interacts with highly nonlinear population dynamics, mainly for single species. The PIs will also develop the statistical approaches to better detect the signal of the predicted variance scaling relationships from empirical population surveys. This work will be the first to determine how increases in external variability can drive increases in the stability of biological systems, an essential step in constructing a more nuanced description of how nonlinear biological systems interact with and respond to noisy environments.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.