Stochastic Dynamics of Press-Pulse Disturbances

A central problem in ecology is to predict how natural populations respond to disturbances. Accordingly, the last decades have witnessed key theoretical developments in stochastic dynamics, perturbation theory, and transient dynamics. However, these areas have to date been largely disconnected. In our previous research, we introduced an expression for the second derivatives of population growth rate with respect to demographic rates with direct links to transient dynamics using perturbation theory. We then used this connection to develop an intuitive mathematical framework to show how transient responses to pulse disturbances lead to a quantitative description of press disturbances. However, the framework assumes that perturbations that are constant in magnitude over time. In this working group, we propose to extend the framework for perturbations are time-varying, dynamic, and stochastic. The insights into the connections between nonlinearity, transients, and stochastic dynamics can provide valuable tools for understanding and managing population dynamics in a changing world.