Environmental Memory and Delayed Feedback in Population–Environment Systems

Description

This project will investigate the role of environmental memory and delayed feedback in shaping population dynamics under changing conditions. While many ecological models assume that environmental states respond instantaneously to population change or external forcing, real systems often exhibit persistence, inertia, or lagged responses due to processes such as soil nutrient accumulation, habitat recovery, behavioural adaptation, or physiological stress. These memory effects can fundamentally alter stability, persistence, and predictability, yet remain underrepresented in mainstream stochastic population theory.

The proposed research will develop mathematical models in which population dynamics are coupled to environmental variables that evolve with explicit memory, represented through delay differential equations, non-Markovian stochastic processes, or integro-differential formulations. Environmental change may depend not only on current population density but also on its past trajectory, allowing feedback mechanisms to accumulate and decay over time. External variability—such as climatic forcing or episodic disturbances—will be incorporated alongside internal memory-driven dynamics, creating systems with interacting timescales and histories.

A key objective is to identify how environmental memory modifies classical ecological outcomes, including thresholds for persistence, extinction risk, and regime shifts. The project will explore phenomena such as hysteresis, delayed collapse, resilience debt, and history-dependent recovery, where populations with identical present conditions diverge due to differing past dynamics. Particular attention will be given to how memory can either buffer populations against short-term shocks or amplify long-term instability through delayed negative feedback.

The research will combine analytical approaches with computational experiments to characterise stability, bifurcation structure, and long-run statistical behaviour. By explicitly accounting for environmental memory, the project aims to provide a richer theoretical framework for understanding slow degradation, legacy effects, and delayed responses in ecological and managed systems, with potential applications to conservation biology, renewable resource management, and eco-epidemiology.