When Noise Matters: Population Dynamics in Changing Environments

Description

This project will examine population dynamics in variable environments influenced by both exogenous and endogenous processes, with particular attention to how different sources of variability affect population persistence, stability, and resilience. Traditional population models often assume fixed parameters or treat environmental fluctuations as externally imposed (exogenous), such as random climate forcing or seasonal variation. Although stochastic population models are well established in the literature, comparatively less attention has been given to frameworks that clearly distinguish and integrate externally driven variability with internally generated environmental feedback within a unified mathematical structure.

The proposed research will develop and analyse mathematical models in which population growth and survival depend on an environmental state that evolves through a combination of exogenous forcing (e.g. stochastic climate variation, regime switching, or coloured noise) and endogenous dynamics driven by population–environment feedback (e.g. resource depletion, habitat modification, or delayed density dependence). These interactions will be modelled using tools such as stochastic differential equations, hybrid deterministic–stochastic systems or coupled slow–fast dynamics. This approach allows the investigation of how exogenous shocks interact with internally generated variability to produce emergent behaviours not captured by classical models.

A central aim of the project is to characterise noise-driven and feedback-induced phenomena, including noise-induced stabilisation or destabilisation, shifts in effective carrying capacity, and transitions between dynamic regimes. By comparing systems dominated by exogenous variability with those where endogenous feedback plays a significant role, the project will provide new insights into when environmental noise merely perturbs population dynamics and when it fundamentally reshapes long-term outcomes. Analytical methods will be supported by numerical simulations, offering a flexible framework applicable to ecological, epidemiological, and resource-management contexts.