Many studies have suggested that ecosystems may exhibit multiple stable states and abrupt responses to changes in underlying environmental conditions/drivers. Traditionally, researchers have relied on statistical indicators, such as bimodal frequency distributions, to infer the presence of alternative stable states (bistability) from observational data. However, real-world ecosystems are inherently noisy and rarely stationary, often driven by periodic external forces like seasonal rainfall or temperature cycles.

In Chapter 1, we investigate the interplay of stochasticity and seasonality in ecosystem dynamics. Using canonical ecosystem models and satellite-derived vegetation data (EVI) across a large rainfall gradient, we first demonstrate a critical vulnerability in traditional statistical heuristics. We show that slow seasonal forcing can drive simple unistable systems to exhibit spurious bimodal distributions, and in contrast, in some bistable systems, the interplay of seasonality and stochasticity can mask the underlying bistability of a system by exhibiting unimodal distributions. These counterintuitive impacts of seasonality on ecosystems highlight the dangers of relying solely on statistical patterns to study the underlying ecosystem stability and underscore the need for methods capable of directly uncovering the mechanistic governing equations from data.

To address this, in Chapter 2, we systematically evaluate PyDaDDy, a modern, data-driven equation-discovery framework based on sparse regression. Through rigorous sensitivity analyses, we establish the fundamental limits of this method under ecological data constraints. We reveal a critical bias-variance trade-off governing deterministic drift estimation: sampling too frequently leads to overfitting to environmental noise, while sampling too coarsely yields a biased, flattened model. We quantitatively confirm that drift and diffusion must be characterised at different optimal timescales.

Building on this methodological foundation, in Chapter 3, we develop a novel extension to the sparse regression framework to tackle time-non-homogeneous, seasonally forced systems. We demonstrate that naive applications of equation discovery to seasonal data fail catastrophically, misattributing extrinsic forcing to intrinsic dynamics. By explicitly incorporating the known seasonal driver as an additional input variable, our extended method mathematically decouples these effects. It successfully recovers the true underlying stability landscapes of complex bistable systems across a wide range of seasonal periods and noise levels.

Ultimately, this thesis provides a robust, practical methodology for ecologists to disentangle intrinsic dynamics from periodic external drivers, offering a potential, mechanistic tool to uncover the true resilience of ecosystems in a periodically changing world.