Robust calibration of generalised Lotka-Volterra models

Generalised Lotka-Volterra (GLV) models provide an interpretable framework for inferring microbial interaction networks from time-series data. However, these models often exhibit blow-up-like (rapidly diverging) trajectories for certain parameter values, leading to numerical instability and rendering global optimisation methods ineffective, particularly when using wide parameter bounds. We present a robust strategy for parameter estimation that combines initially tight, biologically plausible bounds with an iterative re-optimisation procedure using moving bounds that gradually expand the search space. This approach avoids early exploration of divergent trajectories, enables global optimisers to initialise feasible populations, and incrementally guides the search toward parameter regions yielding good fits. While our method specifically targets the practical obstacle of blow-up-like trajectories, it also mitigates two other common pitfalls: convergence to local optima and overfitting. We validate the approach on case studies of increasing complexity. Finally, we demonstrate that experimental design critically affects practical identifiability and emphasise the often-overlooked distinction between achieving a good fit and recovering true parameter values, a caveat essential for ecological interpretation. This work contributes both a methodological advance and a conceptual clarification broadly applicable to parameter estimation in complex microbial ecology models.