Giorgos Minas | Searcharxiv

arXiv2026

Simulating stochastic population dynamics: The Linear Noise Approximation can capture non-linear phenomena

Population dynamics in fields such as molecular biology, epidemiology, and ecology exhibit highly stochastic and non-linear behaviour. In gene regulatory systems in particular, oscillations and multi-stability are especially common. Despite this, none of the currently available stochastic models for population dynamics are both accurate and computationally efficient for long-term predictions. A prominent model in this field, the Linear Noise Approximation (LNA), is computationally efficient for tasks such as simulation, sensitivity analysis, and parameter estimation; however, it is only accurate for linear systems and short-time predictions. Other models may achieve greater accuracy across a broader range of systems, but they sacrifice computational efficiency and analytical tractability. This paper demonstrates that, with specific modifications, the LNA can accurately capture non-linear dynamics in population processes. We introduce a new framework based on centre manifold theory, a classical concept from non-linear dynamical systems. This approach enables the identification of simple, system-specific modifications to the LNA, tailored to classes of qualitatively similar non-linear dynamical systems. With these modifications, the LNA can achieve accurate long-term simulations without compromising computational efficiency. We apply our methodology to classes of oscillatory and bi-stable systems, and present multiple examples from molecular population dynamics that demonstrate accurate long-term simulations alongside significant improvements in computational efficiency.

q-bio.QM↗

arXiv2024

Bayesian inference for stochastic oscillatory systems using the phase-corrected Linear Noise Approximation

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple systems. Recent advances in analytically tractable approximations to the underlying conditional probability distributions enable long-term dynamics to be accurately modelled, and make the large number of model evaluations required for exact Bayesian inference much more feasible. We propose a new methodology for inference in stochastic non-linear dynamical systems exhibiting oscillatory behaviour and show the parameters in these models can be realistically estimated from simulated data. Preliminary analyses based on the Fisher Information Matrix of the model can guide the implementation of Bayesian inference. We show that this parameter sensitivity analysis can predict which parameters are practically identifiable. Several Markov chain Monte Carlo algorithms are compared, with our results suggesting a parallel tempering algorithm consistently gives the best approach for these systems, which are shown to frequently exhibit multi-modal posterior distributions.

stat.CO↗