Simulating stochastic population dynamics: The Linear Noise Approximation can capture non-linear phenomena
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913113064865792 |
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| author | Truman-Williams, Frederick Minas, Giorgos |
| author_facet | Truman-Williams, Frederick Minas, Giorgos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulating stochastic population dynamics: The Linear Noise Approximation can capture non-linear phenomena Truman-Williams, Frederick Minas, Giorgos Quantitative Methods Probability Chemical Physics Molecular Networks 37N25, 92-10 (Primary) 692C42, 92D25 (Secondary) 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. |
| title | Simulating stochastic population dynamics: The Linear Noise Approximation can capture non-linear phenomena |
| topic | Quantitative Methods Probability Chemical Physics Molecular Networks 37N25, 92-10 (Primary) 692C42, 92D25 (Secondary) |
| url | https://arxiv.org/abs/2504.15166 |