Davide Valenti — Università degli Studi di Palermo #
Role of the noise and stochastic modeling in biological systems #
We present two examples of complex systems modeled by stochastic differential equations: i) an ecosystem consisting of two interacting bacterial populations in a food product [1]; ii) a marine ecosystem described by the 0-dimensional stochastic version of the well known biogeochemical flux model (BFM) [2]. In the first system, two generalized Lotka-Volterra equations are used to describe the time behaviour of Listeria monocytogenes and lactic acid bacteria (LAB), during the fermentation period (168 h) of a typical Sicilian salami [1]. The two differential equations are set with the temperature (T ), pH, and water activity (aw ) being treated as stochastic variables. The dynamics of each of these variables indeed is governed by two ”drivers”: a linear decrease as a function of the time t; an additive noise term which mimics the effects of random fluctuations. Suitably setting both the values of the interaction coefficients between LAB and L. monocytogenes and the noise intensities, the model provides results in a better agreement with the experimental data in comparison with those obtained by the corresponding deterministic model. In the second system, starting from the experimental data of the solar irradiance, collected on the marine surface, which clearly show an intrinsic stochasticity, the ecosystem dynamics is studied by modeling the noisy fluctuations of the irradiance as a self-correlated Gaussian noise [2]. Nonmonotonic behaviours of the coefficient of variation (a proxy of the variance) of the biomasses are found as a function of both the intensity and the autocorrelation time of the noise source, which indicates a noise-induced transition of the ecosystem to an out-of-equilibrium steady state. Moreover, evidence of noise-induced effects on the organic carbon cycling processes, underlying the food web dynamics, are highlighted. We conclude noting that the stochastic modeling of biological systems can be fruitfully used to devise more realistic models for the dynamics of an ”agricoltural ecosystem”, a natural (open) system governed by nonlinear dynamics, including the effects of both deterministic environmental forcings and randomly varying perturbations. This idea agrees with the approach, used during the last two decades in predictive microbiology, which allowed to get better and more reliable predictions for bacterial growth in food products [1, 3]. [1] A. Giuffrida, DV, G. Ziino, B. Spagnolo, A. Panebianco, A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian salami, Eur. Food Res. Technol. 228, 767 (2009). [2] R. Grimaudo, P. Lazzari, C. Solidoro, DV, Effects of solar irradiance noise on a complex marine trophic web, Sci. Rep. 12, 12163 (2022). [3] DV, G. Denaro, F. Giarratana, A. Giuffrida, S. Mazzola, G. Basilone, S. Aronica, A. Bonanno, B. Spagnolo, Modeling of sensory characteristics based on the growth of food spoilage bacteria, Math. Model. Nat. Phenom. 11, 119 (2016).