Stochastic models for phytoplankton dynamics in Mediterranean Sea

Dynamics of a stochastic hybrid delay food chain model with jumps in an impulsive polluted environment

In this paper, a stochastic hybrid delay food chain model with jumps in an impulsive polluted environment is investigated. We obtain the sufficient and necessary conditions for persistence in mean and extinction of each species. The results show that the stochastic dynamics of the system are closely correlated with both time delays and environmental noises. Some numerical examples are introduced to illustrate the main results.

Axion Field Influence on Josephson Junction Quasipotential

The direct effect of an axion field on Josephson junctions is analyzed through the consequences on the effective potential barrier that prevents the junction from switching from the superconducting to the finite-voltage state. We describe a method to reliably compute the quasipotential with stochastic simulations, which allows for the spanning of the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain an axion field that induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.

Effect of seasonally forced noisy environment on aquatic prey-predator model with water level fluctuations

In this paper, the impact of environmental noise on prey-predator interactions with seasonal fluctuations in water levels has been studied. Both intensity of noise and water level variations together play a significant role in the dynamics of an aquatic prey-predator system. Analytically, we have shown the existence of a positive solution and its uniqueness, the ultimate bound of the system's solutions, and the global attractivity of the solution. Moreover, parametric conditions for which model species either persist (strongly or weakly) in the system or go into extinction are derived and their biological significance is also discussed. The sufficient condition of stochastic permanence is also analyzed. To justify the analytical results, we have performed numerical simulations of both deterministic and stochastic systems and observed some significant dynamics in the considered system.

A coral reef benthic system with grazing intensity and immigrated macroalgae in deterministic and stochastic environments

As the most diverse, productive but vulnerable marine habitats in the world, coral reefs are easily affected by the ubiquitous environmental fluctuations, which could change the population dynamics and induce phase shifts of the ecosystem. In this paper, we consider a coral reef benthic system, where macroalgae, corals and algal turfs compete for the available space on a given region of the seabed with grazing intensity and immigrated macroalgae in both deterministic and stochastic environments. For the deterministic system, we analyze the existence and stability of equilibria, as well as the existence of bifurcations. For the stochastic system, sufficient conditions for the existence of the unique ergodic stationary distribution as well as the extinction of corals are obtained, by choosing suitable Lyapunov functions. Moreover, for the scenario that the system exhibits bistability between a macroalgal-coral coexistence equilibrium and a coral-free equilibrium in the absence of environmental fluctuation, we further investigate the irreversible noise-induced transition from macroalgal-coral coexistence to coral extirpation, and numerically estimate the critical values of noise intensity for the occurrence of such transition with the aids of the technique of stochastic sensitivity functions.

Robust parameter estimation based on the generalized log-likelihood in the context of Sharma-Taneja-Mittal measure

The problem of obtaining physical parameters that cannot be directly measured from observed data arises in several scientific fields. In the classic approach, the well-known maximum likelihood estimation associated with a Gaussian distribution is employed to obtain the model parameters of a complex system. Although this approach is quite popular in statistical physics, only a handful of spurious observations (outliers) make this approach ineffective, violating the Gauss-Markov theorem. In this work, starting from the generalized logarithmic function associated to the Sharma-Taneja-Mittal (STM) information measure, we propose an outlier-resistant approach based on the generalized log-likelihood estimation. In particular, our proposal deforms the Gaussian distribution based on a two-parameter generalization of the ordinary logarithmic function. We have tested the effectiveness of our proposal considering a classic geophysical inverse problem with a very noisy data set. The results show that the task of obtaining physical parameters based on the STM measure from noisy data with several outliers outperforms the classic approach, and therefore, our proposal is a useful tool for statistical physics, information theory, and statistical inference problems.

Low complexity model to study scale dependence of phytoplankton dynamics in the tropical Pacific

We demonstrate that a simple model based on reaction-diffusion-advection (RDA) equation forced by realistic surface velocities and nutrients is skilled in reproducing the distributions of the surface phytoplankton chlorophyll in the tropical Pacific. We use the low-complexity RDA model to investigate the scale relationships in the impact of different drivers (turbulent diffusion, mean and eddy advection, primary productivity) on the phytoplankton chlorophyll concentrations. We find that in the 1/4^{∘} (∼25 km) model, advection has a substantial impact on the rate of primary productivity, while the turbulent diffusion term has a fairly negligible impact. Turbulent diffusion has an impact on the phytoplankton variability, with the impact being scale propagated and amplified by the larger scale surface currents. We investigate the impact of a surface nutrient decline and some changes to mesoscale eddy kinetic energy (climate change projections) on the surface phytoplankton concentrations. The RDA model suggests that unless mesoscale eddies radically change, phytoplankton chlorophyll scales sublinearly with the nutrients, and it is relatively stable with respect to the nutrient concentrations. Furthermore, we explore how a white multiplicative Gaussian noise introduced into the RDA model on its resolution scale propagates across spatial scales through the nonlinear model dynamics under different sets of phytoplankton drivers. The unifying message of this work is that the low-complexity (e.g., RDA) models can be successfully used to realistically model some specific aspects of marine ecosystem dynamics and by using those models one can explore many questions that would be beyond computational affordability of the higher-complexity ecosystem models.

Multi-Collocation-Based Estimation of Wave Climate in a Non-Tidal Bay: The Case Study of Bagnoli-Coroglio Bay (Tyrrhenian Sea)

In this paper, the advantages of shaping a non-conventional triple collocation-based calibration of a wave propagation model is pointed out. Illustrated through a case study in the Bagnoli-Coroglio Bay (central Tyrrhenian Sea, Italy), a multi-comparison between numerical data and direct measurements have been carried out. The nearshore wave propagation model output has been compared with measurements from an acoustic Doppler current profiler (ADCP) and an innovative low-cost drifter-derived GPS-based wave buoy located outside the bay. The triple collocation—buoy, ADCP and virtual numerical point—make possible an implicit validation between instrumentations and between instrumentation and numerical model. The procedure presented here advocates for an alternative “two-step” strategy. Indeed, the triple collocation technique has been used solely to provide a first “rough” calibration of one numerical domain in which the input open boundary has been placed, so that the main wave direction is orthogonally aligned. The need for a fast and sufficiently accurate estimation of wave model parameters (first step) and then an ensemble of five different offshore boundary orientations have been considered, referencing for a more detailed calibration to a short time series of a GPS-buoy installed in the study area (second step). Such a stage involves the introduction of an enhancement factor for the European Centre for Medium-Range Weather Forecasts (ECMWF) dataset, used as input for the model. Finally, validation of the final model’s predictions has been carried out by comparing ADCP measurements in the bay. Despite some limitations, the results reveal that the approach is promising and an excellent correlation can be found, especially in terms of significant wave height.

Spatio-temporal dynamics of a planktonic system and chlorophyll distribution in a 2D spatial domain: matching model and data

Field data on chlorophyll distribution are investigated in a two-dimensional spatial domain of the Mediterranean Sea by using for phytoplankton abundances an advection-diffusion-reaction model, which includes real values for physical and biological variables. The study exploits indeed hydrological and nutrients data acquired in situ, and includes intraspecific competition for limiting factors, i.e. light intensity and phosphate concentration. As a result, the model allows to analyze how both the velocity field of marine currents and the two components of turbulent diffusivity affect the spatial distributions of phytoplankton abundances in the Modified Atlantic Water, the upper layer of the water column of the Mediterranean Sea. Specifically, the spatio-temporal dynamics of four phytoplankton populations, responsible for about 80% of the total chlorophyll a, are reproduced. Results for phytoplankton abundances obtained by the model are converted in chlorophyll a concentrations and compared with field data collected in twelve marine sites along the Cape Passero (Sicily)- Misurata (Libya) transect. Statistical checks indicate a good agreement between theoretical and experimental distributions of chlorophyll concentration. The study can be extended to predict the spatio-temporal behaviour of the primary production, and to prevent the consequent decline of some fish species in the Mediterranean Sea.