Modelling spatio-temporal dynamics of phytoplankton distributions in Mediterranean Sea

Recently, theoretical studies were able to reproduce real vertical distributions of phytoplankton biomass in marine ecosystems. However, seasonal variations are not usually included in models which analyze the spatio-temporal dynamics of phytoplankton distributions in real aquatic systems. On the other hand, random and deterministic changes in environmental variables are responsible for significative consequences throughout the food chain, in particular in fish species, whose abundances are strictly connected with seasonal changes in the chlorophyll concentration, a marker of phytoplankton species. Here we present a one-dimensional stochastic reaction-diffusion-taxis model which allows to reproduce the spatio-temporal dynamics of five picophytoplankton populations distributed along a water column in a marine ecosystem. The model consists of stochastic differential equations, which include the effects of random and deterministic (seasonal) variations of environmental variables. The equations of the model are solved by numerical integration for different values of the noise intensity, obtaining for each picophytoplankton population the vertical distribution of biomass concentration as a function of the time. The numerical results, expressed in cell/m3, are converted in total concentration of chlorophyll a (chl a) and divinilchlorophyll a (Dvchl a), obtaining chlorophyll distributions along the water column. These theoretical profiles are compared with experimental data for the chlorophyll concentration collected in a site of the Tyrrhenian Sea during four different periods of the year. In particular, for suitable values of the noise intensity a good agreement (checked by chi-squared goodness-of-fit test) between theoretical and experimental chlorophyll distributions is obtained for all periods (seasons) investigated. Our findings confirm that the phytoplankton abundance is strongly dependent on the oscillations of light intensity and depth of thermocline, deterministic (seasonal) spatio-temporal behaviour of the vertical turbulent diffusivity, and random fluctuations of environmental variables. These results could be useful to analyze phytoplankton dynamics in different marine ecosystems and predict future changes in phytoplankton abundance, contributing to devise strategies able to prevent the reduction of phytoplankton biomass and consequent decrease of fish species.