Reaction-diffusion-taxis model for spatio-temporal dynamics of five picophytoplankton populations

Abstract

Recently new models were devised to study spatio-temporal dynamics of phytoplankton populations in view of obtaining more precise predictions of the vertical biomass distributions in marine ecosystems. These studies can be crucial from the point of view of shery. Indeed the abundance of fi sh species is strictly connected with primary production, i.e. phytoplankton biomass, responsible for chlorophyll concentration. In this work a one-dimensional deterministic reaction-di ffusion-taxis model is used to reproduce the spatio-temporal dynamics, along a water column, of five picophytoplankton populations sampled in a real ecosystem. In our analysis, to better reproduce the spatio-temporal behaviour of picophyto-plankton populations we take into account the periodical changes of the light intensity and pro les of vertical turbulent di ffusivity, obtaining the time evolution of the system over a period of fi ve years. Moreover, the seasonal variations of both depth of thermocline and thickness of the upper mixed layer close to the water surface are considered. As a first step, the spatio-temporal behaviour of biomass concentration of each picophytoplankton population is calculated by numerically solving the equations of the model. Afterwards, the numerical results for biomass concentration, expressed in cell/m^3, are converted in total concentration of chlorophyll a (chl a) and divinil-chlorophyll a (Dvchl a), obtaining the chlorophyll distributions along the whole water column. These theoretical profi les are compared with experimental data for chlorophyll concentration collected in a site of the Tyrrhenian Sea in four diff erent days of diff erent seasons of the year. Statistical analysis, based on chi^2 goodness-of-fi t test, shows that numerical results are in a good agreement with real chlorophyll distributions for all seasons investigated. In particular, numerical results indicate that the primary production of phytoplankton biomass is strongly influenced by the light intensity and vertical turbulent diff usivity, which take on diff erent values along the water column, depending also on seasonal variations. These findings could contribute to predict future changes in phytoplankton distributions due to global warming, and to devise strategies which can prevent the decline of primary production and consequent decrease of fish abundance.