 |
The objective of this work is to analyse the ability of a spatial moment model (SMM) to approximate an individual-based model (IBM) dedicated to the study of the aggregation phenomenon in a mobile phytoplankton population. The dynamic system of spatial moments is a system of integro-differential equations derived from a phytoplankton IBM. The later is built on the basis of stochastic processes describing the dynamics of phytoplankton cells and their interactions. These processes are the movement of cells which takes into account the random dispersion of cells in water and the attraction between cells due to their chemosensory abilities, and the branching process (cell division or cell death) in which the effect of local competition for nutrient resources on the cell's division process is taken into account through the use of density dependent division rate.
We solve numerically the SMM and then simulate the two models (IBM and SMM) for to analyze the aggregation in the population. The numerical results have led to the conclusion that in contrast to the meanfield model (MFM), the method of spatial moments is efficient to capture the dynamics of
the IBM. Further, the SMM easily permits the prediction of long term behavior of phytoplankton cells and their spatial structure.
Regardless of competition intensity, in the long term the population tends to be stable with formation of aggregates, as a result of the equilibrium between different mechanisms, including reproduction, competition, diffusion and cells attractions due to chemosensory abilities.
