The influence of light irradiance and rainfall patterns on phytoplankton dynamics

The effects of light irradiance and nutrient availability on the dynamics of a phytoplankton model are studied for four species of phytoplankton, two with photoinhibition and two without photoinhibition. In particular, the dynamical effects of changes of nutrient availability and levels of irradiance associated with rainfall and storm conditions are examined. For constant nutrient input and light irradiance, it is proved analytically that the model has a trivial equilibrium point (zero phytoplankton population) which always exists and a nontrivial equilibrium point (positive phytoplankton population) which exists only if the trivial point is unstable. It is also proved analytically that if the nontrivial point exists, then it is locally and globally stable and that limit cycles cannot occur. Results of numerical simulations are presented showing the differing dynamics of species with and without photoinhibition under conditions of constant nutrient input and a range of values of constant irradiance. Results of numerical simulations are also presented showing the dynamics during and after periods of heavy rainfall and storms on the assumption that the heavy rainfall increases the nutrient input, the irradiance is reduced during the rainfall, and strong sunlight returns after the rain stops. The simulations show that increased phytoplankton densities and algal blooms can occur at the end of a period of heavy rainfall followed by a return of sunlight, and that a double algal bloom can occur in some phytoplankton species if the increase in nutrient flow lasts long enough during and after rainfall.