Dynamical model of buoyant cyanobacteria

Mathematical modelling of microbial and algalpopulations has a long tradition (e.g. Hallam,1996), whereas modelling of cyanobacteria with itsability to regulate cellular buoyancy has only becomepossible in recent years after thorough experimentalinvestigation of the vacuolate cell's properties (Fay& Van Baalen, 1987). The dynamical model for buoyantcyanobacteria development (Belov & Wiltshire, 1995)consists of seven differential andintegro-differential equations of which thephenomenological function for algal growth and decay,the light attenuation, nutrient cycling and intake arediscussed here. Analysis of these equationsdemonstrates the strong coupling of the modelvariables. Using convenient simplifying assumptionsabout the isothermal, calm and nutrient reservoir, theremaining equations represent the light-driven buoyantcyanobacterial population dynamics in a water column.Diurnal cyclicity of light is an important factor forbuoyant behaviour of cyanobacteria. The simplifiedmodel comprises of the non-linear differentialequation for algal population density and is suitablefor modelling the evolution of the cell colony in awater column and bloom occurrence. In order toinvestigate the properties of this highly non-lineardifferential equation, it is assumed that the buoyancyof the cyanobacterial element varies with the diurnalcycle and declines with depth according to theBouguer-Beer Law. The analytical solution of theequation has been found, and several scenarios ofpopulation growth are demonstrated.