Mathematical modelling of the development of cyanobacteria (blue-green algae) in an eutrophical lake, including aspects of toxicology
Cyanobacteria (blue-green algae) are present in most natural water systems throughout the world. They have a tendency, under certain conditions, to become over-buoyant and thus form a water bloom or "surface scum". Often, in conjunc­ tion with the formation of a water bloom, a release of cyanobacterially produced toxin occurs. This toxin can be harmful to local wildlife and surrounding human populations. One distinguishing feature of common strains of cyanobacteria such as Oscillatoria, Microcystis and Anabaena is the ability of the cell to regulate its density and, hence, buoyancy in relation to incident light irradiation. This regula­ tion of buoyancy allows the cyanobacterial cell to alter its vertical position within the water column in order to find an optimal position. The development of a cyanobacterial population is described by a dynamical model which accounts for a number of factors including algal growth, degradation and light driven buoyancy. The work in this thesis describes the development of a cyanobacterial cell buoyancy function which is then used, in conjunction with the dynamical model, to find an algal population density distribution. An analytic solution is found using an approximation function for the cell density function, then a numerical scheme is developed to allow the full function for cell density to be used. The numerical scheme is developed using the object-oriented paradigm for programme construction which allows easy extensions to be made to the model when further experimental data becomes available. Finally, a semi-empirical model for cyanobacterial toxin release in a water column is used, together with the population density results, to develop a plausible description of a cyanobacterial population and of the subsequent toxicity of the water body.
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