Mathematical model for photophobic accumulations of blue-green algae in light traps

Summary Accumulations of the filamentous Cyanophyceae Phormidium uncinatum in light traps result from repeated photophobic reactions at the light-dark border. The time course of accumulations shows an initial linear part and reaches a saturation level after longer periods of time. A mathematical model is proposed based on a limited number of fundamental assumptions, which can be justified by the experimental data. A set of differential equations, which can be solved in a closed form, describe the current density j of the net influx of trichomes into the light trap. Absorption by the accumulating organisms diminishes the initial light intensity I₀ to a limiting intensity I₁ below which no more organisms react phobically. I₁ depends on the initial light intensity I₀. Furthermore the absorbance of a single layer of organisms has been calculated from the experimental data.