Uncertainties of cell number estimation in cyanobacterial colonies and the potential use of sphere packing

Cyanobacteria are notorious bloom formers causing various water quality concerns, such as toxin production, extreme diurnal variation of oxygen, or pH, etc., therefore, their monitoring is essential to protect the ecological status of aquatic systems. Cyanobacterial cell counts and biovolumes are currently being used in water management and water quality alert systems. In this study, we investigated the accuracy of colonial biovolume and cell count estimation approaches used in the everyday practice. Using real like 3-dimensional images of cyanobacterial colonies, we demonstrated that their shape cannot be approximated by ellipsoids. We also showed that despite the significant relationship between overall colony volume and cell biovolumes because of the considerable scatter of cell count data the regressions give biased estimates for cyanobacterial cell counts. We proposed a novel approach to estimate cell counts in colonies that was based on the random close sphere packing method. This method provided good results only in those cases when overall colony volumes could be accurately measured. The visual investigation of colonies done by skilled experts has given precise but lower estimates for cell counts. Estimation results of several experts were surprisingly good which suggest that this capability can be improved, and estimation bias can be reduced to the level acceptable for water quality estimations. Highlights ### Competing Interest Statement The authors have declared no competing interest.