How size and shape affect the vertical velocity of cyanobacterial colonies

Cyanobacterial colonies often exploit their buoyancy and large size to float upwards rapidly and form dense surface blooms, which can degrade water quality, threaten ecosystems and public health, and impose substantial economic costs. Yet, how the morphology of cyanobacterial colonies controls their vertical velocity remains poorly understood. We conducted detailed three-dimensional morphological characterization of colonies of the cyanobacterium Microcystis in lake samples at the single-colony level and performed controlled flotation experiments in a stratified fluid. Using particle tracking in a vertical density gradient, we separately quantified the contributions of colony shape and buoyant density at the level of individual colonies. Our results show that the shape factor in Stokes' law varies systematically with colony size. Consequently, the vertical velocity of colonies does not scale with the square of colony size but only with a power of 1.13, as larger colonies have a more irregular shape and therefore experience enhanced drag. We therefore correct the commonly used Stokes' law to account for the size-dependent change in the shape factor. Interestingly, implementation of this power law relationship in a vertical migration model shows widespread chaotic dynamics in the migration trajectories of Microcystis colonies. These results highlight the importance of morphological plasticity in cyanobacterial colonies and can inform predictive models and hydrodynamic control strategies for toxic blooms. Our methodology to simultaneously determine the density, shape factor and velocity is broadly applicable to suspended aggregates with complex shapes in freshwater and marine systems.