A theoretical modeling framework for motile and colonial harmful algae

Abstract

Climate change is leading to an increase in severity, frequency, and distribution of harmful algal blooms across the globe. For many harmful algae species in eutrophic lakes, the formation of such blooms is controlled by three factors: the lake hydrodynamics, the vertical motility of the algae organisms, and the ability of the organisms to form colonies. Here, using the common cyanobacterium Microcystis aeruginosa as an example, we develop a model that accounts for both vertical transport and colony dynamics. At the core of this treatment is a model for aggregation. For this, we used Smoluchowski dynamics containing parameters related to Brownian motion, turbulent shear, differential setting, and cell‐to‐cell adhesion. To arrive at a complete description of bloom formation, we place the Smoluchowski treatment as a reaction term in a set of one‐dimensional advection‐diffusion equations, which account for the vertical motion of the algal cells through molecular and turbulent diffusion and self‐regulating buoyant motion. Results indicate that Smoluchowski aggregation qualitatively describes the colony dynamics of M. aeruginosa . Further, the model demonstrates wind‐induced mixing is the dominant aggregation process, and the rate of aggregation is inversely proportional to algal concentration. Because blooms of Microcystis typically consist of large colonies, both of these findings have direct consequences to harmful algal bloom formation. While the theoretical framework outlined in this manuscript was derived for M. aeruginosa , both motility and colony formation are common among bloom‐forming algae. As such, this coupling of vertical transport and colony dynamics is a useful step for improving forecasts of surface harmful algal blooms.

Selection of photosynthetic traits by turbulent mixing governs formation of cyanobacterial blooms in shallow eutrophic lakes

“…trait group g 1 ) can stratify, if the turbulent diffusivity is <10 −3 m 2 s −1 ( Fig. S6B , see online supplementary material for a colour version of this figure), similar to findings in previous studies [ 33 , 42 ]. By the intraspecific diversification of the photosynthetic capacity, the Microcystis population can accumulate traits with the fittest photosynthetic capacity (accompanied by changes in population composition) across variable environmental conditions, optimizing the utilization of light resources for growth.…”

“…In our simulations, the water depth was fixed to 3 m with a resolution of the vertical discretization of 0.05 m, the cell tissue density ranged from 996 to 1130 kg m −3 with a resolution of 3.35 kg m −3 [ 31 ], and the colony size ranged from 10 to 420 μm with resolution of 10 μm [ 42 ]. No-flux conditions are applied at the boundaries of z , ρ , and d axes.…”

Spatiotemporal velocities, aggregation, and false dispersion: numerical considerations for the modeling of colonial and motile harmful algae

“…The larger diameters and fractal morphology of colonies ensure enhanced motility with respect to single cells. Mechanistic models concerning the aggregation of phytoplankton typically use Smoluchowski kinetic coagulation dynamics (Ackleh and Miller, 2018;Jackson, 1990;Smoluchowski, 1917); however, the coupling of aggregation dynamics with vertical transport is a more recent endeavor (Taylor et al, 2022). HFF 33,8…”

“…An advection–dispersion–reaction model has previously been developed to describe the one-dimensional transport of motile and colonial harmful algae in a stratified lake environment (Taylor et al , 2022). Packaged into this model are features of general interest for the study of numerical methods of fluid flow.…”

Modeling Physical and Physiological Processes Reveals the Role of Turbulence in the Prerequisites for Microcystis Blooms

“…Previous modeling studies have considered the important effects of turbulence on blooms, focusing on the spatial distribution of Microcystis under the physical transport processes of vertical turbulence‐induced mixing and horizontal drift (Feng et al., 2018; Taylor et al., 2022). Among them, vertical turbulence‐induced mixing is usually combined with buoyancy control to determine the movement of Microcystis .…”