Time-fractional modeling framework for Microcystis blooms and microcystin dynamics

Microcystin risk in cyanobacterial harmful algal blooms cannot be inferred reliably from total biomass alone because toxin concentrations depend on toxigenic biomass, toxin synthesis, intracellular retention, extracellular release, removal, and transport. This study developed a toxin-explicit, spatiotemporal time-fractional advection-dispersion-reaction (TF-ADR) framework for coupled cyanobacterial biomass and microcystin dynamics, using Lake Pontchartrain Estuary as a case-study implementation. The model resolves four transported state variables: toxigenic Microcystis biomass, non-toxigenic Microcystis biomass, intracellular microcystin, and extracellular microcystin. Environmental forcing fields, hydrodynamic velocities, and field observations from July-December 2021 were used to evaluate biomass structure, toxin partitioning, biomass-toxin decoupling, and process-level source-sink controls. Results showed that biomass-growth and toxin-synthesis favorability were related but not identical, reflecting different environmental controls on biomass accumulation and toxin production. The biomass module reproduced broad bloom structure, while the toxin simulation showed that microcystin was dominated by the intracellular pool, with median modeled intracellular and extracellular fractions of 0.978 and 0.022, respectively. Estuary-wide diagnostics showed that upper-tail total microcystin peaked before upper-tail total biomass, despite strong temporal association between the two signals. Pooled station-node analysis also showed a monotonic but non-linear biomass-toxin relationship, with total microcystin more strongly associated with toxigenic biomass than with total biomass. Process diagnostics indicated that toxin behavior reflected intracellular synthesis, release to the extracellular pool, dissolved-phase removal, and hydrodynamic redistribution. These findings demonstrate that separating toxigenic biomass, non-toxigenic biomass, intracellular toxin, and extracellular toxin provides a process-based modeling framework for interpreting microcystin risk in spatially heterogeneous estuarine systems, allowing government agencies to take proactive measures for protecting seafood and human health.