  Monod's model describes the growth of microorganisms using a hyperbolic
function of extracellular resource concentration. Under fluctuating or limited
resource concentrations this model performs poorly against experimental data,
motivating the more complex Droop model with a time-varying internal storage
pool. We extend the Monod model to incorporate memory of past conditions,
adding a single parameter motivated by a fractional calculus analysis. We show
how to interpret the memory element in a biological context and describe its
connection to a resource storage pool. Under nitrogen starvation at
non-equilibrium conditions, we validate the model with simulations and
empirical data obtained from lab cultures of diatoms (T. pseudonana and T.
weissflogii) and prasinophytes (Micromonas sp. and O. tauri), globally
influential phytoplankton taxa. Using statistical analysis, we show that our
Monod-memory model estimates the growth rate, cell density, and resource
concentration as well as the Droop model while requiring one less state
variable. Our simple model may improve descriptions of phytoplankton dynamics
in complex earth system models at a lower computational cost than is presently
achievable.
