Ecological Stoichiometry

Phytoplankton nutrient dynamics: the Droop model tracks internal nutrient quota Q rather than just external supply, capturing luxury uptake and lag in growth response.

Supply nutrient S₀: 10.0 μM

Max uptake Vmax: 0.50

Uptake half-sat Ks: 2.0

Max growth μmax: 0.80 d⁻¹

Min quota Q_min: 0.04

Dilution rate D: 0.30 d⁻¹

Droop Model (1968): dS/dt = D(S₀−S) − ρ(S)·B; dQ/dt = ρ(S)/B − μ(Q)·Q; dB/dt = (μ(Q)−D)·B. Uptake ρ = Vmax·S/(Ks+S) (Michaelis-Menten). Growth μ = μmax·(1−Qmin/Q) (Droop equation). Unlike Monod's model, Droop separates nutrient uptake from growth — cells can store nutrients (luxury uptake), causing a lag. The equilibrium cell quota Q* = S*/(Ks+S*)·Vmax/μ* links external supply to internal stoichiometry. Widely used for modeling nitrogen, phosphorus, and iron limitation in marine phytoplankton.

Ecological Stoichiometry — Droop Cell Quota Model