Ecological Stoichiometry — Liebig's Law of the Minimum
Nutrient co-limitation, growth dynamics, and stoichiometric ratios
Growth rate μ
—
Limiting nutrient
—
N:P ratio
—
Biomass B
—
Liebig's Law of the Minimum states that growth is limited by the scarcest essential resource. In the Droop model for phytoplankton, growth depends on cellular quotas Q_N and Q_P:
μ = μ_max · min(1 − Q_N,min/Q_N, 1 − Q_P,min/Q_P)
Stoichiometric flexibility: organisms have optimal N:P ratios (Redfield ratio ~16:1 for marine phytoplankton) but can tolerate deviations. Colimitation occurs when both nutrients are near-limiting. The left panel shows nutrient concentrations; right shows the growth isoclines (ZNGI — zero net growth isoclines).