The Continuous Culture of Phytoplankton: Mathematical Equivalence Among Three Steady-State Models

Abstract

Within a framework of three-state variables-and the corresponding differential conservation equations-three alternative models of phytoplankton growth in a steady-state continuous culture are formulated, based on commonly accepted uptake and growth functions. Simple algebraic analysis of the three models proves them strictly equivalent, making them merely three (of many) minimal representations of one underlying metamodel. Correspondingly, and as sometimes implied (Droop 1973a, 1973b; Chisholm 1976), each of the three models is an equally valid (or equally invalid) formal description of algal growth at steady state. Experimental results from chemostats are not in principle applicable to dynamic conditions. Neither do they permit the distinction between internal and external nutrient pools as the determinant of growth.