Multiple nutrient limitation in unicellulars: reconstructing Liebigʹs law

Liebigʹs law of the Minimum is reformulated in terms of biomass composition dynamics. The doctrine of the single limiting nutrient is shown to be invalid generally. The nutritional status of a unicellular organism is expressed in terms of state variables; one which represents the subsistence composition and a number of reserve surplus type variables. It is proposed that the property of being limiting should be defined in terms of the reserve surplus variables. On the basis of this definition, it can be decided whether a nutrient, or combination of nutrients, is limiting, both in transient and steady states. The concept of multiple limitation is shown to have two distinct meanings on these definitions. A non-interactive minimum model, based on a `hardʹ minimum operator, is introduced. Smooth interactive models may be formulated which have this minimum model as a limiting case. One such model is described. Numerical simulations show how the behaviour of this smooth model can approximate that of the minimum model: apparently hard non-linearities can arise in the smooth model, through time-scale separation.