Theory for growth of plants derived from the nitrogen productivity concept

A theory is developed on the assumption that growth of plants is determined by the current amount of nitrogen in the plants. The nitrogen-growth relation is formalized in the nitrogen productivity concept (amount of biomass produced per amount of nitrogen in the biomass and per unit of time), which is essentially a constant for a given species under fixed environmental conditions. A number of results follow for increases in whole plant biomass: (A) The relative growth rate is a linear function of the internal nitrogen concentration. (B) The maximal relative growth rate uniquely determines the scaling of the time axis. (C) Exponential growth is consistent only with stable internal nitrogen concentration. Dose-response curves expressed in reduced variables (the ratio between a variable and the same variable for a plant growing under optimal conditions) are universal, so that all species and all environmental conditions yield the same curve. This is confirmed by experimental data. The shape (linear, exponential, etc.) of the nitrogen uptake curve is the only parameter differentiating these universal curves. The Mitscherlich curve or variations of it can be fitted very closely to the derived dose-response curves, except under exponential growth. A conclusion drawn from the analysis is that the results of nutrition experiments cannot be properly interpreted unless the variation with time of the amount of nitrogen in the plant is known. The theory can be extended to more complex situations, for example, time-varying environmental conditions.