A simple model for nitrogen-limited plant growth and nitrogen allocation

and Aims In many studies of nitrogen-limited plant growth a linear relationship has been found between relative growth rate and plant nitrogen concentration, showing a negative intercept at a plant nitrogen concentration of zero. This relationship forms the basis of the nitrogen productivity theory. On the basis of empirical findings, several authors have suggested that there is also a distinctive relationship between allocation and plant nitrogen concentration. The primary aim of this paper is to develop a simple plant growth model that quantifies this relationship in mathematical terms. The model was focused on nitrogen allocation to avoid the complexity of differences in nitrogen concentrations in the different plant compartments. The secondary aim is to use the model for examining the processes that underlie the empirically based nitrogen productivity theory.

In the construction of the model we focused on the formation and degradation of biologically active nitrogen in enzymes involved in the photosynthetic process (photosynthetic nitrogen). It was assumed that, in nitrogen-limiting conditions, the formation of photosynthetic nitrogen is proportional to nitrogen uptake. Furthermore it was assumed that the degradation of photosynthetic nitrogen is governed by first-order kinetics. Model predictions of nitrogen allocation were compared with data from literature describing four studies of growth. Model predictions of whole plant growth were compared with the above-mentioned nitrogen productivity theory.

Allocation predictions agreed well with the investigated empirical data. The ratio of leaf nitrogen and plant nitrogen declines linearly with the inverse of plant nitrogen concentration. Nitrogen productivity is proportional to this ratio. Predictions for whole-plant growth were in accordance with the nitrogen productivity theory.

The agreement between model predictions and empirical findings suggests that the derived equation for nitrogen allocation and its relationship to plant nitrogen concentration might be generally applicable. The negative intercept in the linear relationship between relative growth rate and plant nitrogen concentration is interpreted as being equal to the degradation constant of photosynthetic nitrogen.