Optimization of Plant Root: Shoot Ratios and Internal Nitrogen Concentration

A general theoretical approach is developed to analyze the morphological and physiological responses of plants to nitrogen availability. The optimal leaf-nitrogen concentration and corresponding optimal root: shoot ratio which maximize relative growth rate are found quantitatively as a function of root—specific activity which is assumed to be a function of soil nitrogen availability. The cost of increasing tissue nitrogen concentration is found to be primarily related to an increase in allocation to roots. Predictions of the analysis are consistent with previous theories and general empirical findings, suggesting that plants respond optimally to soil nitrogen. Relative growth rate is predicted to be a nearly linear function of whole-plant nitrogen concentration and shoot fraction is a monotonically increasing function of tissue nitrogen concentration when plants respond optimally to soil nitrogen availability.