Nutrient limitation on terrestrial plant growth--modeling the interaction between nitrogen and phosphorus

Growth of plants in terrestrial ecosystems is often limited by the availability of nitrogen (N) or phosphorous (P) Liebig's law of the minimum states that the nutrient in least supply relative to the plant's requirement will limit the plant's growth. An alternative to the law of the minimum is the multiple limitation hypothesis (MLH) which states that plants adjust their growth patterns such that they are limited by several resources simultaneously. We use a simple model of plant growth and nutrient uptake to explore the consequences for the plant's relative growth rate of letting plants invest differentially in N and P uptake. We find a smooth transition between limiting elements, in contrast to the strict transition in Liebig's law of the minimum. At N : P supply ratios where the two elements simultaneously limit growth, an increase in either of the nutrients will increase the growth rate because more resources can be allocated towards the limiting element, as suggested by the multiple limitation hypothesis. However, the further the supply ratio deviates from these supply rates, the more the plants will follow the law of the minimum. Liebig's law of the minimum will in many cases be a useful first-order approximation.