The functional form of resource uptake and tissue cost equations have important implications for terrestrial net primary productivity

Background/Question/Methods Plants harvest resources from the environment by producing tissues; for example water and nutrients are harvested by roots and carbon is fixed by photosynthesis inside of leaves. Plants are known to invest in tissues until the marginal benefits of resource harvest balance the marginal costs of production. Modeling production therefore requires equations for harvest, and equations for cost. It is straightforward to analytically show that the harvest function must have diminishing returns to tissue production. However, the cost function cannot be derived from first principals: what is the correct functional form of equations that describe cost? There are two scenarios that are possible based on the biologically reasonable functional forms for cost: 1) cost increases linearly with tissue production; 2) cost increases exponentially with tissue production. Second, we develop a coupled model of root and shoot growth based on Michaelis–Menten for resource harvest and Farquhar model for photosynthesis rate (i.e. carbon harvest), and parameterize it from the literature. We use the model to examine how these models predict root and shoot net primary production (NPP), and more specifically to determine how different functional forms for cost alter predictions.

Results/Conclusions The model predicts that photosynthetic rate has a larger effect on NPP, than nutrient uptake, but shows how nutrient uptake limits total photosynthesis and can predict progressive nitrogen limitation. By including Michaelis–Menten and Farquhar equation makes our model more sophisticated and give us a better understanding of plant responses in different scenarios. However, different cost equations (linear or exponential) give quite different predictions for net primary production. The most important conclusion is that the models show that the functional forms of equations used to model plant growth have different effects on predictions about NPP and data are needed to test these alternative models. These differences are both qualitative and quantitative.