MULTIDIMENSIONAL SENSITIVITY ANALYSIS AND ECOLOGICAL IMPLICATIONS OF A NUTRIENT-UPTAKE MODEL

Mechanistic models of nutrient uptake are essential to the study of pl ant-soil interactions. In these models, uptake rates depend on the sup ply of the nutrient through the soil and the uptake capacity of the ro ots. The behaviour of the models is complex, although only six to ten parameters are used. Our goal was to demonstrate a comprehensive and e fficient method of exploring a steady-state uptake model with variatio n in parameters across a range of values described in the literature. We employed two analytical techniques: the first a statistical analysi s of variance, and the second a graphical representation of the simula ted response surface. The quantitative statistical technique allows ob jective comparison of parameter and interaction sensitivity. The graph ical technique uses a judicious arrangement of figures to present the shape of the response surface in five dimensions. We found that the mo st important parameters controlling uptake per unit length of root are the average dissolved nutrient concentration and the maximal rate of nutrient uptake. Root radius is influential if rates are expressed per unit root length; on a surface area basis, this parameter is less imp ortant. The next most important parameter is the effective diffusion c oefficient, especially in the uptake of phosphorus. The interactions o f parameters were extremely important and included three and four dime nsional effects. For example, limitation by maximal nutrient influx ra te is approached more rapidly with increasing nutrient solution concen tration when the effective diffusion coefficient is high. We also note the ecological implications of the response surface. For example, in nutrient-limited conditions, the rate of uptake is best augmented by e xtending root length; when nutrients are plentiful increasing uptake k inetics will have greater effect.