A theoretical framework to study potassium utilization efficiency in response to withdrawal of potassium

An important objective of plant research is to improve the efficiency in the utilization of major nutrients, particularly nitrogen, phosphorus, and potassium. Several definitions of internal nutrient utilization efficiency (NUE) have been proposed, but the theoretical consistence of their use has been poorly explored. Here, a non-mechanistic approach was developed to theoretically examine the dynamics of commonly used NUE indicators following complete potassium deprivation. This approach was used to study the sensitivity of NUE indicators to changes in the actual NUE (NUEa) of K(+) in virtual plants. Three empirically based models that differ in the relationship between NUE and the internal K(+) concentration were examined. Frequently used indicators (potassium use efficiency, utilization efficiency, physiological efficiency, and nutrient productivity) and two additional ones introduced here (accumulated productivity and physiological ratio) differed in their capacity to reflect differences in NUEa. They also exhibited large disparities in their temporal variation and in their responsiveness to the concentration of K(+) before the beginning of the deprivation period. According to this analysis, the simultaneous use of several indicators could help to refine plant breeding for high NUE. The data also suggest that a trade off between plant productivity and the time necessary to reduce the concentration of K(+) by half is inherent to the dynamics of plant systems. Finally, it is proposed that for some plant species selection for high NUEa would not always be in conflict with selection for improved relative plant performance in low K(+) environments.