Abstract
Crop genotypes that make best use of potassium (K) fertilizers can promote agricultural sustainability. However, screening germplasm collections for responses to K fertilizers is often laborious and expensive. To reduce costs, the number of K fertilizer treatments required to identify better genotypes should be minimized. This might be achieved by exploiting the mathematical relationships between biomass, plant K content, and K supply. This study employed 14 barley (Hordeum vulgare L.) genotypes growing in a hydroponics system that allowed the K supply to roots to be controlled through the K concentration in a flowing solution. It sought to determine the minimal number of treatments required to model the relationships between (a) shoot biomass and K supply, (b) plant K content and K supply, and (c) shoot biomass and plant K content. The relationships between (a) shoot biomass and K supply and (b) plant K content and K supply for any given genotype could be fitted by Michaelis-Menten equations and each of these could be estimated from data obtained at two, appropriately-chosen, rates of K supply. The relationship between shoot biomass and plant K content could be estimated from these relationships. However, the optimum K supply required for accurate estimates differed between genotypes and whether shoot biomass or plant K content was to be estimated. It is, therefore, suggested that the relationships between shoot biomass, plant K content, and K supply might best be determined from measurements of biomass and K content at three, carefully-selected, rates of K supply.