From nutrient concentrations to nutrient balances

Transforming concentrations to balances between concentrations not only frees compositional data from their total sum constraint: it also offers a sound framework to interpret the ionome. To transform concentrations to nutrient balances, we need to apply a function to concentration data and, optionally, a balance scheme. As shown in Figure \ref{273738}, the only rule to design a valid balance scheme is to split groups of variables sequentially until each group contain a single part, like a strictly bifurcating tree. So long as this rule is respected, the scheme can be anything you want, but balances can be organized so that they can be interpreted.