Figure \ref{920181} shows that Al, Cu and Mn are apparently in excess, but that in K, Fe and P are apparently deficient. Importantly, this interpretation should be done with a multivariate and compositional data perspective in mind. This implies that (1) a univariate or an incomplete multivariate perspective (e.g. focusing on extreme excesses and deficiencies) could miss a high yield region (a parachutist adjusting her fall following only one axis will likely miss the island) and (2) changes of concentrations in a closed system are relative, i.e. increasing the concentration of a component will inevitably decrease the concentration of at least another one.
Conclusion
All in all, the approach is fairly simple:
- explode concentrations to balances of concentrations with the isometric log-ratio transformation,
- identify a healthy state,
- fit a predictive model the identify the healthy hyper-volume,
- run the model to predict the yield class of a new ionome,
- if unhealthy, identify the targeted ionome and
- express the needed perturbation as a concentration ratios.
A perturbation indicates the change needed, not how to achieve this change, which could be done by identifying what happened in targetted balanced cases or by fertilizer trials. It should be noted that the closest healthy point might not be the easiest to reach, and professional agronomist must adapt results to local conditions and may select a solution not appearing at the closest point. For example, if the concentration of aluminium is too high, this could be corrected by increasing soil pH. But if increasing pH is not a viable solution, the agronomist could look for a high yield zone in the hyper-volume where Al is still high but less damageable due to other interactions.