since the isometric log-ratio transformation explodes data from closed to real orthonormal space (orthogonal axes with equal scales), and balances defines the orthonormal axes where the exploded points are mapped. Switching from a balance design to another only rotates the axes across the cloud of data, from the origin. In the end, we obtain orthogonal coordinates of compositions mapped on balance variables, and euclidean distances between observations are the same no matter how you designed your tree.
In this article, I'm de facto ruling out approaches based on concentrations and unorganized ratios and from now on, I will use balances as variables on which diagnoses are performed.

The ionome as a map

Once mapped with isometric log-ratios, ionomic data are literally coordinates,  and analogous to coordinates in geographical maps, like the archipelago of the Îles-de-la-Madeleine, Québec, Canada (Figure \ref{496294}).