At the end, so long as the tree is bifurcating, the design of the tree doesn't matter so much to run multivariate analyses since the isometric log-ratio transformation explodes data from a closed to a real orthonormal space (orthogonal axes with equal scales). Switching from one balance design to another only rotates from the origin the axes across the cloud of data points. Euclidean distances between vectors of balances remain the same no matter how you designed the 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 computed with isometric log-ratios as variables on which diagnoses are performed.

The ionome as a map

Once mapped with isometric log-ratios, ionomic data are  coordinates\cite{2015} and analogous to coordinates in geographical maps, like the archipelago of the Îles-de-la-Madeleine, Québec, Canada (Figure \ref{496294}).