Construction of the natural variables for a tree with 4 generations.

Each natural variable is identified by a source of variation (ℓ, τ), corresponding to the root of a subtree, and a generation g. The + and − at each lineal position illustrate how the original variables are combined to form a natural variable. The 15 natural variables thus defined by the 3-tuple (ℓ, τ, g) are listed in the bottom row. Since the τ coordinates are indistinguishable, only 10 of the natural variables (those with τ = 0, say) are unique.