Spurious correlation is not constrained as a function of feature count, mean, and variance.

A The approximate compositional correlation (based on Eq (3)) between features j and k when σ_X,jk = 0, as a function of the proportion of the total mean and proportion of total variability they contribute. B-D Examples of compositions that display positive (B) and negative (C-D) compositional correlations; in each, the top panel shows the correlation of the unconstrained and unobserved abundances across samples, while the bottom panel shows the correlation of the relative abundances across samples. The spurious correlation can be positive or negative, and of arbitrary magnitude, depending on the characteristics of the unobserved abundances.