Pettifor scale and computing EMD directly as in [20], we instead introduce a pairwise dissimilarity metric (Fig. ) between elements based on the statistical likelihood of species occurring within the same crystal structure (see methods). The advantage of this approach is that while the Pettifor scale assumes a constant distance between adjacent species, the substitutional (dis)similarity approach gives a more chemically meaningful metric. For example, the lanthanide series (La -Yb) covers a range of 14 steps on the Pettifor scale, while the dissimilarity approach gives a range of 0.4. In contrast, Na and F are adjacent on the Pettifor scale (one step), but have a dissimilarity of 4.38.