In order to define the composomes corresponding to each network, we simulated these networks for 1000 generations, and used a k-means clustering algorithm (28) at assembly maximal size (before division) to detect clusters of similar compositions (composomes). We used cosine similarity as the clustering method with a threshold of 0.9. We generated a database of 100 networks and their computed composomes (see Supplementary) and used them as precomputed targets throughout the paper (Figures 3 . Where a single network with a single composome is presented (Figures 3, 4B, 5, 6A), it is β-matrix number 1; in Figure , where a network with two composomes are examined, it is β-matrix number 5. The Nmol molecular repertoire of a composome is defined as the count of lipid types whose copy number averaged across all members of a composome-defining cluster are at least 1.