Simulations.

We assessed the expected number of homoplasies that might be introduced by convergent mutations in each of the datasets through simulations as in ref. 21. We built a maximum likelihood tree for the core genomes in each genus or cluster with RAxML v8.2.7 (75) under a GTR model. Then, using SeqGen v1.3.3 (76), the resulting tree was applied to generate an alignment that maintained the nucleotide composition, the number of genomes, and the length of the alignment. Because phylogenetic inference considers recombination events as multiple independent mutation events (thereby overestimating the number of mutations that accumulated in the simulated alignments), we rescaled the length of the branches of the trees uniformly to match the level of polymorphisms in the simulated alignments and the real data. Each simulated alignment was then subjected to the same resampling strategy to detect homoplasies.