The pan-genome rarefaction curve did not level out, indicating the pan-genome is “open” (i.e., not fully sampled) for the 19 Legionella, species (Supplementary Figure 2B). The Heaps law parameter α, a measure of the rate of novel information discovery24, was estimated to be 0.63. Values of α greater than 1 suggest a closed pan-genome. Using the matrix of gene family distribution across Legionella, we fitted a binomial mixture model implemented by the binomixEstimate function in the micropan R package25. This function estimated a series of mixture models with increasing complexity and used the Bayesian Information Criterion (BIC), estimating the optimum Legionella pan-genome size to be 30,275 genes (Supplementary Figure 2C).