Gene family evolution
We estimated gene turnover rates, the number of gene gains and losses across the phylogeny lineages, and inferred gene family contractions and expansions using BadiRate 1.7 (Librado, Vieira, & Rozas, 2012). For the analysis we first inferred the orthogroups with OrthoFinder 2.3.8, and we used the calibrated ultrametric tree estimated with r8s. We tested, under the Birth-Death-Innovation (BDI) model for turnover rates, several biological relevant hypotheses with three different branch models: Free Rates (FR), Global Rates (GR) and Branch-specific Rates (BR), and chose the best model based on the lowest AIC value. To ensure an appropriate convergence we ran multiple times each model.