Host and parasite characterization
Following the model proposed by Higgs & Derrida (1991), parasite individuals are explicitly modeled by biallelic sequences of infinite sites, a simplified form to represent their genomes and heritable trait. Individuals are monoic and engage in sexual reproduction, with non-overlapping generations. The empirical data have evolutionary times in the order of millions of years, and to maintain this time scale in the model would demand a higher computational cost. As proposed by Costa et al. (2019), in our approach we adopted a higher value of mutation rate in order to decrease the number of iterations necessary for speciation (time steps or generations) to happen. Furthermore, we assumed that, due to the shorter life cycle of parasites, they have a faster speciation rate (Dowton & Austin 1995; Light & Hafner 2007). To satisfy these conditions, we rescaled the whole host phylogeny assuming that the smaller branch length consists of the minimal time for parasites to speciate in allopatry (𝞃agenerations - see the details in supplemental information I). The simulation starts with a clonal parasite population using a unique host species. The first host speciation occurs only after𝞃a generations, accumulating genetic variation before the first host speciation (the root of the host phylogeny). Each host species imposes a carrying capacity of K parasite individuals. Thus, the overall carrying capacity increases by Kindividuals at each new host speciation.