All simulation parameters were chosen to be broadly similar to those observed in or estimated from the Pseudacris data set.
First, 30 species trees were simulated according to a birth-death process (Gernhard 2008 (link)) using biopy with 21 extant species, a speciation rate of 100 and a death rate of 30. This corresponds to a net diversification rate of 70 and an extinction fraction of 0.3. Haploid population sizes for each branch were chosen independently from a gamma distribution with a shape of 2 and a scale of 0.002. For a species with annual generation times, as is the case for at least some Pseudacris species (Caldwell 1987 ), and a substitution rate of per year this corresponds to an effective population size Ne of around two million individuals per generation. Species branch rates were chosen from a log-normal distribution with a mean in real space of 1 and a standard deviation of 0.3, then scaled so that the mean of the branch rates for a given species tree was exactly 1. This ensured that per-branch rates always reflected relative differences in substitution rates.
For each species tree, 130 gene trees with two sampled haplotype sequences per species were simulated according to the MSC process using biopy. The mean clock rate for each locus was chosen from a log-normal distribution with a mean in real space of 1 and a standard deviation of 0.6.
For each gene tree, 600 nt long sequence alignments were simulated using Seq-Gen (Rambaut and Grassly 1997 (link)). An HKY model was used for all sequence alignments with equal base frequencies, a κ value of 3, and a four rate category discretized gamma model of among-site rate variation with a shape α value of 0.2. Hence all inference based on simulated data applied the HKY + Γ substitution model to all loci.
The same combinations of clock models, population size integration and new operators were explored using the simulated data as for Pseudacris to provide more generally applicable results regarding those new techniques. The same number of loci, convergence strategy and calculations of ESS rates were used for both. Both haplotype sequences were used for each species for *BEAST and StarBEAST2.
First, 30 species trees were simulated according to a birth-death process (Gernhard 2008 (link)) using biopy with 21 extant species, a speciation rate of 100 and a death rate of 30. This corresponds to a net diversification rate of 70 and an extinction fraction of 0.3. Haploid population sizes for each branch were chosen independently from a gamma distribution with a shape of 2 and a scale of 0.002. For a species with annual generation times, as is the case for at least some Pseudacris species (Caldwell 1987 ), and a substitution rate of per year this corresponds to an effective population size Ne of around two million individuals per generation. Species branch rates were chosen from a log-normal distribution with a mean in real space of 1 and a standard deviation of 0.3, then scaled so that the mean of the branch rates for a given species tree was exactly 1. This ensured that per-branch rates always reflected relative differences in substitution rates.
For each species tree, 130 gene trees with two sampled haplotype sequences per species were simulated according to the MSC process using biopy. The mean clock rate for each locus was chosen from a log-normal distribution with a mean in real space of 1 and a standard deviation of 0.6.
For each gene tree, 600 nt long sequence alignments were simulated using Seq-Gen (Rambaut and Grassly 1997 (link)). An HKY model was used for all sequence alignments with equal base frequencies, a κ value of 3, and a four rate category discretized gamma model of among-site rate variation with a shape α value of 0.2. Hence all inference based on simulated data applied the HKY + Γ substitution model to all loci.
The same combinations of clock models, population size integration and new operators were explored using the simulated data as for Pseudacris to provide more generally applicable results regarding those new techniques. The same number of loci, convergence strategy and calculations of ESS rates were used for both. Both haplotype sequences were used for each species for *BEAST and StarBEAST2.
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