Correction for Burbrink and Pyron (2011)

Correction for Burbrink and Pyron (2011) Here, we correct branch lengths for simulated species trees in Burbrink and Pyron (2011), and discuss the implication of these corrections on gene tree and diversification estimates under different values of the population size parameter, θ (Neμ), and scaled coalescent units. In Burbrink and Pyron (2011), we simulated species trees using the birthdeath.tree function in GEIGER (Harmon et al. 2008), which, given the conditions of our simulations, yielded average branch lengths (edge lengths) generally greater than 1.0. For example, we simulated 100 50-taxon trees in 50 time units under a Yule model with λ (speciation rate) = 0.064, that yields average edge lengths across all trees of 7.52 (standard deviation = 1.14). Unfortunately, we failed to realize that that when simulating gene trees under a clocklike model using different values of θ in the R package “phybase” (Liu 2009), branch lengths are required to be given in terms of mutation units (T) for the species trees, which is equivalent to mutation rate per site per generation across all populations (μ), multiplied by the number of generations (t). Therefore, given our simulated species trees, the average branch lengths in units of time >1 would generally be very large in terms of mutation units. To scale this properly, we here use a standard rate of substitution from mtDNA studies (Brown et al. 1979; Zink et al. 2004; Weir and Schluter 2008), in which rates have been reported to be approximately 2% per million years between taxa (or 1 × 10−8/lineage/year). To simplify these calculations, an organism with a generation time of one year would yield a μ of 1 × 10−8 substitutions/site/year. To scale the branch lengths on the species tree, which are in absolute time units, we make the assumption that the time units are given in millions of years (now equal to generations), which is standard for most chronograms. Therefore, for an organism with one generation per year and the simulated trees now scaled in millions of generations (average = 7.52 × 106), we correct these branch lengths by multiplying all simulated tree edge lengths by 1×10−8. This yields trees with branch lengths in terms of mutational units (T), which is suitable for coalescent simulations in phybase. To examine the impact of diversification estimation (using Pybus and Harvey’s γ, 2000) under different values of θ, we turn our discussion to coalescent units, here defined as T/θ. In Burbrink and Pyron (2011), we discussed absolute values of θ on the improperly scaled species trees, when we should have discussed θ in terms of coalescent units. Using the corrected branch lengths for the 50-taxon species tree, we use the same methods for generating 100 gene trees within each species tree (for 100 species trees) as in Burbrink and Pyron (2011) but using coalescent units ranging from 0.2 to 2.0. We show that the trend is the same as before, in which increasing values of θ (lower coalescent units) yield greater γ-error (Eγ), which represents the difference between the mean gene tree γ (γ̄gt )and the true value of γ from the species tree (γS): Eγ = γ̄gt − γsr . The pattern remains the same for Robinson–Foulds distances (RF; Robinson and Foulds 1981) as well. However, for realistic values with trees properly scaled in mutation units, lower values of θ than those discussed in Burbrink and Pyron (2011) produce greater Eγ and higher RF distances (Fig.1).