Figure 8

Estimates of the mean, dispersion index and number of divergence times given empirical data. Panels A, B and C depict joint posterior densities of two hyper-parameter summaries that characterize the average divergence time (E(τ)) and dispersion index of divergence times Ω = Var(τ)/E(τ)) across three avian taxon-pairs that span the Carpentarian barrier in northern Australia. Each point is from a data set simulated using parameters randomly drawn from the prior and subsequently accepted using ABC with local linear regression (500 accepted points in total out of 3,000,000 simulated data sets) and a summary statistic vector D _m that only included mean values of π _b across loci from every taxon-pair. Panels D, E, and F depict hyper-prior and hyper-posterior densities of Ψ, the number of divergence times across taxon-pairs. Panels A and D results are under a model of total isolation after divergence, panels B and E results are under a model allowing for low migration after divergence, with each taxon independently having Nm = 0.0 - 1.0 between sister taxa after divergence. Panels C and F are results using a mixed model where the posterior is averaged across the two models while weighting for the relative posterior probability under the two models. Divergence times assume an average rate across loci of 5.0 × 10^-9 per site per generation and two year generation times.