Hyper-posterior and Hyper-prior samples given Marquesas DNA sequence data (seven taxon-pairs). Dashed lines depict hyper-prior distributions and solid lines depict hyper-posterior distributions. Stage 1 hyper-parameter estimates: (A) Average effective population size E((θ
)2) of the putatively colonized endemic populations at the seven isolation times (T
). (B) The number of descendent populations per seven (Y) taxon-pairs that arise by colonization at times . Stage 2 hyper-parameter estimates where hyper-prior is conditional given constant value of Z = 7: (C) ΩC dispersion index of Z = 7 colonization times; Ω C = Var(τ
) where τ
is colonization time. (D) E(τ
), average colonization time across Z = 7 colonization times. For each estimate, tolerance was 0.001 (2,000 accepted draws) using the local regression algorithm.