Multi-locus coalescent species delimitation (*BEAST)

Using the same partitioning schemes and models as those applied for BEAST, we tested multiple species hypotheses based on supported clades recovered in analyses of individual and concatenated datasets that had a COI divergence >2%. Eight species hypotheses, ranging from two to six species, were tested (Table 4) by assigning terminals to different taxa and comparing the marginal likelihood values of the different hypotheses after the species tree was generated.

Con: concatenated dataset. Clade names are based on Fig 1.

Each run started from a random tree and was sampled every 5000 generations. We implemented two models of population size, “piecewise linear and constant root” (PLCR) and “piecewise linear” (PL), rather than the piecewise constant population size model because P. nigra is extremely widespread [20] and is likely to have undergone a population expansion. Each hypothesis was run under both Yule [79] and birth-death [81] speciation processes separately. Convergence of each *BEAST run was assessed in the same manner as for BEAST. The number of generations/run (200 to 600 million) and the burn-in (5 to 200 million) required for stationarity varied for each analysis.

The harmonic means [82] of runs for each species hypothesis were estimated in BEAST 1.8.0. The favored hypothesis was that with the lowest harmonic mean that was significantly different from other means, with significant difference assessed using Bayes Factors [74]. Because the harmonic mean method might not be sufficiently sensitive [83], we also used a posterior simulation-based approach (Akaike’s information criterion through Markov chain Monte Carlo (AICM) comparisons [84]) to identify the best species hypothesis. The hypothesis with the lowest AICM was assumed to be best, with the P values from calculating the exponential value ((minimum AICM–maximum AICM)/2) indicating whether any two hypotheses were significantly different from each other (P < 0.05, d.f. = 1).