Null and observed genes tree-to-tree distance distributions.

<p>(A) Tree-to-tree distances between 20 trees drawn from the posterior distribution of each observed gene tree from one another (right hand side; 400 combinations per pair wise comparison) and the observed gene trees to 20 simulated gene trees that makes up the null distribution for each observed gene tree (left hand side). The position of the 80% critical value for each of the three null distributions is marked (blue: MDH, red: LGT and green: HYB asterisks; left hand side). The lower boundary of the 95% credibility interval of each observed pair of genes’ tree-to-tree distances are marked (purple: LGT-HYB, light blur: HYB-MDH and orange: HYB-LGT asterisks; right hand side). The test statistic, φ, is the distance between the closest left and right hand asterisks and does not overlap, thereby indicating a rejection of the null hypothesis of lineage sorting alone. (B) Tree-to-tree distances as in A, but after the removal of individuals with a putative hybrid origin. Asterisks also as in A. In this case, removal of individuals of putative hybrid origin results in a zero result for φ, thereby indicating that the null hypothesis of lineage sorting alone cannot be rejected. The interpretation is that those individuals that have been removed (compared to A) require an alternative explanation beyond lineage sorting in order to account for their incongruent placement among the three gene trees, whereas those that remain in B do not.