Fig. 6

All internal nodes can be rotated without changing the topology. Although they may look quite different, the four trees shown here are exactly equivalent to one another. This is because it is the order of branching events—the topology—that is relevant. Each internal node can be rotated without affecting the topology because this does not alter the groupings of species. For example, all four trees retain F + G as sister taxa, with the next closest relative of these species being E, then D, and so on. The reader is encouraged to confirm that the topologies of these trees are identical. To convert from the tree at the top left into the one at the top right (arrow 1), one need only rotate the node joining B to [C + D + E + F + G] and the node joining A to [B + C + D + E + F + G], as indicated in the figure. To convert this second tree to the one at the bottom right (arrow 2), one must rotate the node joining [E + F + G] and the node joining A to [C + D + E + F + G + B]. The reader is invited to identify the node rotations necessary to convert this third tree to the one at the bottom left (arrow 3) and thence back to the original tree at the top left (arrow 4)