On agreement forests

Tree rearrangement operations are widely used to measure the dissimilarity between phylogenetic trees with identical leaf sets. The tree bisection and reconnection (tbr) distance for unrooted trees can be equivalently defined in terms of agreement forests. For both the tbr distance and the less general subtree prune and regraft (spr) distance, we use such forests to derive new upper and lower bounds on the maximal possible distance between two trees with n leaves.