Note on the hybridization number and subtree distance in phylogenetics

For two rooted phylogenetic trees T and T ′, the rooted subtree prune and regraft distance between T and T ′ has often been used as a replacement for the hybridization number of T and T ′. However, Baroni et al. [1] constructed particular instances that showed both the difference and the ratio between this number and distance can be arbitrarily large. In this note, we show that the difference and ratio values obtained in [1] are the best possible, thus answering a problem posed in [2].