k-Nearest Common Leaves algorithm for phylogenetic tree completion

Phylogenetic trees represent the evolutionary histories of taxa and support tasks such as clustering and Tree of Life reconstruction. Many established comparison methods, including the Robinson-Foulds (RF) distance, assume identical taxon sets. A methodological gap remains for trees with distinct but overlapping taxa. Existing approaches either prune non-common leaves, which can discard information, or complete both trees such that they share the same taxa. Completion is more comprehensive, but current methods typically ignore branch lengths, which are essential for identifying evolutionary patterns. This paper introduces k-Nearest Common Leaves (k-NCL), an algorithm for completing rooted phylogenetic trees defined on different but overlapping taxa. The method uses branch lengths and topological characteristics and does not rely on a specific distance measure. The k-NCL algorithm is designed to preserve evolutionary relationships in the trees under comparison. The running time is O(n2), where n is the size of the union of the two leaf sets. Additional properties include preservation of original distances and topology, symmetry, and uniqueness of the completion. Implemented in Python, k-NCL is evaluated on biological datasets of amphibians, birds, mammals, and sharks. Experimental results show that RF combined with k-NCL improves phylogenetic tree clustering performance compared to the RF(+) tree completion approach. Availability and implementationAn open-source implementation of k-NCL in Python and the datasets used in this study are available at https://github.com/tahiri-lab/KNCL.