On branch lengths assignment methods for trees with fixed topology and related biological applications

Distance-guided tree construction with unknown tree topology and branch lengths has been a long studied problem. In contrast, distance-guided branch lengths assignment with fixed tree topology has not yet been systematically investigated, despite having significant applications. In this paper, we provide a formal mathematical formulation of this problem and propose two representative methods for solving this problem, each with its own strength. We evaluate the performance of these two methods under various settings using simulated data, providing guidance for the choice of methods in respective cases. We demonstrate a practical application of this operation through an extension we termed FunUniFrac, which quantifies the differences in functional units between metagenomic samples over a functional tree with assigned branch lengths, allowing clustering of metagenomic samples by functional similarity instead of taxonomic similarity in traditional methods, thus expanding the realm of comparative studies in metagenomics.