Hyb-Adam-UA: additivity-aware refinement of minimax-initialized mtDNA distance matrices

Mitochondrial DNA (mtDNA) distance matrices are standard inputs for distance-based phylogenetic inference. Missing entries can affect both topology reconstruction and branch-length estimation, whereas generic matrix-completion methods do not explicitly promote the tree-metric structure relevant to phylogenetic interpretation. We propose Hyb-Adam-UA (hybrid Adam, ultrametrically initialized and additivity-aware), a two-stage completion method that initializes missing entries by minimax-path distances on the observed graph and then refines only those entries using a four-point additivity objective with a triangle-inequality guard, while preserving all observed distances. We evaluated Hyb-Adam-UA on two 15 × 15 mtDNA benchmarks: a closely related Cercopithecidae dataset and a taxonomically heterogeneous primate dataset. Complete reference matrices were constructed from MAFFT multiple-sequence alignments using pairwise-deletion p -distances. Symmetric missingness masks were applied at 30%, 50%, 65%, and 85% missingness, with 30 replicates per level. Hyb-Adam-UA and its Stage 1-only ablation were compared with MW ⋆ -proj, NJ ⋆ -proj, LRMC, KNN-impute, and MDS-SMACOF using hidden-entry error, topology, patristic-distance, and branch-length criteria. For the heterogeneous dataset, the Stage 2 refinement significantly reduced hidden-entry RMSE relative to Stage 1 at 30%, 50%, and 65% missingness and relative to MW ⋆ -proj at 30%, 65%, and 85%. It also improved several branch-length results. For the Cercopithecidae dataset, however, the refinement provided no consistent advantage and was inferior to Stage 1 in some settings. Improvements in hidden-entry reconstruction produced only limited and inconsistent improvements in tree topology. A five-replicate synthetic 30 × 30 benchmark further demonstrated the effectiveness of Hyb-Adam-UA beyond the empirical 15 × 15 setting: among methods successful in all five replicates, it achieved the lowest mean hidden-entry RMSE at three of the four missingness levels and the lowest mean MAE at all four. Hyb-Adam-UA provides an additivity-aware framework for completing partially observed phylogenetic distance matrices without imposing a strict molecular-clock assumption. Its benefit is dataset-dependent: the method can improve hidden-distance reconstruction and branch-length estimation for taxonomically heterogeneous data, but the minimax-path initialization is itself a strong completion method. Lower matrix-reconstruction error does not necessarily produce a more accurate phylogenetic topology; matrix-level, branch-length, and topology criteria should therefore be evaluated separately.