The Duplicate Monophyly Criterion: An Empirical Approach to Bootstrapping Distance-Based Structural Phylogenies

Distance-based structural phylogenies summarise relationships between proteins using pairwise structural similarity scores. Unlike character-based methods, however, they lack a natural analogue of the non-parametric bootstrap. Because distances derived from continuous, high-dimensional folds provide no discrete sites to resample, rigorous support estimation would ideally rely on conformational ensembles from Molecular Dynamics or Monte Carlo simulations, which is computationally prohibitive at scale. A practical alternative is parametric bootstrapping in distance space, but this introduces a calibration problem: without an objective estimate of the signal-to-noise ratio, the perturbation magnitude cannot be chosen in a principled way. Here, we introduce the Duplicate Monophyly Criterion (DMC), an empirical strategy for calibrating distance-matrix perturbations using synthetic taxon duplicates as internal controls. We expand the observed distance matrix with virtual copies of each taxon, assign each original-duplicate pair a small baseline distance, and apply a floor-augmented heteroscedastic noise model directly in distance space. The central hypothesis is that loss of duplicate monophyly (i.e., failure of taxon-duplicate pairs to form two-tip cherries) marks a regime in which perturbations overwhelm intrinsic phylogenetic signal, thereby defining a conservative operating range for stability-based (bootstrap-like) support estimation. As a practical use case, we select a dataset-specific perturbation level{lambda} * as the largest noise level that retains a target fraction of duplicate pairings (e.g., [≥] 90%), and report split frequencies across replicate trees generated at{lambda} * as support values. We validate the framework in a geometric toy model where evolving two-dimensional shapes provide a known ground-truth topology, and in an empirical globin benchmark using distances derived from 1 - TM-score. Across both settings, duplicate monophyly tracks the erosion of tree structure under distance-matrix noise, establishing an internally calibrated "resolution limit" for assigning confidence in distance-based structural phylogenetics.