What happened
Glycan motifs are the standard readout of comparative glycomics, and pipelines treat them as independent features. Here, we show they are not. Motifs are partially ordered by substructure containment, so a parent motif's abundance dominates each of its children. We make that order explicit as a directed acyclic graph, which stratifies the multiple-testing family correctly and, together with an empirical-Bayes variance prior taken from each motif's containment neighborhood, raises estimated true positives across 45 glycomics datasets from 300 to 442 (+47%, p = 0.0001) after controlling for permutation-null false positives. Because a parent's children and its residual form a genuine sub-composition, their logratio balances need no reference frame and no scale model, and they separate a motif's own change from one inherited from its contexts. Of 337 significant parent motifs, 150 (45%) thus carry no signal of their own, while 138 motifs move only in the decomposition. We present case studies for both glycomics and glycoproteomics, including a recurrent reapportioning of core-1 sialylation at the immune-inhibitory disialyl-T antigen across eight human O-glycomes, and a colorectal fucosylation shift confined to the antenna, neither of which any marginal analysis reports.