A response-geometry framework separates microbiome movement magnitude from directional coherence in intervention studies

Dietary and lifestyle microbiome interventions often produce mild but heterogeneous remodeling rather than uniform community shifts. In this setting, scalar diversity or group-level summaries can appear weak or inconclusive even when participants move in organized but magnitude-limited directions, or move substantially in divergent directions. We developed a response-geometry framework that jointly describes baseline-referenced response magnitude and cross-participant directional coherence within a compositional feature space. The framework complements diversity, ordination, trajectory, PERMANOVA, PERMDISP, and beta-diversity analyses by asking whether paired responses differ in size, shared direction, or both. MethodsA response vector for each participant was defined as the follow-up minus baseline profile after adding a 0.5 pseudocount and applying centered log-ratio transformation in Aitchison-based response space. Response magnitude was the Euclidean length of this vector. Directional coherence was quantified as cosine alignment between participant-level response vectors and the mean group response vector, with sign-flip permutations as a paired-structure-preserving diagnostic null. We evaluated the framework using workflow-sensitive diversity comparisons, 198,000 logistic-normal compositional simulations with 100 or 500 features and small-to-large shared-direction effects, public-data-derived implementation stress tests, a synbiotic and dietary-intervention cohort, and a fiber/fermented-food application in 16S rRNA gene amplicon and shotgun-derived CAZyme gene-family feature spaces. A beta research-preview repository accompanying the preprint is available at https://github.com/carolyyszeto/microbiome-response-interpreter-beta as v6.5-beta, including documented scripts, a toy dataset, environment notes, output-interpretation guidance, and exploratory implementation utilities. ResultsWorkflow comparisons showed that richness-sensitive differences were concentrated in rare-tail and low-abundance structure, informing the analytical feature-space context for response interpretation. In simulations, null and magnitude-only random-direction scenarios showed near-null detection rates of 0.061 and 0.062, close to nominal alpha = 0.05, whereas shared-direction scenarios showed increasing coherence with stronger effects and larger sample sizes. Mixed-responder and opposing-subgroup scenarios attenuated or cancelled pooled coherence, supporting separation between response magnitude and directional organization. The synbiotic and dietary-intervention cohort showed modest, heterogeneous displacement with limited within-arm coherence, with permutation p values from 0.575 to 0.653. In the fiber/fermented-food application, fermented-food exposure showed stronger 16S response organization than the baseline-period reference, while CAZyme estimates used non-identical sampling endpoints and remained feature-space-specific. ConclusionsThis response-geometry framework helps distinguish paired microbiome movement size from shared response orientation. It is intended as an interpretively cautious response-organization descriptor for mild, heterogeneous intervention settings, not as a replacement for existing multivariate methods. Its interpretation depends on sample size, effect structure, endpoint alignment, zero handling, group-direction stability, and feature-space definition. The framework does not convert weak, null, endpoint-limited, or sensitivity-dependent findings into efficacy, predictive, or mechanistic claims.