# Reported plant diversity and gut microbial composition
Analysis date: 8 October 2026. Historical American Gut processed data; local Python Notebook analysis.

A small community-level association was detected between reported plant-type categories and microbial composition. Country adjustment changed its magnitude little. However, geographic generalization is weak, complete-case and regional sensitivity tests were less conclusive after multiplicity correction, and differing within-group dispersion complicates a pure community-centroid interpretation. These results do not show that eating more plant types causes a healthier microbiome.

## Data and cohort
The source is the public [biocore/American-Gut repository at pinned commit 68fd6d4](https://github.com/biocore/American-Gut/tree/68fd6d4b2fa6aeb5b4f5272c6f1006defe5b160e). The [README](https://github.com/biocore/American-Gut/blob/68fd6d4b2fa6aeb5b4f5272c6f1006defe5b160e/README.md) says these tables represent May 2015 or earlier and an earlier dietary questionnaire. AG_100nt.biom records creation on 28 March 2015 using QIIME 1.9.0. This is not a replication of later American Gut publications.

The BIOM and metadata tables contain 4,827 matching sample IDs and 22,742 original microbial features. Selection retained stool samples, age >=18 in years, numeric participant identifiers, and >=1,000 reads, then one highest-depth sample per participant with a deterministic ID tie break. Numeric subject suffixes were conservatively deduplicated across optional study-prefix formats. Selection flow: 4,827 matched; 3,679 stool; 3,304 adults with valid identifiers; 3,061 depth-qualified; 2,719 unique participants. Country-proportional fixed-seed sampling selected 600 adults, independently of plant response and microbial outcomes.

There were 571 US participants (95.2%). Other countries were too small for supported country-specific inference. The main analysis includes 564 people with validated plant responses and known country; 34 plant responses and two country responses are missing in the 600-person cohort. Main exposure counts are 37, 129, 188, 113, and 97 for “Less than 5”, “6 to 10”, “11 to 20”, “21 to 30”, and “More than 30”, respectively.

The exposure is TYPES_OF_PLANTS, not PLANT_PER. Exact labels are retained without invented midpoints. A numeric “28” response in the source is unvalidated. Downloaded historical documentation did not establish the exact survey wording or recall interval; the analysis therefore refers to reported plant-type categories, not a verified weekly count. No undocumented recoding of “Less than 5” to “5 or fewer” was made.

## Calculations
All 9,089 features nonzero in the selected cohort were retained. Counts were divided by each sample's total; no new sequencing processing, rarefaction, or prevalence selection was performed.

Bray–Curtis distances had 259 materially negative eigenvalues (minimum -0.3808589145). Lingoes correction added 2c to off-diagonal squared distances, with c=0.3808589145 and zero diagonal. All 598 positive corrected coordinate dimensions above numerical tolerance were retained. Reconstructed distances agreed within 1.51e-14. A single corrected geometry was used across every model, subgroup, and dispersion check. Reported R-squared values describe this corrected distance geometry, not percentages of biological variation in raw counts.

Nested multivariate least-squares models tested the categorical plant term. Incremental R-squared is added sum of squares divided by total centered inertia; partial R-squared divides by reduced-model residual inertia. Pseudo-F uses added and residual degrees of freedom. There were 999 fixed-seed Freedman–Lane residual permutations, restricted within country or state for geography-adjusted tests. P-values use (exceedances+1)/1,000 and have finite Monte Carlo uncertainty and resolution 0.001. Tests assume exchangeable residuals within the permitted strata.

Only two axes appear in the ordination plot (4.40% and 2.47% of corrected inertia); no inferential calculation used this display truncation. Pre-estimation selection, support, geometry, and model rules are in analysis_rules.md.

## Results
| Plant-term comparison | n | Incremental R² (%) | Pseudo-F | Permutation p | Holm p, sensitivity family |
|---|---:|---:|---:|---:|---:|
| Main, unadjusted | 564 | 0.815 | 1.148 | .002 | — |
| Main, country-adjusted (primary) | 564 | 0.804 | 1.134 | .004 | — |
| Complete cases, unadjusted | 479 | 0.937 | 1.121 | .013 | .065 |
| Complete cases, country-adjusted | 479 | 0.916 | 1.097 | .029 | .087 |
| Complete cases, fully adjusted | 479 | 0.917 | 1.104 | .020 | .080 |
| US only | 540 | 0.833 | 1.124 | .009 | .054 |
| Eight US states, unadjusted | 300 | 1.450 | 1.085 | .039 | .087 |
| Same eight states, state-adjusted | 300 | 1.435 | 1.075 | .062 | .087 |

The primary test has 4 and 549 degrees of freedom; partial R² is 0.820%. All other degrees of freedom and full precision estimates are in model_results.csv.

**Geography.** On identical participants, country adjustment reduces incremental R² from 0.815% to 0.804%, providing little evidence that broad country differences alone explain the association in this US-dominated cohort. Only the US meets the prespecified subgroup support rules. Eight states (CA, CO, IL, MA, NY, TX, VA, WA) support a 300-person regional subset. Within this identical subset, state adjustment changes R² little, while the test is less conclusive (p=.062). Sparse non-US data prevent a reliable test of geographic consistency or plant-by-country interaction.

**Questionnaire information.** Among 600 participants, plant types are missing/unvalidated for 34 (5.7%), sex for 51 (8.5%), BMI for 56 (9.3%), antibiotics for seven (1.2%), state for ten (1.7%), and country for two (0.3%). Complete-case adjustment for country, age, sex, BMI, and antibiotic recency retains 479/564 participants, losing 85 (15.1%). Comparing country-adjusted and fully adjusted models on those SAME 479 participants changes R² from 0.916% to 0.917%. Thus measured covariate adjustment has little effect within complete cases. The larger R² than in the broad cohort must not be called a stronger biological effect: subset composition and the sample-size dependence of unadjusted R² both change.

Plant nonresponse is geographically uneven: 31/571 US participants versus 3/5 UK participants lack validated responses. The UK denominator is too small for stable inference. Among 598 country-known participants, respondent versus nonrespondent composition tests explain 0.140% unadjusted (p=.994) and 0.147% after country adjustment (p=.948; both Holm p=1). This is absence of detected difference, not evidence of equivalence or missing-at-random. Unobserved diet responses cannot be recovered from these diagnostics. Those excluded from complete-case adjustment have mean age 48.31 versus 48.67 years among complete cases, and median sequencing depth 20,079 versus 16,841.

**Dispersion.** Bias-adjusted mean distance to the plant-category centroid decreases from 0.841 in “Less than 5” to 0.808 in “More than 30”. The scalar centroid-distance permutation diagnostic gives F(4,559)=2.399, p=.046. It is computed using all corrected coordinates. This flags possible unequal within-group dispersion; a significant multivariate association cannot be attributed exclusively to centroid shifts, especially with unequal group sizes. The diagnostic's own permutation assumptions and sample-centroid estimation also limit interpretation.

## Interpretation and limits
The evidence supports a small association in this selected historical cohort, rather than a large separation of communities. Country adjustment has little numerical influence, but country imbalance prevents broad geographic claims. Missing covariates reduce the usable sample substantially; complete-case effects are similar within matched samples, while multiplicity-adjusted sensitivity tests are not below .05. Differences between significant and nonsignificant p-values do not themselves demonstrate effect differences.

R² is positive even under the null: for a simple four-degree-of-freedom term at n=564, df/(n-1) is about 0.71%, illustrating why the observed 0.82% should not be oversold. Lingoes correction is substantial and defines the reported metric. Effect-size confidence intervals were not estimated; permutation p-values characterize a null comparison, not precision or geographic transportability.

Additional limitations include self-reported diet, uncertain historical survey interval, nonrandom volunteer recruitment, residual diet/health/lifestyle and technical confounding, processed 100-nt OTU-era data, depth variation, conservative participant deduplication, the fixed 600-person cap, and lack of country interaction support. No claim is made about specific taxa, microbial function, alpha diversity, dietary benefit, or causation.

## Reproducibility and files
The provided bundle preserves all original downloaded bytes with pinned URLs and SHA-256 checksums, the executable Python workflow, pre-estimation rules, source-field dictionary, cohort and feature IDs, every model result, missingness/support tables, geometry diagnostics, and PNG/PDF figures. The script was executed in a fresh local Notebook namespace from the saved inputs. Cohort IDs, feature IDs, input hashes, full corrected geometry, and all model results matched (rtol=1e-10, atol=1e-12). Checks also covered a univariate regression identity, fixed-seed permutations, restricted permutations, and orthogonal invariance. Both exported PNG figures were visually inspected.

Figure 1: ordination of all 564 main-analysis participants; colors and marker shapes identify reported categories. Extensive overlap is visible; the display accounts for only 6.87% of corrected inertia. Figure 2: point estimates of added plant-term R² (no confidence intervals) and questionnaire missing counts. Different subsets should not be compared as if they were identical cohorts.

See README.md inside the bundle for local rerun instructions. All computation was local; no extra plugins or remote scientific services were used.
