[hyperpolymath]

ALDEx2 (v0.2.0)

This adds two-group ALDEx2 (aldex2) as native Julia, plus the RCall reference extension and an R oracle. The method is defined by docs/ALDEx2-SPEC.md.

What changed and why

The first native version, built from Fernandes et al. 2013/2014, disagreed with Bioconductor ALDEx2 1.42.0 by more than Monte-Carlo noise. On gut, the Welch p differed by 0.24 against R-vs-R noise of 0.066. On soil, the effect differed by 0.18 against noise of 0.03.

The causes were two definitions the papers leave open:

1. Expected p and expected BH. These are consistent-sign posterior values. Each direction's one-sided p is doubled and capped at 1, then averaged over instances, and the smaller of the two directions is reported. BH is applied per instance and per direction.
2. Effect size. The between-group and within-group pairs are drawn independently, with m = min(n1·mc, n2·mc).

Provenance (clean-room)

• To diagnose the gap, the coding agent read the GPL-3 R source of aldex.ttest, t.fast, wilcox.fast and aldex.effect. No code was copied.
• The owner then ruled for a separate re-derivation:
  • The spec was committed alone, as 87a6316, before any implementation.
  • A separate agent wrote src/Methods/ALDEx2.jl from the spec. It had no access to the R library, could not deparse R functions, and could not search the web for the source. It confirmed it complied.
  • Its implementation commit is c163e5f.
• This is also recorded in the spec's Provenance section.

Evidence

• Pkg.test(): 55/55 pass. This covers P1/P5, P3 (CLR centring) and P6 (feature-relabelling equivariance), each with a planted mutant that the property kills.
• Oracle at MC 512: 13/13 pass. Log: developer/logs/compositionalda-oracle-20261002d.log.

dataset	effect native-vs-R (R-vs-R)	Welch p	Wilcoxon p
mock	0.099 (0.125)	0.022 (0.028)	0.050 (0.040)
gut	0.032 (0.033)	0.061 (0.066)	0.056 (0.069)
soil	0.030 (0.030)	0.051 (0.043)	0.038 (0.039)

On mock, the q<0.05 call sets are identical: mock1–5 on both sides.

Not proved

ALDEx2's calibration is tested against the reference, not proved. P3 and P6 are property-tested, not Agda-proved. See proofs/PROOF-STATUS.md.

Deliberate departure from the reference

The effect-size index permutations are drawn once and shared across features, where the reference draws them per feature. Each feature's marginal distribution is unchanged. Only the cross-feature correlation differs, and sharing is what makes P6 hold exactly.

Tested with Julia 1.12 (local) and the CI matrix 1.10/1.12, R 4.5.0, Bioconductor 3.22, and ALDEx2 1.42.0.

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https://claude.ai/code/session_019Y6e175rh1LbrsEhQvCrJ1

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⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Advanced

Run ID: 2915bd82-7916-4b1d-83cf-386dc9fbc46e

📥 Commits

Reviewing files that changed from the base of the PR and between 76c1970 and 61f7c7b.

⛔ Files ignored due to path filters (4)

• test/oracle/fixtures/gut_counts.tsv is excluded by !**/*.tsv
• test/oracle/fixtures/gut_groups.tsv is excluded by !**/*.tsv
• test/oracle/fixtures/soil_counts.tsv is excluded by !**/*.tsv
• test/oracle/fixtures/soil_groups.tsv is excluded by !**/*.tsv

📒 Files selected for processing (22)

• .github/workflows/ci.yml
• .gitignore
• Project.toml
• README.md
• docs/ALDEx2-SPEC.md
• docs/DATASETS.md
• docs/R-SUNSET.md
• ext/CompositionalDARCallExt.jl
• src/CompositionalDA.jl
• src/Methods/ALDEx2.jl
• test/mutants.jl
• test/oracle/Project.toml
• test/oracle/datasets.jl
• test/oracle/fixtures/gut_counts.tsv.license
• test/oracle/fixtures/gut_groups.tsv.license
• test/oracle/fixtures/soil_counts.tsv.license
• test/oracle/fixtures/soil_groups.tsv.license
• test/oracle/make_fixtures.jl
• test/oracle/runoracle.jl
• test/properties.jl
• test/property_aldex2.jl
• test/runtests.jl

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