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      lex: "1. Different methodological character. Soroye et al. 2020 fit one GLMM at the CEA grid and reported a continental-scale extirpation summary. This Study does NOT refit the GLMM \342\200\224 it uses the substrate-fit GLMMs from the two upstream replications and asks how their per-species PROJECTION rankings concord across substrates. The substrate-coupling diagnostic is downstream of Soroye\'s mechanism, not a direct replication of it.\n\n2. Variant (c) tested as approximation. The most rigorous test of \"shared reference standardisation alone fixes substrate coupling\" is to refit the GLMM with shared (\316\274, \317\203) and re-project. Variant (c) here uses substrate-local \316\262 with shared-\317\203 predictors at projection time \342\200\224 mathematically equivalent to a constant scaling of \316\267, refuting the hypothesis as a standalone fix BUT not the same as testing a full refit. Documented in the Outcome\'s Limitations as a deferred follow-up.\n\n3. Substrate-invariant physical metrics added. Variants (d) and (d2) compute per-species mean future TEI and fraction TEI_future>0.5 \342\200\224 physical-unit metrics that bypass the GLMM entirely. These are NOT in Soroye\'s original analysis; they are introduced here as a substrate-invariant cross-check."
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      lex: "METHOD\n\nThe diagnostic reads input artefacts from two upstream substrate replications (the canonical nside=64 sibling and the nside=128 substrate-extension sibling) and computes five candidate per-species rankings at each substrate, plus a mechanistic per-species \316\267 decomposition.\n\nInputs (per substrate; symlinked from sibling repos in development, fetched from Zenodo in v0.2.0):\n  - GLMM coefficient posterior (variational-Bayes summary): healpix_port/outputs_iberia/posterior_vb_summary.csv\n  - Species random intercepts (full NUTS posterior): results/posterior_bambi_healpix.nc\n  - Substrate-local predictor scaling (\316\274, \317\203): healpix_port/outputs_iberia/dataGLMM_extinction.parquet\n  - Per-species niche limits T_min_spp, T_max_spp, P_min_spp, P_max_spp: healpix_port/outputs_iberia/climate_tei_pei_healpix.nc\n  - Future-period predictors (per species per cell): climate_tei_pei_future_<horizon>_healpix.nc\n  - Per-species observation mask: presence_absence_healpix.nc\n  - Per-cell sampling effort: sampling_continent_healpix.nc\n\nFive projection variants (notebooks/02_decompose.py and 03_variants.py):\n  (a) Full GLMM \316\267, within-substrate predictor standardisation.\n  (b) Main-effects-only \316\267, within-substrate standardisation (drop the four interaction terms at projection only; keep them in the fit).\n  (c) Full GLMM \316\267, shared CEA reference standardisation (substrate-fit \316\262 + shared (\316\274, \317\203) computed from the original Soroye CEA pool; tested as a refit-equivalent approximation).\n  (d) Mean future TEI per species (substrate-invariant physical metric, no GLMM).\n  (d2) Fraction of cells with future TEI > 0.5 per species (substrate-invariant threshold metric).\n\nFor each variant, compute per-species community-mean \316\267 (or fraction) across the species\' currently-occupied + active cells, at both substrates and both horizons. Apply four n_cells filters (\342\211\2451, \342\211\2455, \342\211\24510, \342\211\24520). Compute Spearman rank correlation between nside=64 and nside=128 rankings under each (variant, filter) combination.\n\nMechanistic decomposition (scripts/compare_substrates.py): for a diagnostic set of 12 species spanning the n_cells distribution, decompose per-species \316\267 into its 10 GLMM-term contributions plus the species random intercept at each substrate. Identify which term(s) are responsible for substrate-coupling.\n\nCode: scripts/compare_substrates.py, scripts/compare_variants.py, scripts/plot_variant_concordance.py. Notebooks: 01_inputs_fetch.py, 02_decompose.py, 03_variants.py, 04_figures.py."
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