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      lex: "This methodological diagnostic compares two single-substrate replications of Soroye et al. (2020) for Iberian Bombus under DestinE Climate DT SSP3-7.0 \342\200\224 at HEALPix nside=64 (~92 km, weatherxbiodiversity-projection) and nside=128 (~46 km, weatherxbiodiversity-projection-nside128). Both upstream Outcomes confirm Soroye\'s TEI mechanism is substrate-robust at fit time (sc_TEI_delta within \302\26130% across three substrates including the original CEA grid).\n\nHeadline finding: per-species ranking under SSP3-7.0 IS grid-coupled at the projection step. The same physical climate signal at the same Iberian location produces per-species \316\267 swings of 1\342\200\2239 logits between nside=64 and nside=128 for species observed in fewer than ~10 historical cells.\n\nThe substrate-coupling is not caused by per-species random-effect refit (substrate-stable, \316\224RE \342\211\244 0.6 logits across all species), nor by per-species niche-limit refit (modest, \316\224T_range = 0\342\200\2233\302\260C; species with identical T_range still show 8.8-logit projection swings). It is caused by two mechanisms acting together:\n\n(i) Per-species sample size at projection time. Below ~10 occupied + active cells per substrate, per-cell extrapolation noise dominates the species-mean \316\267 regardless of which projection variant is used.\n\n(ii) The GLMM interaction term sc_TEI_delta:sc_PEI_delta \342\200\224 the largest single contributor to projection \316\267 at SSP3-7.0 \342\200\224 compounds substrate-specific predictor standardisation quadratically when future predictors extrapolate 2\342\200\2234\317\203 outside the training distribution. The same physical climate signal z-scores to opposite tails of the standardised distribution under each substrate\'s local (\316\274, \317\203); the interaction term scales as the product, amplifying the divergence.\n\nThese two mechanisms are diagnosable, mechanistic, and fixable. Three principled fixes are validated empirically:\n\n(a) Per-species cell-count filter. Restricting reporting to species with at least 10 occupied + active cells per substrate brings cross-substrate Spearman \317\201 from +0.27 (full GLMM, all species) to +0.59 at the same variant, +0.97 at variant (b) below.\n\n(b) Drop the GLMM interaction terms at projection time only. Keep them in the fit (they are part of Soroye\'s specification) but do NOT use them to extrapolate. At n\342\211\24510 + main-effects-only \316\267, cross-substrate Spearman \317\201 = +0.97 (mid-term horizon) \342\200\224 near-perfect agreement.\n\n(c) Cross-check against substrate-invariant physical metrics. Mean future TEI per species and fraction of cells where future TEI exceeds 0.5 are physically grounded and substrate-invariant in physical units; \317\201 \342\211\245 +0.66 at all sample sizes (better than any GLMM-based variant for low-N species).\n\nRefuted hypothesis: re-standardising future predictors against a shared CEA reference (without refitting \316\262) does NOT decouple the substrate. The GLMM \316\262 coefficients are fit against substrate-local \317\203; just rescaling the predictors at projection time is mathematically equivalent to a constant scale shift and does not change the ranking. Properly testing this fix requires refitting the GLMM with shared standardisation (out of scope here).\n\nThe mechanism IS substrate-robust at fit time. Its per-species PROJECTION at the species-cell level is qualified \342\200\224 reliable above the n_cells filter, not below it. Both upstream Outcomes report rankings filtered per the recommended protocol from this chain."
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      lex: "Five projection variants tested at both horizons (2020\342\200\2232029 + 2030\342\200\2232039) and four per-species n_cells filters (\342\211\2451, \342\211\2455, \342\211\24510, \342\211\24520) on 31 Iberian Bombus species shared between the two upstream substrate replications.\n\nVariants:\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); refuted as a standalone fix).\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\nCross-substrate Spearman \317\201 between nside=64 and nside=128 rankings, mid-term horizon 2030\342\200\2232039:\n\n                                  n\342\211\2451  n\342\211\2455  n\342\211\24510  n\342\211\24520\n                                  (31) (27) (13)  (10)\n  (a) Full GLMM \316\267                 +0.27 +0.51 +0.59 +0.77\n  (b) Main-effects only \316\267         +0.40 +0.52 +0.97 +0.98\n  (c) Shared CEA reference \316\267      +0.27 +0.49 +0.52 +0.55\n  (d) Mean future TEI             +0.66 +0.69 +0.90 +0.82\n  (d2) Frac TEI_future>0.5        +0.66 +0.71 +0.88 +0.83\n\nHeadline: variant (b) at n\342\211\24510 lifts \317\201 from +0.59 (variant a same filter) to +0.97 \342\200\224 substrate-stable. Same qualitative pattern at the near-term horizon.\n\nMechanistic decomposition. Per-species \316\267 at the SSP3-7.0 mid-term horizon was decomposed into its 10 GLMM-term contributions plus the species random intercept, at both substrates. For the four most-divergent species (norvegicus, mendax, jonellus, sylvestris):\n\n  - sc_TEI_delta:sc_PEI_delta term contributions differ by 1.0\342\200\2236.3 logits between substrates (largest single driver in every case).\n  - sc_TEI_delta term contributions differ by 0.5\342\200\2232.5 logits (next largest).\n  - All other terms (Intercept, sc_sampling, main TEI/PEI, all other interactions, species RE) differ by \342\211\244 0.6 logits each (substrate-stable).\n\nRefuted hypotheses verified empirically:\n  - Random-intercept refit. \316\224RE across all 12 species in the diagnostic set \342\211\244 0.6 logits \342\200\224 substrate-stable.\n  - Niche-limit refit. \316\224T_range across the 12 species = 0.0\342\200\2232.9\302\260C; norvegicus has \316\224T_range = +0.01\302\260C yet shows 8.8-logit \316\224\316\267 \342\200\224 refuted as the dominant cause.\n  - Shared-reference standardisation alone. Variant (c) Spearman \317\201 stays \342\211\210 variant (a) at every cell-count filter.\n\nFiles: results/SUBSTRATE_SENSITIVITY_FINDINGS.md, results/variant_comparison_2030_2039.{csv,json}, results/variant_comparison_2020_2029.{csv,json}, results/substrate_comparison_decomposition_2030_2039.txt, figures/variant_concordance_{2020_2029,2030_2039}.png, figures/variant_pairs_{2020_2029,2030_2039}.png.\n\nRepository: https://github.com/annefou/weatherxbiodiversity-substrate-sensitivity"
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