1.1.1 · Current state —
The first five methods keep the same site-as-unit mean and disagree only on how sure we may claim to be. The sixth — Bayes hierarchical — is the per-stratum face of the change-of-support roll-up (§2.4) and is different in kind: it borrows the other strata's data (partial pooling), so it can shift the mean too (shrinkage), not just the interval. In the grey line under each plot, every ± is that method's 95% half-width (so ± and the bracket always agree); (SE …) marks the standard error where one exists — the 95% interval is t×SE (e.g. t=3.18 at n=4), never ±SE.
- Estimate — the method's central value: the site-as-unit mean for naive/IM/boot/wild, the posterior mean for Bayes, the partial-pooling θ for hier.
- SE (standard error) — how precisely the estimate is determined. Analytic for naive/IM; for the bootstraps it is the SD of the resampled means; for the Bayesian methods the SD of the posterior draws.
- 95% interval — the range that reflects the statistical uncertainty around the estimate. For t-based methods it is Estimate ± t*×SE, where t* is the 97.5% quantile of the t-distribution at n−1 degrees of freedom (n=4 sites → df 3 → t*=3.182; n=3 → 4.303; naive uses ≈2 because it — wrongly — counts hundreds of quadrats). Bootstrap intervals are percentile-based and Bayesian intervals are credible ranges — both can sit asymmetric around the estimate.
- The ± shown is always the half-width of the 95% interval, so ± and [interval] always agree.
- Shrub / Tree — line-intercept canopy: overhead woody canopy from the .6 line-intercept method (canopy distance ÷ belt length). Shrub COMBINES the report's Preferred Browse + Other Shrub classes; Tree = tree species only.
- Shrub / Tree — quadrat cover: the same tree/shrub split measured as Daubenmire quadrat cover (ground-level presence, not overhead canopy).
- .7 herbaceous groups: the report's four DWR-Lifeform classes — Perennial Grass, Annual Grass, Perennial Forb, Annual & Biennial Forb (combined, per the report). Nested frequency = per-quadrat MAX converted score summed over 100 quadrats (0–500 index, DWR's stable trend metric); quadrat cover = Daubenmire mean.
- Ground classes: Bare Ground, Litter, Vegetation (surface under any live plant). Rock, Pavement and Cryptogams excluded by decision; Pellet Group data excluded.
1.1.2 · Trajectories over time —
One chart per report variable (same order as the state panel above) — each chart shows ONLY its own variable. All sites (default): every site’s own trajectory, coloured by its ESD stratum, with its site code at the line’s end; dashed = temporally gated (the line simply stops at its last read); the soft colour fill is each n≥2 stratum’s between-site range (min–max of the sites read that year) — visible spread, not a confidence interval. All strata — means: one line per stratum = the site-as-unit mean per year over whichever member sites were read that year (solid n≥2, dashed single-site). A plant name inside a line label there is part of the STRATUM’s name — NRCS names an ecological site by its soil + characteristic plant (e.g. “High Mountain Loam (Aspen)”) — never a species data series. Stratum chips zoom to that stratum’s sites alone. One chart per variable no matter how many strata or sites the AOI holds; state estimates never pool these years (spec §7); trajectory is a separate product.
2.1 · Dominant species — the 2-D matrix (species × sites)
Every species whose quadrat cover reaches ≥5% at any site (top 20 by peak cover), shown across ALL sites at once — no per-species plots. Each cell carries BOTH report metrics: the number + green fill = quadrat cover % (how MUCH), and the thin blue bar along the cell bottom = nested frequency, its width spanning 0–500 (how WIDESPREAD — DWR's stable trend metric). Hover any cell for both exact values + the site's stratum. The right-hand column is occupancy — sites present / n (computed on quadrat cover). A · cell is a true absence (structural zero — cover 0 AND frequency 0), not missing data; covers under 10% keep one decimal and trace cover shows as <0.1, so a displayed value can never round down to a fake absence; a "0" with a blue bar = zero quadrat cover but detected in nested frequency.
2.2 · Species richness — grows with sites, pool by union
"Pool by union" answers: how do you combine site counts into an AOI count? Three candidates, only one right (example: the stratum):
- Sum () — wrong: species living at several sites are counted several times.
- Average () — wrong: it describes no ecological quantity; the AOI doesn't "have species."
- Union () — right: list every species seen anywhere, count each once. Note it exceeds even the richest single site () — sites hold different species, so combining sites reveals diversity no single site contains. That is why averaging fails: richness is non-linear in sites.
Two more properties: richness is not area-weighted (Wh doesn't apply to a count — the table reports the monitored sites' pooled inventory, full stop), and the per-stratum contrast is itself the ecology: — the diversity gap between ecosystems of the same AOI.
2.3 · Why we refuse a single unit-wide average
Each blue dot is one ESD stratum (hover: the site — or "MEAN of n sites" — then the stratum, then the value). The amber tick is the naive equal-site pooled "unit average": it describes no place on the ground (e.g. "% shrub canopy" in an AOI whose strata run % by line-intercept), and its weighting is a site-count accident, not area. This panel is the reason the study reports per-stratum first and allows one cross-strata number only via real area weights Wh (§2.4).
2.4 · Area weights (SSURGO-derived) → the AOI numbers
Sections 1–5 refuse any single AOI-wide number; real area weights are what finally permit one — this section derives the weights, then applies them. Stratum area fractions derived from the AOI’s official boundary ( km²) × NRCS SSURGO ecological sites, via a site-anchored crosswalk (DWR's legacy ESD ids no longer exist in current SSURGO — correlation drift — so each stratum inherits the ecoclasses its own sites map onto; confidence flagged per row).
Monitored + weightable strata cover of the AOI — the rest is ecological sites with no monitoring site (%) and rock/badland with no ecological site at all (%). The AOI numbers below therefore describe the monitored rangeland strata of this AOI, area-weighted — never the whole AOI.
Two weights, two jobs: Wh = stratum km² ÷ whole-AOI km² (the column above) — the stratum's share of the entire unit; used for HONESTY: it shows how small the monitored footprint is (they sum to the coverage %, not to 1). W̃h = stratum km² ÷ monitored km² — the same areas renormalized to sum to 1; used for the ARITHMETIC: the AOI table below is Σ W̃h·meanh (e.g. : / km² = Wh for the coverage story, but / km² = W̃h inside the weighted average). Using raw Wh in the sum would silently treat the unmonitored 93% of the unit as zeros.
One point estimate, two uncertainty readings. The estimate is AOI = Σ W̃h·meanh over the weightable cells (weights renormalized within their coverage); n=1 cells carry a conservative borrowed SE (largest between-site SD observed) in the post-stratified column. [case-study note: the merged Browse/Black-Sage cell contributes its own real n=2 SE; site 13A-06’s stratum is monitored but unweightable (no defensible current-SSURGO analog) — reported separately, excluded here.]
- post-stratified ± 2×SE — closed-form arithmetic on the data: Var = Σ W̃h²·SEh², ± = 2×SE — a symmetric normal-approximation band with no priors and no sharing between strata. It is not the Ibragimov–Müller method: IM — like the bootstraps and Bayes-RE — is one of the per-stratum state-panel (section 1) interval methods; all five share the same site-as-unit mean (the very means this table weights), and IM's t-multiplier lives at one stratum's n−1 df, so it cannot carry over to a mix of strata with different n. At AOI level the arithmetic settles for the cruder ±2×SE.
- Bayes hierarchical [95% CrI] — the change-of-support model (yhs ~ N(θh, ω²) · θh ~ N(μ, σ²) · half-Cauchy priors on ω, σ; deliberately no spatial field — unidentifiable at 2–7 sites per cell and it can bias the means, Hodges & Reich 2010). The AOI value Σ W̃hθh is computed on each of 4,000 exact-marginalization posterior draws; the CrI is the middle 95% of those draws (clamped at 0 for display), so it can sit asymmetric; the ± shown is the CrI's half-width — where the CrI is asymmetric, the bracket is the authoritative range. It differs from the arithmetic in three honest ways: partial pooling — single-site cells borrow strength from the other strata (the per-cell table below) instead of the ad-hoc borrowed SE; fuller uncertainty — the spreads ω and σ are themselves uncertain and that flows into the interval; meaning — "given this model, 95% probability the value lies here".
- Which to use: quote the post-stratified estimate as the point value (assumption-light, reproducible arithmetic) with the Bayes hierarchical CrI as the preferred AOI-level uncertainty. On most rows the two intervals agree — then the choice changes nothing and the agreement confirms the model is not distorting anything; where they visibly differ, the row leans on n=1 cells and the hierarchical interval is the defensible one.
The walking sentence is the physical translation of "area-weighted average": imagine one long walk through only the monitored strata, allocating your distance by their real areas — , and so on. Over that whole walk, about 1 step in (%) would have a tree crown directly overhead. The honest range % is the 95% interval (±, clamped at 0): with one or two sites in most strata the data permit anything from "almost no trees" to "1 step in " — claiming more precision would be the false-precision sin this study exists to avoid.
- Encroachment pressure: on sagebrush rangelands the defining slow transformation is pinyon–juniper (PJ) moving in — shading out sagebrush and grass, changing fire behavior, degrading habitat. Tree-LI is the direct dial for that process: exactly the quantity that climbs as PJ closes in. [case-study note, 13A: the two PJ-transitioning sites (11, 13) independently probe onto PJ ecological sites in current SSURGO — field trend and soil map agree.]
- Structure, not amount: % canopy says how much ground is shaded and sheltered — wildlife thermal/security cover, canopy-fuel presence (torching potential). It does NOT give tree biomass: the same cover could be a few big old trees or many saplings. Different question, different measurement.
- Satellite-shaped: a satellite looks straight down and estimates the fraction of a pixel covered by crowns — the vertical projection of canopy onto the ground. That is, word for word, what line-intercept measures with a tape; quadrat cover measures at ground level (what occupies a ¼-m² frame), a different geometry. For field-vs-satellite tree cover, LI is the apples-to-apples measure — the reason both woody metrics are carried.
- Scope: a weighted average over the monitored strata only — % of this AOI. Ecosystems with no monitoring sites sit outside these strata, so this is emphatically not "the AOI's tree cover." [case-study note, 13A: the La Sal high-elevation forest and canyon woodlands are among the unmonitored areas.]
Read the n=1 rows: one site cannot pin its stratum's mean when between-site spread ω is large, so the posterior honestly widens and pulls toward μ — that IS the borrowing of strength. Cells with n≥2 stay close to their observed means.
2.5 · Reading guide
- IM site-t (Ibragimov–Müller) is the few-cluster-robust reference — the "you may not claim more than this" interval.
- Cluster and wild bootstrap agree on scale; wild runs slightly tight at 3–4 clusters.
- Bayes RE = weak half-Cauchy prior on the between-site SD — engineered honesty at few sites.
- Intervals on bounded quantities are clamped at 0 for display; nested-frequency variables are on the report's 0–500 index scale, everything else is %.
- Target of every number: the monitored sites of each stratum — never the wall-to-wall landscape.