Spatial mark-resight (SMR) and generalized spatial mark-resight (gSMR)

• Few marked animals (<= 5): posterior-mean N/density biased upward by ~15% (gate FAIL, section 5) though coverage is nominal; ~4-12% of fast-setting fits do not reach R-hat < 1.05. Telemetry on all 5 marked animals reduces the bias to +10.8% and gives 100% convergence, but still narrowly fails the gate (section 6). Mark more animals (section 7); run longer chains; report the interval rather than the point estimate.
• Conventional SMR after spatially concentrated marking is badly biased (-31% N, coverage 0.10; section 3). Supply the marking captures (gSMR) whenever marking happened at traps inside the study area.
• Upward small-sample bias of +4-7% in N/density at realistic designs (posterior mean of a skewed posterior), inside the gate.
• secr cross-check for gSMR: secr's joint marking + sighting fit was biased low (-26% N, coverage 0.60) on our gSMR simulations, while the Nimble gSMR was unbiased; the cause was not resolved (section 8). For gSMR, use secr only as a reference for sigma and detection rates; N was cross-checked against secr SCR on the marking captures alone.
• Status mis-scoring (marked animal recorded as unmarked), mark loss, individual heterogeneity in sighting rate (e.g. collar effects), non-independent photos, and open populations are not modelled. The posterior predictive "sightings per marked animal" check flags strong heterogeneity.
• The Bernoulli resight model uses the Poisson approximation of Chandler & Royle (2013) for pooled unmarked and unidentified counts; only the Poisson model was validated at nsim = 100 here.
• Telemetry fixes are assumed independent draws from the bivariate-normal space use around the activity centre; autocorrelated GPS data must be thinned.
• Unmarked-only data (no marked animals) are rejected: density from unmarked counts alone is weakly identified (Chandler & Royle 2013).

All recovery runs: bin/Rscript core/run.R recover scr-smr --config modules/scr-smr/validation/<cfg>.yaml --nsim 100 --cores 16 on njobvu (SLURM, 16 cores) with the module fast_settings (Nimble, custom joint s/z sampler + adaptive RW and RW_block on top-level parameters; 3 chains x 9,000 iterations, 3,000 burn-in, thin 2) unless stated. Raw results: results/scr-smr/recover_<label>/ (summary CSV, per-replicate CSV, HTML report).

Gate (core/R/recovery.R::recovery_gate, thresholds NOT changed): |bias| <= max(10% of truth, 3 MC SE) (truth 0: 0.1 x empirical SD); 95% interval coverage >= 0.95 - 3 MC SE (here 0.88); max R-hat < 1.05 in >= 90% of all replicates attempted. "conv" = replicates with max R-hat < 1.05 / 100.

Default design (module defaults, model: smr): 49 cameras (7 x 7 grid, 1,500 m = 1.5 sigma spacing), 10 weekly occasions, 10% of cameras fail part-way, half on trails; state space = cameras + 4,000 m buffer (289 km2, 500 m pixels); density 0.25 / km2 (~73 animals), 20 marked animals that are a random sample of the population (e.g. collared earlier), Poisson resighting lambda0 = 0.30 per week off-trail, on-trail log effect 0.7, sigma = 1,000 m, P(mark readable) delta = 0.8 (the rest recorded as "marked, unidentified"), canopy log-density effect 0.5 per SD.

Timing (selftest, 4 replicates): ~120-300 s per replicate including Nimble compile; a 100-replicate run takes 25-35 min on 16 cores. Median per-replicate time 198 s (default), 229 s (gSMR), 233 s (5 marked; one replicate needed the automatic M refit and took 88 min).

The Nimble warning "No samplers assigned for 1 node" in SMR runs is expected: the marking-phase parameter pm0 is unused (and its sampler removed) when marking is not modelled.

Gate: all 9 estimands PASS; conv 98/100; 0 failures. The +5% upward bias in N/density is the usual small-sample bias of the posterior mean of a right-skewed posterior (the scr module shows the same +4.6%).

Same population and cameras, but the marked animals are those caught in 5 nights at a 5 x 5 box-trap grid (1,500 m spacing) in the centre of the camera grid (pm0 = 0.3), so marked animals are concentrated in the centre (mean ~22 marked). Fitted with model: gsmr (marking captures modelled jointly).

Gate: all 10 PASS; conv 100/100. (resight_rate coverage 0.89 is just above the 0.885 bound.)

neg_ignore_marking.yaml: the same gSMR data-generating design as section 2 (marking concentrated at the central box traps), fitted with conventional SMR (settings: model: smr), i.e. marked animals treated as a random sample.

The marked animals live where the cameras see them best, so SMR thinks a larger share of the population is marked and underestimates N by a third, with confidently wrong intervals (coverage 10%). Section 2 shows gSMR on the same design removes the bias (+4.5%, coverage 0.96). This reproduces the direction of Whittington et al. (2018): conventional SMR 7.4 vs gSMR 12.4 grizzlies / 1000 km2 when marking was concentrated. The gate can fail.

Default SMR design with density_beta_canopy = 0 and detection_beta_on_trail = 0.

Both false-positive rates (95% interval excludes 0) are at or below the nominal 5%. All 9 estimands PASS; conv 100/100.

Density 0.14 / km2 (~41 animals), only 5 marked (random sample), otherwise default.

conv 96/100 (one replicate: posterior of N 111-957, R-hat 1.48, after the automatic M refit). Coverage stays nominal (0.95) but the posterior mean of N is 15% high (median error +4 animals): with 5 marked animals lambda0 and sigma rest on 5 individuals, the posterior of N is long right-tailed, and the mean is pulled up. Intervals are wide (mean 95% width 49 animals for N = 41). Treat point estimates from <= 5 marked animals as rough and report the interval. See section 6 for the remedy with telemetry and section 7 for how the bias shrinks with more marked animals.

Same design as section 5 (density 0.14 / km2, ~41 animals, 5 randomly marked), but all 5 marked animals carry GPS collars contributing 30 independent fixes each (bivariate normal around the activity centre with the same sigma; Sollmann et al. 2013), fitted jointly.

conv 100/100 (vs 96/100 without telemetry). Telemetry fixes sigma almost exactly (RMSE 33 m vs 97 m without telemetry), which removes most of the long right tail of N: RMSE of N falls from 13.3 to 9.7 animals, the 95% interval narrows from 49 to 41 animals, the median error falls from +4.2 to +3.0 animals, and the relative bias of the posterior mean falls from +15.1% to +10.8%. This is still just outside the gate (|bias| 4.2 animals vs the allowed max(10% of truth = 4.1, 3 MC SE = 2.6)), so this design stays a documented limit: telemetry helps substantially but does not fully fix the point estimate with only 5 marked animals. The remaining bias comes from the sighting rate lambda0 and the unmarked counts, which telemetry does not inform. Coverage (0.99) is conservative.

bin/Rscript core/run.R power scr-smr --config modules/scr-smr/validation/power_n_marked.yaml --vary n_marked=5,10,20,40 --nsim 50 --cores 16 --out results/scr-smr/power_n_marked (default SMR design, density 0.25 / km2, ~73 animals). Rows with R-hat >= 1.05 excluded (44/50 converged at 5 and 10 marked; 50/50 at 20 and 40).

Precision of N improves steeply with the number of marked animals (interval width 80 -> 30 animals from 5 to 40 marked); marking 20+ animals (about a quarter of the population) gives intervals under +-30%. With 5 marked animals coverage of N drops to 0.86 and 12% of fits do not converge in the fast settings, so longer runs are needed. Power for a 0.5-per-SD habitat effect on density reaches 0.8 only at about 40 marked animals.

SMR (dev/scr-smr/crosscheck.R smr 48 16; 48 default-design datasets, each fitted by the Nimble engine and by secr 5.5.1 maximum pseudo-likelihood mark-resight, Efford & Hunter 2018; sighting-only occasions, knownmarks, Poisson counts, pID, c-hat by 50 simulations). Results in results/scr-smr/crosscheck/crosscheck_smr*.csv.

The two implementations agree on N, density, marked fraction and sigma (mean ratio 0.97-1.02, correlation 0.81-0.87). secr's intervals for N are wider (60 vs 41 animals) because its pseudo-likelihood treats the unmarked counts as independent Poisson counts with an overdispersion inflation; secr's camera covariate is on the logit scale of g0 (not comparable to the Bayesian log scale), and its density-covariate coefficient is attenuated (-25%), as expected when only marked animals and the total unmarked count inform the density surface.

gSMR: 48 gSMR datasets (default population, marking at the central 5 x 5 box-trap grid; dev/scr-smr/crosscheck.R gsmr 48 16, then dev/scr-smr/t_secr_gsmr2.R). Results: results/scr-smr/crosscheck/crosscheck_gsmr*.csv.

(a) secr joint marking + sighting fit (sighting-only occasions after proximity marking occasions, markocc, knownmarks, g0 ~ ts + camera covariates, pID). This fit was biased low against the truth on these data, while the Nimble gSMR was not:

The two implementations agree on the detection parameters (sigma, home range, marking and resighting rates: mean ratio 0.97-1.08, correlation 0.89-0.91) but not on N. Diagnosis on 12 datasets (logs/scr-smr_secr_gsmr_diag*.log): secr fitted to the marking captures alone gives N/N_true ~ 0.97 (median); adding the unmarked counts Tu gives 0.85 and adding Tu + Tm gives 0.69, with or without the density covariate. So the downward bias enters through secr's pseudo-likelihood for the pooled sighting counts when marking is spatially concentrated (or through how we pass those data to secr; we did not find an error). We did not resolve which; secr's joint gSMR fit is therefore not used as a reference, and in a gSMR fit the module's engine-comparison figure flags this.

(b) Independent check of N: secr conventional SCR on the marking captures only (box-trap data, no camera data; a different likelihood that is unbiased by construction but less precise), same 48 datasets:

Both are consistent with the truth (secr's mean is pulled up by a few datasets with < 12 marked animals and very wide intervals); the median ratio Nimble / secr-marking-only is 0.93 and the correlation is 0.42 (low because the marking-only estimate is so noisy). Using the camera data in gSMR cuts the interval width about three-fold without introducing bias.

Literature / code review. Checked R/nimble_engine.R line by line against Chandler & Royle 2013 (identified sightings Pois(K delta lam_ij); unmarked counts pooled Pois(K sum_i z_i (1 - mk_i) lam_ij), exact by Poisson superposition), Jimenez et al. 2019 (marked-unidentified counts with expectation (1 - delta) times the summed marked rates), Sollmann et al. 2013 (telemetry N(s_i, sigma^2 I), same sigma; sufficient-statistic likelihood correct) and Whittington et al. 2018 (gSMR: every augmented row has psi and a binomial proximity marking likelihood, (1 - p)^K for never-caught rows). SMR fixes z = 1 for the m marked rows (N = m + Bin(M - m, psi)). The joint s/z sampler's z flip uses the correct prior ratio for the uniform pseudo-prior on s when z = 0. Density covariates are standardised over the mask, detection covariates over cameras. simulate() and fit() share no code apart from the data structure.

Independent planted truth (own simulator dev/scr-smr/verify/vsim.R, no module code; continuous-space rejection sampling of activity centres on a 13 x 11 km state space, a continuous elevation surface, 48 jittered cameras with random 15% outages, K = 8, a continuous distance-to-road camera covariate, D = 0.6 / km2 (~86 animals), sigma = 700 m, lambda0 = 0.5, delta = 0.65, telemetry on 5 animals; gSMR uses an off-centre 4 x 4 box-trap grid at 900 m, 4 nights, pm0 = 0.25, ~9.5 marked animals). The module's fit() uses fast_settings and the core summarise_recovery / recovery_gate. Driver: dev/scr-smr/verify/vrun.R. Results: results/scr-smr/verify/indep_*.

The builder's default recovery was rerun (results/scr-smr/verify/rerun_default) and reproduced the reported numbers (N +5.1%, coverage 0.98, all PASS). The other builder summaries (gSMR, negative control, null, hard designs) were checked against their CSVs and match VALIDATION.md.

Two more runs with the same simulator were launched to test whether the pm0 under-coverage is real: a second gSMR batch with disjoint seeds (indep_gsmr2) and the Bernoulli resight model, lambda0 = p0 = 0.2 (indep_bern). They had not finished when this section was written; read results/scr-smr/verify/indep_gsmr2/summary.csv and indep_bern/summary.csv (logs logs/scr-smr_verify_{gsmr2,bern}.log).

Usability. Messy example variants (dev/scr-smr/verify/messy/a-f) had an NA covariate, a missing coordinate, an unknown status, an empty animal ID, wrong column names, misspelled camera and trap IDs, and IDs not in the marked list. Fixed: check_data() crashed ("missing value where TRUE/FALSE needed") when a camera had a missing coordinate. The camera-outside-mask test now skips cameras without coordinates. read_data() now also gives a clear "file not found" message and no longer emits a spurious colClasses warning when the usage column is misnamed. All variants now give clear, actionable messages. The example report's interpretation sentences were checked against the estimates table (density, N, marked fraction, sigma, 2,471 m radius, rates, rate ratios, and the 10th and 90th percentile densities, recomputed independently): all correct, with associative wording and detection kept separate from density. All required scr-family figures are present, and the PNGs were inspected with no defects found. The example-report HTML still embeds the engine-comparison figure drawn before the builder's last tick-label fix (builder's own note). Refresh it with bin/Rscript core/run.R fit scr-smr --config modules/scr-smr/example/config.yaml --out results/scr-smr/example.