17-gps-selection-scale
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
REPORT.md
# 17 — Selection Depends on Scale (`gps-selection-scale`)
- Source: Incoprea Theory, Volume XXIX (`gps-selection-scale`)
- Claim: Measured habitat selection strength depends on the sampling interval, so studies at different intervals disagree without either being wrong.
- Prediction: Selection should weaken at longer intervals.
- Refutation: Selection invariant to interval would remove the availability definition.
## Test performed
**(1) Model-based test (evidence class: model, run now).** A correlated random walk (1-min steps, von Mises turning) was simulated with habitat preference implemented exactly as the hypothesis suggests — bias in turning angle: high directional persistence inside the preferred habitat, turn-around bias plus soft bounce at boundaries in the non-preferred habitat. Positions were sampled at fix intervals of 1/3/6/12/24 h and resource-selection ratios were estimated two ways: (i) step-paired availability (SSF-style: 50 random points on a circle of the observed step length around each previous fix) and (ii) global (landscape-wide) availability. Two landscapes: a coarse half-plane (preferred = west half) and a fine-grained 100 m checkerboard (50% preferred). Script: [code/01_simulate_intervals.py](code/01_simulate_intervals.py). **(2) Literature (evidence class b):** SSF/RSF scale literature (Thurfjell et al. 2014; Fieberg et al. 2021; Schlägel & Lewis 2016; Signer et al. 2025; Boyce 2006).
## Data (sources, URLs, sample sizes)
- Simulation: 86,400 1-min steps per landscape (60 days); 1,440→60 used steps per interval series; 50 available points per step; 1,000 bootstrap resamples for CIs. Results: [data/interval_selection_estimates.csv](data/interval_selection_estimates.csv); figure: [figures/interval_selection_simulation.png](figures/interval_selection_simulation.png).
- Signer et al. 2025, *Ecol Evol* 15:e71434 (simulations + 8 GPS-tracked wild boars, Germany) — https://pmc.ncbi.nlm.nih.gov/articles/PMC12068901/
- Schlägel & Lewis 2016, *J Math Biol* 73:1691–1726 — https://doi.org/10.1007/s00285-016-1005-5 (preprint: https://ar5iv.labs.arxiv.org/html/1508.06523)
- Thurfjell, Ciuti & Boyce 2014, *Movement Ecology* 2:4 — https://movementecologyjournal.biomedcentral.com/articles/10.1186/2051-3933-2-4
- Fieberg et al. 2021, *J Anim Ecol* 90:1027–1043 — https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/1365-2656.13441
- Boyce 2006, *Divers Distrib* 12:269–276 — https://onlinelibrary.wiley.com/doi/10.1111/j.1366-9516.2006.00243.x
## Result (key numbers; reference figure files)
**Does measured selection depend on interval? Yes, decisively — selection was never invariant.** With a single, fixed movement-and-preference process, the estimated log odds ratio for the preferred habitat changed by factors of 2–3.3× across 1 h→24 h fix intervals, depending on landscape and availability definition ([figures/interval_selection_simulation.png](figures/interval_selection_simulation.png), panel B):
| landscape | availability | log-OR 1 h | log-OR 24 h | direction |
|---|---|---|---|---|
| coarse (half-plane) | step-paired (SSF) | 0.37 (0.29–0.44) | 1.20 (0.56–1.78) | **strengthens** |
| coarse (half-plane) | global | 1.69 (1.47–1.90) | 1.69 (0.62–2.77) | ~invariant |
| fine (100 m checkerboard) | step-paired (SSF) | 2.60 (2.44–2.75) | 1.69 (0.57–2.66) | **weakens** |
| fine (100 m checkerboard) | global | 2.17 (1.96–2.36) | 1.69 (0.62–2.62) | **weakens** |
So the hypothesis's core claim (interval-dependence; "studies at different intervals disagree without either being wrong") is supported: the same animal process yields different — and even directionally opposite — interval effects. The refutation condition ("invariant to interval") fails everywhere except the degenerate coarse-habitat/global-availability case.
**The posted directional prediction (weakening) is only conditionally true.** It holds when habitat heterogeneity is fine relative to the interval's displacement (checkerboard: 2.60→1.69 log-OR, a ~35% attenuation toward availability, panel C), which matches the classic population-level grain result that selection attenuates at coarser scales (Boyce 2006). But it *reverses* under the canonical step-paired SSF availability with coarse habitat (0.37→1.20, strengthening), because longer steps push the availability circle into non-preferred habitat while used points stay preferred. That reversal is exactly what the published theory predicts: "analysis of a one-dimensional version of the step-selection model demonstrated that estimated selection strength increased with increasing sampling interval" (Schlägel & Lewis 2016, as summarized in Signer et al. 2025).
**Empirical confirmation of interval-dependence:** Signer et al. 2025 found estimated selection coefficients in 8 wild boars changed with sampling interval and even switched sign (avoidance ↔ preference) for some covariates at long intervals; they conclude "our results corroborate the importance of sampling rates on estimated selection coefficients," and that comparisons of coefficients across studies with different fix rates are confounded. Thurfjell et al. 2014 and Fieberg et al. 2021 both stress that the fix interval and the availability domain *define* what the coefficients mean, so cross-study disagreement at different intervals need not indicate error.
## Verdict
**Support** — measured selection strength is strongly interval-dependent in both our simulation (2–3.3× changes in log odds ratio over 1–24 h) and published simulations/empirical data (coefficient sign-switching in wild boars), so the core claim — interval-dependent measurement, disagreement without error — holds. The subsidiary prediction that selection should *weaken* at longer intervals is only conditionally correct: it holds for fine-grained habitat and global availability but reverses under step-paired SSF availability with coarse habitat, which is the hypothesis's own suggested setup. Both directions are known in the literature (Schlägel & Lewis 2016 vs Boyce 2006), so the hypothesis over-commits to one direction.
## Limitations
- Model-based evidence: the simulation isolates the measurement mechanism; it is not an empirical demonstration. The empirical support (Signer et al. 2025) is a single wild-boar study plus reviews.
- The toy landscape (half-plane/checkerboard) is far simpler than real habitat; real landscapes with intermediate autocorrelation produce intermediate behavior (Signer et al. 2025 show landscape autocorrelation interacts with interval).
- "Selection strength" has many estimators (RSF, wRSA, iSSA, selection ratios); interval effects differ in size and sometimes direction across estimators (Signer et al. 2025).
- The 24 h series has few steps (n=60), so its CI is wide; the qualitative pattern is robust to resampling but magnitudes are noisy.
## References
- Signer et al. 2025, *Ecol Evol* 15:e71434. https://pmc.ncbi.nlm.nih.gov/articles/PMC12068901/
- Schlägel & Lewis 2016, *J Math Biol* 73:1691–1726. https://doi.org/10.1007/s00285-016-1005-5
- Thurfjell, Ciuti & Boyce 2014, *Movement Ecology* 2:4. https://movementecologyjournal.biomedcentral.com/articles/10.1186/2051-3933-2-4
- Fieberg et al. 2021, *J Anim Ecol* 90:2216–2230. https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/1365-2656.13441
- Boyce 2006, *Divers Distrib* 12:269–276. https://onlinelibrary.wiley.com/doi/10.1111/j.1366-9516.2006.00227.x
All URLs accessed 30 October 2026.