Pigauto validation results and limits

This article summarizes pigauto’s validation evidence, including a campaign completed in October 2026. It describes the tested source, simulation settings, run accounting, and scientific findings. Each result applies to the stated scenarios; it does not certify performance for every dataset or use.

Quick guide to the results

Can I assume the prediction intervals give 95% coverage?: No. Across the tested scenarios, mean coverage was below 95% when the GNN was off (gnn = FALSE, the package default) for continuous traits, counts, and proportions. The results varied by scenario. For your analysis: check coverage for a prediction task like yours in Prediction interval results.
Did the optional GNN improve prediction?: It improved predictions over the same fitted model with its neural contribution removed in two confirmatory repeated-observation scenarios with covariates. It did not consistently beat non-neural reference methods. For your analysis: compare methods on held-out data that match your task in When does the neural component add predictive value?.
Do these results validate downstream inference?: None of the tested scenarios for downstream inference met all criteria for support. Some failures also occurred in complete-data controls. For your analysis: treat inference as requiring further evidence for your model and missingness process. See Inferential results.

What was tested

The campaign used a frozen manifest of 151 configurations and 32,240 dataset-generation or masking attempts. It covered the eight supported trait types, mixed-type input, prediction under several evolutionary and missingness conditions, zero-inflated counts, compositions, repeated observations, covariates, posterior-tree workflows, posterior inference, analysis-aware inference, and available real-data examples. Most simulation scenarios used 200 replicates; selected inferential scenarios used 500. The complete scenario definitions and data-generating contract are retained with the campaign records.

The package contract tests exercised type encoding and decoding, preservation of observed values, valid ranges and simplex constraints, alignment, seed reproducibility, prediction, and save/reload behaviour. The Totoro development test suite reported 3,554 passes, no failures, 182 warnings, and 9 skips. The skips were retained as skips; they are not evidence of passing optional integrations.

Run accounting

Of the 32,240 production attempts, 32,199 completed successfully, one was retained as failed, and 40 were unavailable because the registered PanTHERIA and FishBase inputs were absent. The available AVONET and configured BIEN examples each contributed 20 repeated masks; these are not independent dataset generations. The production results contain 1,122,060 metric rows, including expected unavailable metrics where a measure does not apply.

The single failed attempt was an OU prediction scenario with 100 species, phylogenetic signal parameter 0.3, trait correlation 0.5, observed-variable MAR missingness, and 30% missing values. Some GNN-off conformal interval metrics were non-finite or absent. It remains in the denominator and is not counted as a package crash.

Prediction interval results

Across 82 prediction scenarios with 200 planned replicates each, the equal-weighted mean scenario-level 95% conformal coverage for GNN-off fits was 91.2% for the first simulated continuous trait, 91.1% for the second simulated continuous trait, 92.3% for counts, and 92.1% for proportions. Scenario means ranged from 69.5% to 97.7% across these four trait families.

Coverage is the fraction of held-out values that fall inside their prediction intervals. The percentages above average that fraction across the 82 tested scenarios. They do not guarantee coverage for a new dataset.

These observed rates are below nominal 95% on average. They show that the split-conformal intervals did not attain nominal coverage in every tested regime. Phylogenetic dependence and structured missingness can violate the exchangeability conditions behind the usual split-conformal guarantee, so these results do not support a blanket distribution-free coverage claim.

When does the neural component add predictive value?

Pigauto combines a phylogenetic baseline with a gated neural component. The broader question is whether the neural component improves predictions for unobserved data. The evidence here addresses one candidate setting: repeated observations with environmental covariates for a continuous response. Each scenario used 500 independent datasets with 500 species, about five observations per species, ten covariates per observation, a Brownian species effect, and independent observation error. Half the species were fully withheld; 20% of observations among the remaining species were masked. The confirmatory policy used phylo_signal_gate = FALSE and lambda_mode = "estimate", the current defaults for these settings. It set gnn = TRUE explicitly to test the neural component; the package default is gnn = FALSE.

We compare predictions from the same fitted pigauto model with the neural component switched on and off. When it is off, its weight is reassigned to the Brownian baseline; the mean-baseline weight and fitted linear covariate effect stay the same. This tests the full neural branch, including the observation-level network, rather than graph message passing alone.

The two confirmatory scenarios use curved covariate effects and effects that depend on combinations of covariates. A Brownian variance multiplier of 0.3 sets the variance of the simulated Brownian species effect; it is not Pagel’s lambda. For each scenario, we compare prediction errors on the same 500 simulated datasets. The paired tests and simultaneous 95% intervals quantify uncertainty in the average difference in mean squared error (MSE). Both scenarios met the prespecified support rule: the Holm-adjusted paired tests and Bonferroni intervals favoured the full model, and its root mean squared error (RMSE) was more than 2% lower than with the neural component switched off. This result applies to these simulated settings, not every dataset.

Held-out observation-level RMSE by simulated scenario. Lower values indicate better prediction. Neural on and off are paired predictions from the same fitted pigauto model.
Scenario	Pigauto, neural on	Pigauto, neural off	Relative RMSE reduction (95% dataset-bootstrap interval)	Phylogenetic GLS
Nonlinear, variance multiplier 0.3	0.764	0.924	17.3% (17.2%, 17.5%)	0.768
Interactive, variance multiplier 0.3	0.911	1.213	24.9% (24.8%, 25.0%)	0.602
Nonlinear, variance multiplier 0.05	0.709	0.882	19.7% (19.5%, 19.8%)	0.720
Linear recovery	0.654	0.787	16.8% (16.7%, 17.0%)	0.603
No covariate signal	0.593	0.591	-0.2% (-0.3%, -0.2%)	0.603

RMSE is the square root of mean dataset-level MSE, giving equal weight to independent datasets. The reduction interval resamples datasets.

The first two rows are confirmatory; the other rows are descriptive controls. The no-signal control shows a small deterioration from the neural branch. The separately fitted phylogenetic GLS uses the same observed rows, tree, and linear, quadratic, and pairwise-interaction covariate basis. It is a reference method; it does not define a universal performance ceiling. In the interactive scenario, the polynomial OLS basis exactly represented the generated covariate function. GLS RMSE was 0.602 and polynomial OLS RMSE was 0.742, both below pigauto’s 0.911. This study therefore does not show that the neural model outperforms these non-neural references in every setting.

In the nonlinear scenario, overall pooled RMSE was near parity (0.764 for pigauto and 0.768 for GLS). For fully withheld species, pooled RMSE was 0.756 for pigauto and 0.771 for GLS; among partly observed species it was 0.802 for pigauto and 0.750 for GLS.

Under the confirmatory policy, relative RMSE reductions for fully withheld versus partly observed species were 15.1% and 25.4% in the nonlinear scenario, and 23.7% and 29.7% in the interactive scenario. These stratum-specific results are descriptive. A separate phylo_signal_gate = TRUE policy-sensitivity arm triggered in 8.6% of nonlinear, 12.2% of interactive, and 89.6% of low-signal datasets; it is not a second confirmatory analysis. All five scenarios completed 500/500 datasets. The audit reconciled 2,500 datasets, 5,000 gate fits, and 30,000 method attempts with no failures or nonconvergence, and the summary regenerated from retained replicate records.

These results suggest a candidate setting in which to test pigauto: prediction from repeated observations when observation-level covariates carry signal, including nonlinear or interactive signal. In the tested signal scenarios, the neural component improved predictions relative to the same fitted model with that contribution removed. The no-signal control showed a small loss.

This within-fit gain does not mean pigauto will outperform a well-specified non-neural model. GLS and polynomial regression performed better in some comparisons, and GLS did better for partly observed species in the nonlinear scenario.

For an applied dataset, compare pigauto with a covariate-aware non-neural model using held-out data that match the intended prediction task. Report fully withheld and partly observed species separately. A direct test of whether graph message passing adds value would compare this branch with a matched observation-level neural network without graph message passing. Broader recommendations require testing other sample sizes, numbers of repeat observations, covariate signal strengths, and missingness patterns. These results do not establish performance for those settings or uncertainty calibration. The full GNN report and paired summary table give the scenario criteria, paired uncertainty, gate behaviour, and reproducibility records.

Inferential results

The assessment used prespecified bands for nominal 95% coverage, reported standard-error calibration, and standardized bias. None of the tested scenarios for downstream inference met all criteria for support. Of 44 inferential results, 12 were classified as failed and 32 as indeterminate. “Indeterminate” means the simulation was too imprecise to decide whether its criteria were met. This includes complete-data controls, so the observed failures are not all attributable to imputation.

For the eight posterior slope regimes with an independently defined truth, five were classified as failed and three as indeterminate. Empirical 95% coverage ranged from 86.2% to 95.2%; reported-to-empirical standard-error ratios ranged from 0.750 to 1.039. This ratio compares the model-reported standard errors with the observed variation in estimates across repeated simulated datasets; values below 1 mean the reported errors were smaller than that variation. In the analysis-aware simulations, 23 of 24 rows were indeterminate and one binomial-logit GLM row failed. None was classified as supported.

These classifications describe the registered regimes and criteria. They do not establish that every use of pigauto will fail, nor do the indeterminate rows establish calibration. Users should treat inferential use as requiring further evidence for their model, data, and missingness process.