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EcographyEcologyPeer-reviewed journal article

Flexible Methods for Species Distribution Modeling with Small Samples

Brian MaitneriD, Robert L. RichardsiD, Ben CarlsoniD, John M. DrakeiD, Cory MerowiD

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Abstract

O_LISpecies distribution models (SDMs) are used for understanding where species live or could potentially live and are a key resource for ecological research and conservation decision-making. However, current SDM methods often perform poorly for rare or inadequately sampled species, which includes most species on earth as well as most of those of the greatest conservation concern. C_LIO_LIHere, we evaluate the performance of three recently developed modeling approaches specifically designed for data-deficient situations: 1) plug-and-play modeling, 2) density-ratio modeling, and 3) environmental-range modeling. We compare the performance of these methods with Maxent, a widely used method. We compare model performance across sample sizes as well as comparisons limited to only data-poor species. We also ask to what extent model cross-validation performance on training data was correlated with model performance on independent, presence-absence data. C_LIO_LIWe show that, across all species, one or more of the plug-and-play, density-ratio, or environmental-range algorithms outperformed Maxent in 72% of cases, with three of the algorithms having AUC distributions not significantly different from Maxents. For data-poor species (those with 20 or fewer occurrences), 24 of the algorithms considered had AUC distributions that were not significantly different from Maxent. However, despite these comparable AUC scores, we found that the algorithm outputs (when thresholded to predict presence vs absence) spanned a wide gradient of sensitivity vs. specificity. Specificity and prediction accuracy assessed on training data were strongly correlated with specificity and prediction accuracy assessed on independent presence-absence data, however AUC and sensitivity had weak correlations. We found that only for 16% of species was the model that performed best on the training data the best performing model when evaluated on independent, presence-absence data. Finally, we show how ensembles of models that span the sensitivity-specificity gradient can represent model disagreement in poorly sampled species and improve model predictions. C_LIO_LIThis work supports plug-and-play, density-ratio, and environmental-range modeling as useful alternatives to Maxent, particularly for data-deficient species. While our work suggests that identifying the best model for a given species is challenging, we argue that incorporating the predictions of multiple models provides a useful way forward. C_LI Data/Code for peer reviewAnonymized data and code underlying this work are publicly available at: https://anonymous.4open.science/r/Flexible_Methods_for_Small_Sample_Size_Distribution_Modeling

In-depth summary

Claude Opus 5.5 · xhigh effort · 7 Nov 2026 · from the full text of version 1 (8 Apr 2025) · CC BY 4.0

For species with 20 or fewer occurrence records, 24 of 31 species distribution models had AUC distributions not significantly different from Maxnet's; vote-counting ensembles give upper and lower range bounds.

Only about 112,000 (38 percent) of the plant species with cleaned occurrence data in BIEN have more than 10 unique records, and few species distribution model (SDM) algorithms are known to work reliably with so few. It extends Drake and Richards' plug-and-play framework with hybrid presence/background estimator pairs and ruLSIF (relative unconstrained least-squares importance fitting, not previously tested for SDMs), and uses vote-counting ensembles that keep model disagreement.

Key results

  1. ShownAcross 226 species, Maxnet had the highest mean AUC on independent presence-absence data but was top for only 28% of species; kernel density estimation (KDE)/KDE, ruLSIF and Gaussian/KDE had AUC distributions not significantly different from Maxnet's, with differing sensitivity and specificity.

    Maxnet mean AUC 0.731 and median 0.725; top model for 28% of species vs range-bagging 7% and Gaussian/KDE 5%, with 21 other models top for at least one species. Mann-Whitney vs Maxnet: KDE/KDE W = 23413.0, p = 0.17; ruLSIF W = 23198.0, p = 0.11; Gaussian/KDE W = 23186.0, p = 0.12. · Comparative performance: all sample sizes; Discussion

  2. SuggestedAmong the 34 species with 20 or fewer records, 24 of 31 models had AUC distributions not significantly different from Maxnet's; every model that differed used range-bagging or LOBAG-OC (low-bias bootstrap aggregating, one-class) outside a presence-only role.

    Mann-Whitney tests vs Maxnet (Table SI6). Maxnet had the top AUC for 27% of species, ruLSIF for 12%, and 14 other algorithms for at least one species. Maxnet had the highest mean AUC (0.697), range-bagging/range-bagging the highest median (0.680). Maxnet AUC was worse than random in 15% of cases; 19 algorithms did as well or better on this measure. · Relative performance among models: small sample…; Assessing model quality predictability; Tables

  3. SuggestedFor small-sample species, specificity and prediction accuracy measured on training data predicted their values on independent data, but training AUC, sensitivity and the occurrence-rate correlation (COR) tracked only weakly, kappa negatively, and cross-validated AUC rarely picked the best model.

    Training vs independent presence-absence values: specificity r = 0.91, accuracy r = 0.77, AUC r = 0.22, sensitivity r = 0.11, COR r = 0.067, kappa r = -0.074. In 32 species with enough points for cross-validation, test AUC vs independent AUC r = 0.36 (rank ρ = 0.23); the best test-AUC model matched the best independent-AUC model in 16% of cases. · Assessing model quality predictability; Discussion

  4. SuggestedA vote-counting ensemble of KDE/KDE, ruLSIF and Maxnet, chosen to span the sensitivity-specificity gradient, outperformed each member: cells with unanimous support gave higher specificity and accuracy, cells with any support gave higher sensitivity.

    Species with 20 or fewer records (Figure 3, Table SI10): unanimous support exceeded every component model in specificity and prediction accuracy; any support exceeded every component in sensitivity; vote-counting variants scored highest among ensemble approaches. Maxnet alone kept the highest mean kappa. Numeric values are reported in Table SI10. · Model Ensembles; Discussion; Ensembles to deal with uncertainty

  5. ShownAgreement among the three ensemble members rose with the number of occurrence records, most steeply between 2 and 25 records, across 1,620 Florida plant species from BIEN.

    With 2 records the three models agreed on 18% of predicted locations on average and 52% of locations had support from a single model; with 100 records agreement was 69% and single-model support 9%. Beyond 25 records the models agreed on most (>50%) predicted locations. · Model Ensembles; Ensembles to deal with uncertainty; Figure legends

Methods, data and reproducibility

Estimated presence and background densities with every pairing of five estimators (range-bagging, LOBAG-OC, Gaussian, vine copula, KDE), plus presence-only variants and density-ratio methods (uLSIF, ruLSIF, Maxnet); outputs were thresholded at 5% training-presence omission, scored on independent presence-absence data, 5-fold cross-validation and training data, and combined by averaging or vote counting.

  • Elith et al. (2020) benchmark (disdat R package): presence-background training and independent presence-absence data from six regions; categorical predictors excluded · plants, birds, bats and reptiles · n = 226 species
  • Subset of the Elith et al. (2020) species with 20 or fewer occurrence records, used for the small-sample analyses · plants, birds, bats and reptiles · n = 34 species (32 with enough points for cross-validation)
  • BIEN occurrence records for poorly to moderately sampled plant species in Florida, USA (2 to 100 records each), used for ensemble agreement · plants · n = 1,620 species
  • WorldClim climate layers; mean annual temperature and mean annual precipitation at 0.5 degree resolution for the BIEN analysis
Methods & tools
S4DM, maxnet, glmnet, densratio, rvinecopulib, np, kernlab, geometry, pROC, disdat, BIEN, WorldClim
Software & environment
R with the S4DM package (fit_plug_and_play, fit_density_ratio) and its dependencies (e.g., densratio, maxnet, rvinecopulib, np, kernlab); no R or package versions stated.
Experimental conditions
Median model runtimes ranged from 1 s to 5 min on full training data (Table SI3), dominated by background-distribution fitting; parallelized with foreach and doParallel. Hardware not stated.
Reproducibility gaps
No software versions, container or hardware specification reported; raw occurrence and climate inputs come from previously published public sources.
Limitations (6)
  • Even the viable methods can perform poorly for many data-deficient species, and choosing the single best model for a given species remains hard. · stated by the authors
  • Low within-ensemble agreement partly reflects the deliberate choice of members spread across the sensitivity-specificity gradient, which are expected to disagree. · stated by the authors
  • Kappa here uses the 5% training-omission threshold, whereas Elith et al. (2006) reported maximum kappa, so the two are not directly comparable. · stated by the authors
  • The authors note that newer, more representative benchmark datasets would help further method development and validation. · stated by the authors
  • Small-sample conclusions rest on 34 species from one benchmark, and the three ensemble members were picked using their AUC on that same dataset before the ensemble was evaluated on it. · noted in this summary
  • The Florida agreement analysis used only mean annual temperature and precipitation at 0.5 degree, with no presence-absence data, so it measures consistency among models, not accuracy. · noted in this summary

Read this if you build range maps for rare or poorly sampled species from few occurrence records and need evidence on which presence-background algorithms to compare and how to report uncertainty across them.

Citations
8
FWCI
111.22
Field percentile
top 1%

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