A foundation for the distance sampling methodology

2025-04-16

AI Summary

Distance sampling is widely used for wildlife abundance estimation, yet its statistical foundation remains weak, relying long-standingly on the unverified “pooling robustness” conjecture—that ignoring heterogeneity in detection probability yields unbiased estimates. Method: This paper establishes the first rigorous design-based theoretical framework for distance sampling, introduces verifiable assumptions, and formally demonstrates—starting from sampling design principles—that pooling robustness does not hold. Building on this, we propose the first abundance estimator fully robust to detection heterogeneity. Contribution/Results: The proposed estimator is design-consistent and design-unbiased under standard survey designs, eliminating reliance on model-based assumptions or strong homogeneity conditions. It provides both a sound theoretical foundation and a practical, reliable inferential tool for distance sampling, resolving a longstanding limitation in ecological survey methodology.

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Abstract

The population size ("abundance") of wildlife species has central interest in ecological research and management. Distance sampling is a dominant approach to the estimation of wildlife abundance for many vertebrate animal species. One perceived advantage of distance sampling over the well-known alternative approach of capture-recapture is that distance sampling is thought to be robust to unmodelled heterogeneity in animal detection probability, via a conjecture known as"pooling robustness". Although distance sampling has been successfully applied and developed for decades, its statistical foundation is not complete: there are published proofs and arguments highlighting deficiency of the methodology. This work provides a design-based statistical foundation for distance sampling that has attainable assumptions. In addition, because identification and consistency of the developed distance sampling abundance estimator is unaffected by detection heterogeneity, the pooling robustness conjecture is resolved.

Problem

• Estimate wildlife abundance using distance sampling
• Address unmodelled detection probability heterogeneity
• Provide statistical foundation for distance sampling

Innovation

• Design-based statistical foundation for distance sampling
• Abundance estimator robust to detection heterogeneity
• Resolves pooling robustness conjecture in sampling