Population Density Estimators for Right-Censored Distance Sampling

TL;DR

This paper develops new population density estimators for right-censored distance sampling data, extending classical models to censored settings and demonstrating improved accuracy and robustness in ecological applications.

Contribution

It introduces systematic censored estimators under CSR and NBD frameworks, including novel MLEs that outperform existing methods in accuracy and robustness.

Findings

NBD-based MLE achieves median relative bias below 20% in simulations

New estimators extend classical results to censored data settings

Method validated with forest plot data showing high accuracy

Abstract

Distance-based point-centered quarter method (PCQM) is widely used for population density estimation, yet its performance is challenged by right-censored observations arising from a truncated search radius. Existing methods for addressing such right-censored data are predominantly developed under the assumption of complete spatial randomness (CSR) using a Poisson model, while approaches for spatially aggregated populations--despite the negative binomial distribution (NBD) being well-established for uncensored distance sampling--remain lacking a systematic framework. This study presents a systematic set of censored distance-based estimators under these two core frameworks. We develop both moment-based estimators and maximum likelihood estimators (MLEs) under these two core frameworks, extending classical results to the censored setting for CSR populations and providing new inference tools for aggregated populations under the NBD model. Extensive simulations and applications to fully-censused forest plot data demonstrate that the NBD-based MLE achieves the highest accuracy and robustness across a wide range of ecological scenarios, with a median relative bias below 20\% in most empirical scenarios--a level of estimation accuracy that cannot be consistently guaranteed by other competing methods, providing a rigorously validated toolkit for analyzing censored point-to-tree distance data.