Unbiased estimation of sampling variance for Simpson's diversity index

TL;DR

This paper introduces a new unbiased estimator for the sampling variance of Simpson's diversity index, improving accuracy in ecological and biological diversity measurements, especially when species richness exceeds sample size.

Contribution

The paper derives a closed-form unbiased estimator for Simpson's diversity index variance, outperforming existing methods and applicable across ecological and biological fields.

Findings

Estimator outperforms existing approaches in numerical tests.

Effective in scenarios with high species richness relative to sample size.

Enables more reliable comparison of biodiversity across samples.

Abstract

Quantification of measurement uncertainty is crucial for robust scientific inference, yet accurate estimates of this uncertainty remain elusive for ecological measures of diversity. Here, we address this longstanding challenge by deriving a closed-form unbiased estimator for the sampling variance of Simpson's diversity index. In numerical tests the estimator consistently outperforms existing approaches, particularly for applications in which species richness exceeds sample size. We apply the estimator to quantify biodiversity loss in marine ecosystems and to demonstrate ligand-dependent contributions of T cell receptor chains to specificity, illustrating its versatility across fields. The novel estimator provides researchers with a reliable method for comparing diversity between samples, essential for quantifying biodiversity trends and making informed conservation decisions.