  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.
