Simpson多样性指数抽样方差的无偏估计
Unbiased estimation of sampling variance for Simpson's diversity index
AI总结：
本文推导了Simpson多样性指数抽样方差的闭式无偏估计量，在物种丰富度超过样本量时优于现有方法，并成功应用于海洋生物多样性丧失量化和T细胞受体特异性分析。
摘要：
测量不确定度的量化对于稳健的科学推断至关重要，然而对于生态学多样性度量而言，准确估计这种不确定度仍然难以实现。在此，我们通过推导Simpson多样性指数抽样方差的闭式无偏估计量来应对这一长期挑战。在数值测试中，该估计量始终优于现有方法，特别是在物种丰富度超过样本量的应用中表现尤为突出。我们应用该估计量来量化海洋生态系统中的生物多样性丧失，并展示T细胞受体链对特异性的配体依赖性贡献，说明其跨领域的通用性。这一新型估计量为研究人员提供了一种可靠的方法来比较样本间的多样性，这对于量化生物多样性趋势和做出明智的保护决策至关重要。
英文摘要：
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.
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