Department of Biology, Stanford University, Stanford, CA 94305, USA.
Department of Biology, Stanford University, Stanford, CA 94305, USA.
Biosystems. 2024 Mar;237:105153. doi: 10.1016/j.biosystems.2024.105153. Epub 2024 Feb 28.
The Hill numbers are statistics for biodiversity measurement in ecological studies, closely related to the Rényi and Shannon entropies from information theory. Recent developments in the mathematics of diversity in the setting of population genetics have produced mathematical constraints that characterize how standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we apply these constraints to diversity statistics in ecology, focusing on the Hill numbers and the Rényi and Shannon entropies. The mathematical bounds can shift perspectives on the diversities of communities, in that when upper and lower bounds on Hill numbers are evaluated in a classic butterfly example, Hill numbers that are initially larger in one community switch positions-so that associated normalized Hill numbers are instead smaller than those of the other community. The new bounds hence add to the tools available for interpreting a commonly used family of statistics for ecological data.
希尔数是生态学研究中用于衡量生物多样性的统计量，与信息论中的瑞尼和香农熵密切相关。群体遗传学中多样性数学的最新发展产生了数学约束，这些约束特征化了标准度量如何依赖离散概率分布中的最高频率类。在这里，我们将这些约束应用于生态学中的多样性统计量，重点关注希尔数和瑞尼及香农熵。数学界可以改变对群落多样性的看法，因为在经典的蝴蝶示例中评估希尔数的上下限时，最初在一个群落中较大的希尔数会改变位置，从而使得相关的归一化希尔数反而小于另一个群落的希尔数。因此，新的界增加了用于解释常用于生态学数据的统计量的工具。
