We discuss recent methodological developments in inhomogeneous summary statistics and envelope testing and study their applications in the field of spatial point pattern analysis. Specifically, we use these methods to test McGill’s theory of biodiversity. This theory is based upon three axioms: individuals of the same species cluster together, many rare species co-exist with a few common ones and individuals of different species grow independently of each other. We assess the validity of the first and third axioms for data obtained from a 50 hectare plot on Barro Colorado Island.

中文翻译：

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使用不均匀的汇总统计数据和全球信封测试测试生物多样性

我们讨论了非均匀汇总统计和包络测试的最新方法发展，并研究了它们在空间点模式分析领域的应用。具体来说，我们使用这些方法来检验麦吉尔的生物多样性理论。该理论基于三个公理：同一物种的个体聚集在一起，许多稀有物种与少数常见物种共存，不同物种的个体相互独立生长。我们评估了从巴罗科罗拉多岛 50 公顷地块获得的数据的第一和第三公理的有效性。