Title: A Statistical Approach to Ecological Modeling by a New Similarity Index Show Chinese title

Title: 一种基于新相似性指数的统计生态建模方法

Abstract: Similarity index is an important scientific tool frequently used to determine whether different pairs of entities are similar with respect to some prefixed characteristics. Some standard measures of similarity index include Jaccard index, S{\o}rensen-Dice index, and Simpson's index. Recently, a better index ($\hat{\alpha}$) for the co-occurrence and/or similarity has been developed, and this measure really outperforms and gives theoretically supported reasonable predictions. However, the measure $\hat{\alpha}$ is not data dependent. In this article we propose a new measure of similarity which depends strongly on the data before introducing randomness in prevalence. Then, we propose a new method of randomization which changes the whole pattern of results. Before randomization our measure is similar to the Jaccard index, while after randomization it is close to $\hat{\alpha}$. We consider the popular ecological dataset from the Tuscan Archipelago, Italy; and compare the performance of the proposed index to other measures. Since our proposed index is data dependent, it has some interesting properties which we illustrate in this article through numerical studies. Show Chinese abstract

Abstract: 相似性指数是一种重要的科学工具，常用于确定不同实体对在某些预定义特征方面是否相似。 一些标准的相似性指数度量包括Jaccard指数、S{\o }rensen-Dice指数和Simpson指数。 最近，开发了一个更好的指数（$\hat{\alpha}$）用于共现和/或相似性，该度量确实表现更好，并提供了理论支持的合理预测。 然而，度量$\hat{\alpha}$不依赖于数据。 在本文中，我们提出了一种新的相似性度量，该度量在引入流行率的随机性之前强烈依赖于数据。 然后，我们提出了一种新的随机化方法，该方法改变了结果的整体模式。 在随机化之前，我们的度量类似于Jaccard指数，而在随机化之后，它接近$\hat{\alpha}$。 我们考虑了来自意大利托斯卡纳群岛的流行生态数据集，并将所提出的指数与其他度量进行比较。 由于我们提出的指数依赖于数据，它具有一些有趣的特性，我们通过数值研究在本文中进行了说明。