In ecological studies niche overlap is often used to quantify species interaction and dynamics. This paper develops a robust, nonparametric statistical framework for quantifying and analyzing multivariate niche overlap. Parametric methods are often constrained by restrictive assumptions and tend to underperform in complex multivariate settings. We introduce a nonparametric overlap index and propose estimators for it. Further, we investigate asymptotic properties of the estimators. We also propose bootstrap-based inference procedures that enable statistical testing and simultaneous confidence intervals in small sample settings. Extensive numerical examples demonstrate that our proposed methods maintain correct size and exhibit robust power across various scenarios. We illustrate the practical utility of our methodology using stable isotope measurements from multiple fish species and provide distinct ecological insights regarding species niche differentiation.

翻译：在生态学研究中，生态位重叠常被用于量化物种间的相互作用与动态变化。本文构建了一个稳健的非参数统计框架，用于多元生态位重叠的量化与分析。参数方法通常受限于严格假设条件，在复杂多元场景中表现欠佳。我们引入了一个非参数重叠指数并提出了其估计量，进一步研究了估计量的渐近性质。同时，我们提出了基于自助法的推断程序，可实现在小样本条件下进行统计检验与同时置信区间构建。大量数值实验表明，所提方法能维持正确检验水平，并在多种场景下展现出稳健的统计功效。我们利用多个鱼类物种的稳定同位素测量数据验证了该方法的应用价值，为物种生态位分化提供了独特的生态学见解。