Ecological Risk Assessment faces the challenge of determining the impact of invasive species on biodiversity conservation. Although many statistical methods have emerged in recent years in order to model the evolution of the spatio-temporal distribution of invasive species, the notion of extent of occurrence, formally defined by the International Union for the Conservation of Nature, has not been properly handled. In this work, a novel and flexible reconstruction of the extent of occurrence from occurrence data will be established from nonparametric support estimation theory. Mathematically, given a random sample of points from some unknown distribution, we establish a new data-driven method for estimating its probability support S in general dimension. Under the mild geometric assumption that S is \(r-\)convex, the smallest \(r-\)convex set which contains the sample points is the natural estimator. A stochastic algorithm is proposed for determining an optimal estimate of r from the data under regularity conditions on the density function. The performance of this estimator is studied by reconstructing the extent of occurrence of an assemblage of invasive plant species in the Azores archipelago.

生态风险评估面临着确定入侵物种对生物多样性保护的影响的挑战。尽管近年来出现了许多统计方法来模拟入侵物种时空分布的演变，但国际自然保护联盟正式定义的发生范围概念并未得到妥善处理。在这项工作中，将根据非参数支持估计理论建立一种新颖且灵活的从发生数据重建发生范围的方法。在数学上，给定来自某个未知分布的随机点样本，我们建立了一种新的数据驱动方法来估计其在一般维度上的概率支持S。在温和的几何假设下，S是\(r-\)凸，包含样本点的最小\(r-\)凸集是自然估计量。提出了一种随机算法，用于在密度函数的规律性条件下根据数据确定r的最佳估计值。通过重建亚速尔群岛入侵植物物种组合的发生范围来研究该估计器的性能。