Abstract
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.
Highlights
Ecological Risk Assessments (ERA) are performed to evaluate the likelihood of negative ecological effects as a result of exposure to a biological, physical or chemical factor that provokes adverse responses in the environment
The route designed to reach this goal can be summarized as follows: (1) Defining the optimal value of r, r0, to be estimated, (2) establishing a nonparametric test to assess the null hypothesis that S is r −convex for a given r > 0, (3) defining the estimator of r0 that strongly relies on the previous test (4) checking that the estimator of r0 and the resulting support reconstruction are consistent and (5) studying the performance of the r −convexity test and the estimation algorithm of r0 through simulations
The definition of the estimator r0 depends on the r −convexity test established that, could be used in an independent way
Summary
Ecological Risk Assessments (ERA) are performed to evaluate the likelihood of negative ecological effects as a result of exposure to a biological, physical or chemical factor that provokes adverse responses in the environment. The problem of EOO reconstruction will be illustrated via the analysis of a real dataset containing 740 geographical coordinates (or occurrences) for 28 species of terrestrial invasive plants distributed in two of the Azorean islands (Terceira and São Miguel) from 2010 until 2018. We will propose a new data-driven support estimator for general dimension and, as a consequence, an original, realistic and easy to use EOO reconstruction that will overcome the limitations derived from convexity restriction. Our proposal considers the smallest r -convex set containing Xn (r −convex hull of Xn, namely Cr (Xn)) as the natural estimator for the unknown support. Proofs of theoretical results are deferred to Sect. 9
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