Spatial distribution of invasive species: an extent of occurrence approach

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 $$r-$$ r - convex, the smallest $$r-$$ 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.

A Generalized Stochastic Framework for Analyzing Rock Slopes Stability and Designing Reliable Remedial Measures with Limited Investigation Data: Theory and Field Implementation

Availability of limited data for rock properties is a very frequently encountered issue for the rock slopes along Himalayan highways due to problems like high costs, manual efforts, geological complexities, difficult terrain etc. involved in rock testing and investigation. Under these conditions, support estimation for rock slides mitigation using traditional deterministic and reliability approaches becomes highly questionable due to inaccuracy in the estimated statistical parameters of rock properties. To resolve this issue, this article proposes a computationally efficient methodology which utilizes Advanced Re-Sampling Reliability Approach (ARRA) along with deterministic approach and Target Reliability Approach (TRA) to estimate required support for rock slides mitigation when limited field and laboratory investigation data is available, with acceptable accuracy and confidence. Proposed methodology was used to design the support measures to mitigate two massive rock slides along a rock-slide prone highway i.e. Rishikesh-Badrinath National Highway (NH-58) in India. It was observed from the analysis that availability of limited test data induces high uncertainty in the statistical parameters (mean and standard deviation) and probability distribution of rock properties. Support estimation carried out using traditional deterministic and reliability approaches with this inaccurate probabilistic characterization of rock properties, can lead to inaccurate support estimates for potential rock slides in the presence of limited data; however these methods when coupled with ARRA can lead to significant improvement in computational efficiency and the designer’s confidence for the estimated support.