Even though there is no doubt that an invasion of a landscape by plants is a function of the abundance and spatial arrangement of different types of habitat, to the best of our knowledge, there has been no analysis of the relation between the patterns of plant invasion and the availability of specific habitats within landscapes invaded. The application of habitat selection functions (HSFs) provides a quantitative measure for determining if specific habitats are more likely to be invaded by a given species. The remarkable dynamics of spread of invasive alien plants makes them an ideal species pool for applying HSFs. This paper discusses the possible application of a bootstrap test of significance for identifying habitat types where the incidence of alien species is higher (preferred) or lower (avoided) than would be expected from a random null model for which all habitat types are invaded in proportion to their availability. In order to demonstrate the usefulness of the proposed approach we explored the habitat selection of a coastal alien plant, Carpobrotus aff. acinaciformis, in the Tyrrhenian coastal dunes of central Italy. According to this bootstrap test of significance, some important habitats of European conservation interest were more readily invaded by Carpobrotus than expected. From an applied research perspective, the use of an HSF approach can help identify the most invasion-prone habitats and, therefore, may facilitate the development of a clear and targeted prevention policy to control the introduction and spread of alien species in a landscape, for example, coastal dune habitats.
We consider, in the framework of multidimensional observations, nonparametric functional estimators, which include, as special cases, the Akaike-Parzen-Rosenblatt kernel density estimators ([1], [18], [20]), and the Nadaraya-Watson kernel regression estimators ([16], [22]). We evaluate the sup-norm, over a given set <span class="tex"><b>I</b></span>, of the difference between the estimator and a non-random functional centering factor (which reduces to the estimator mean for kernel density estimation). We show that, under suitable general conditions, this random quantity is consistently estimated by the sup-norm over <span class="tex"><b>I</b></span> of the difference between the original estimator and a bootstrapped version of this estimator. This provides a simple and flexible way to evaluate the estimator accuracy, through a single bootstrap. The present work generalizes former results of Deheuvels and Derzko [4], given in the setup of density estimation in <b>R</b>.