Abstract
Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.
Highlights
Invasive species are recognized as a significant threat to biodiversity
A number of works have appeared in recent decades which have aimed to mathematically model invasive species at different levels of accuracy
Introduced by Rushton and collaborators in 19979 in the study of red and grey squirrel distribution at landscape scale, Spatially Explicit Population dynamics Models (SEPMs) are models that combine GIS data and a population dynamics approach on separated habitat blocks
Summary
Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Control strategies may aim at extirpation or rely on forcing a component Allee effect by bringing the population below a threshold[4], for instance by increasing the abundance of predators, by culling or inducing habitat fragmentation[5] Another important consideration is the need to account for the temporal dynamics of the invader population. Introduced by Rushton and collaborators in 19979 in the study of red and grey squirrel distribution at landscape scale, SEPMs are models that combine GIS data and a population dynamics approach on separated habitat blocks. These models have been used quite effectively to study the invasive expansion[10] and control[11] of the grey squirrel in northern Italy. While on the one hand such a model can be very effective in the management of an already established population, it lacks the spatial accuracy required to predict an invasion and is of limited use in devising early interventional strategies
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