Biological invasions: deriving the regions at risk from partial measurements

TL;DR

This paper develops a method to predict high-risk regions for invasive species using limited data, combining theoretical proofs and a stochastic algorithm to identify favourable and unfavourable areas.

Contribution

It introduces a novel approach to determine risk regions from partial measurements using reaction-diffusion models and provides an effective stochastic algorithm validated through analysis and numerical tests.

Findings

Theoretical proof of region determination from partial data.

Development of an effective stochastic algorithm.

Successful numerical validation of the method.

Abstract

We consider the problem of forecasting the regions at higher risk for newly introduced invasive species. Favourable and unfavourable regions may indeed not be known a priori, especially for exotic species whose hosts in native range and newly-colonised areas can be different. Assuming that the species is modelled by a logistic-like reaction-diffusion equation, we prove that the spatial arrangement of the favourable and unfavourable regions can theoretically be determined using only partial measurements of the population density: 1) a local "spatio-temporal" measurement, during a short time period and, 2) a "spatial" measurement in the whole region susceptible to colonisation. We then present a stochastic algorithm which is proved analytically, and then on several numerical examples, to be effective in deriving these regions.