%0 Journal Article
%T Biological invasions: deriving the regions at risk from partial measurements
%A Michel Cristofol
%A Lionel Roques
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0907.0991v1