title: Biological invasions: deriving the regions at risk from partial measurements.
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.
authors.affiliation: LATP, CNRS/UMR 6632, CMI, Université de Provence, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France. michel.cristofol@univ-cezanne.fr
authors.forename: Michel
authors.initials: M
authors.lastname: Cristofol
authors.forename: Lionel
authors.initials: L
authors.lastname: Roques
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D004777:Environment; D016015:Logistic Models; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011156:Population Density; D011157:Population Dynamics; D013269:Stochastic Processes