  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.
