Biological invasions: deriving the regions at risk from partial measurements.
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.
Cristofol
Michel
M
LATP, CNRS/UMR 6632, CMI, Université de Provence, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France. michel.cristofol@univ-cezanne.fr
Roques
Lionel
L
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