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# 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.
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Article dans une revue
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https://hal.inrae.fr/hal-02657596
Déposant : Migration Prodinra <>
Soumis le : samedi 30 mai 2020 - 10:49:43
Dernière modification le : vendredi 12 juin 2020 - 10:43:26

### Identifiants

• HAL Id : hal-02657596, version 1
• PRODINRA : 28438

### Citation

Michel Cristofol, Lionel Roques. Biological invasions: Deriving the regions at risk from partial measurements. Mathematical Biosciences, Elsevier, 2008, 215, pp.158-166. ⟨hal-02657596⟩

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