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## Biological invasions: deriving the regions at risk from partial measurements

Michel Cristofol
Lionel Roques

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#### 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.

### Dates and versions

hal-00402037 , version 1 (06-07-2009)

### Identifiers

• HAL Id : hal-00402037 , version 1
• ARXIV :

### Cite

Michel Cristofol, Lionel Roques. Biological invasions: deriving the regions at risk from partial measurements. 2008. ⟨hal-00402037⟩

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