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Modeling the biocontrol of an invasive plant

Mathieu A., Chiroleu F., Quilici S., Flores O., Dumont Y.. 2012. In : International Conference on Mathematical Methods and Models in Biosciences (BIOMATHS 2012), Sofia, Bulgaria, 17-22 June 2012. s.l. : s.n., p. 30-30. International Conference on Mathematical Methods and Models in Biosciences, 2011-06-15/2011-06-18, Sofia (Bulgarie).

The giant bramble, Rubus alceifolius Poir. (Rosaceae) is one of the most invasive plants in la Réunion. In the last decades, mechanical and chemical control have been used to limit its spreading. However, la Réunion being one of the hot spots of endemicity in the world, the use of chemical products is limited. Moreover, parts of the island are completely inaccessible. Thus, control is real!y limited. That is why biological control agents have been considered, like Cibdela janthina Klug (Argidae). This sawfiy is native from Sumatra and can cause severe damages to Rubus alceifolius. After sorne preliminary studies between 2001 and 2007, Cibdela has been released in 2008 in the South-East part of la Réunion. Since then the Cibdela population has spread through the island. The first objective has been reached: Rubus alceifolius has. completely disappeared in sorne places (in particular at low altitudes), while in other places an equilibrium between Rubus and Cibdela has apparently been reached. Altogether, sorne unexpected situations appeared, and that is why new biological and ecological investigations have began two years ago. In this context, mathematical modeling can be a useful tool to formalize al! extensive knowledges about RubusCibdela interactions and to estimate the long term behavior of the bramble, when attacked by the sawfiy, at different altitudes. The aim of this talk is to present sorne preliminary studies about the modeling of these interactions. We will also present sorne theoretical results and illustrate our talk with various simulations.

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