Invasion processes for alien species on sub-Antartic ecosystems, Mathematical understanding of invasion processes in life sciences

• Main Authors: Sebastien Gaucel, Michel Langlais, Dominique Pontier
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2004
• Subjects: antartic*
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.567.5745; http://www.cirm.univ-mrs.fr/liste_rencontre/archives/Resumes04/Rencontre05/gaucel.pdf

We are concerned with the development and analysis of a predator prey sys-tem designed for populations living in insular environments. We look for systems consisting of a native prey without behavioral traits to cope with predation, and introduced predators or competitors. In such systems, introduction of alien species is a major cause of the disappear-ance of native species. First we consider an unstructured model; this yields a singular system of ordi-nary differential equations. We establish that interesting dynamical behaviours like finite time extinction or persistence of populations can appear and we show how it depends in demographic coefficients and initial state. In previous works, it has been shown that ODE’s model do not allow to reproduce all the dynamics observed, so we built a spatially heterogeneous structured model using a reaction diffusion system. Then, using numerical experiments we present some invad-ing processes. We show that invasion success is strongly link to the presence of the alien prey. Finally, we try to take into account the predator preference on juveniles or adults for hunting, leading to an age structured model. References [1] Courchamp, F. and G. Sugihara, G. (1999). Modeling the biological control of an alien predator to protect island species from extinction. Ecological Applications