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The Virgin Island model. (English) Zbl 1197.60091

Summary: A continuous mass population model with local competition is constructed where every emigrant colonizes an unpopulated island. The population founded by an emigrant is modeled as excursion from zero of an one-dimensional diffusion. With this excursion measure, we construct a process which we call Virgin Island model. A necessary and sufficient condition for extinction of the total population is obtained for finite initial total mass.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
92D25 Population dynamics (general)
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