TL;DR
The paper introduces the Virgin Island Model, a continuous population process with local competition where emigrants colonize new islands, and provides conditions for population extinction based on initial mass.
Contribution
It constructs the Virgin Island Model using excursion measures of diffusions and establishes a criterion for population extinction.
Findings
Constructed the Virgin Island Model using diffusion excursions.
Derived a necessary and sufficient condition for population extinction.
Analyzed the model's behavior with respect to initial total mass.
Abstract
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. Furthermore, a necessary and sufficient condition for extinction of the total population is obtained for finite initial total mass.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical and Theoretical Epidemiology and Ecology Models · Complex Systems and Time Series Analysis