On a link between a species survival time in an evolution model and the Bessel distributions

Details On a link between a species survival time in an evolution model and the Bessel distributions On a link between a species survival time in an evolution model and the Bessel distributions

2011-02-14

arxiv.org/abs/1102.2817v1

Mathematics

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13 pages

Scientific paper

We consider a stochastic model for species evolution. A new species is born at rate lambda and a species dies at rate mu. A random number, sampled from a given distribution F, is associated with each new species at the time of birth. Every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time of a species with a given fitness f. We show that the survival time distribution depends crucially on whether ff_c where f_c is a critical fitness that is computed explicitly.

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