On a link between a species survival time in an evolution model and the   Bessel distributions
  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 f<f_c, f=f_c or f>f_c where f_c is a critical fitness that is computed explicitly. 
Herve Guiol (1), Fabio P. Machado (2), Rinaldo B. Schinazi (3) ((1)   TIMC Univ. Grenoble, France, (2) IME-USP, Brasil, (3) ...
math.PR