  We generalize the evolution model introduced by Guiol, Machado and Schinazi
(2010). In our model at odd times a random number X of species is created. Each
species is endowed with a random fitness with arbitrary distribution on $[0,
1]$. At even times a random number Y of species is removed, killing the species
with lower fitness. We show that there is a critical fitness $f_c$ below which
the number of species hits zero i.o. and above of which this number goes to
infinity. We prove uniform convergence for the distribution of surviving
species and describe the phenomena which could not be observed in previous
works with uniformly distributed fitness.
