Survival-extinction phase transition in a bit-string population with   mutation
  A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on environmental flexibility and genetic variability, the model exhibits a phase transtion between extinction and survival. The mean-field theory describes the infinite-size limit, while simulations are used to study quasi-stationary properties. 
Kathia M. Fehsenfeld, Ronald Dickman, and Americo T. Bernardes