Self-organized criticality in an asexual model?

Recent work has shown that the distribution of steady state mutations for an asexual "bacteria" model has features similar to that seen in Self-Organized Critical (SOC) sandpile model of Bak et al. We investigate this coincidence further and search for "self-organized critical" state for bacteria but instead find that the SOC sandpile critical behavior is very sensitive; critical behavior is destroyed with small perturbations effectively when the absorption of sand is introduced. It is only in the limit when the length of the genome of the bacteria tends to infinity that SOC properties are recovered for the asexual model.