Using an artiicial system of self-replicating strings, we show a correlation between the age of a genotype and its abundance that reeects a punctuated rather than gradual picture of evolution, as suggested long ago by Willis. In support of this correlation, we measure genotype abundance distributions and nd universal coee-cients. Finally, we propose a simple stochastic model which describes the...

The structure of a self-similar group G naturally gives rise to a transformation which assigns to any probability measure μ on G and any word w in the alphabet of the group a new probability measure μ. If μ is a convex combination of μ and the δ-measure at the group identity, then the asymptotic entropy of the random walk (G,μ) vanishes; therefore, the random walk is Liouville and the group G i...