Self similarity in a model of genetic microevolution

A mathematical model of genetic microevolution is presented. The model stands for a population of genotypes evolving in the genotypic space. Its dynamics is governed by a master evolution equation which takes into account both the presence of a fluctuating fitness landscape and genotypic variations of the offspring with respect to the parents. We found that, under rather general conditions, the population growth rate exhibits self-similarity. This result provides a clue to universal scaling features of evolution in the large-time scale, as observed from paleobiological evidence.