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We present some results of simulations of population growth and evolution,using the standard asexual Penna model, with individuals characterized by astring of bits representing a genome containing some possible mutations. Afterabout 20000 simulation steps, when only a few genetic families are stillpresent from among rich variety of families at the beginning of the simulationgame, strong peaks in mutation distribution functions are observed. This knowneffect is due to evolution rules with hereditary mechanism. The birth and deathbalance in the simulation game also leads to elimination of families specifiedby different genomes. Number of families $G(t)$ versus time $t$ follow thepower law, $G \propto t^n$. Our results show the power coefficient exponent $n$is changing as the time goes. Starting from about --1, smoothly achieves about--2 after hundreds of steps, and finally has semi-smooth transition to 0, whenonly one family exists in the environment. This is in contrast with constant$n$ about --1 as found, for example, in \cite{bib:evolution}. We suspect thatthis discrepancy may be due to two different time scales in simulations -initial stages follow the $n\approx-1$ law, yet for large number of simulationsteps we get $n\approx-2$, providing random initial population was sufficientlybig to allow for still reliable statistical analysis. The $n\approx-1$evolution stage seems to be associated with the Verhulst mechanism ofpopulation elimination due to the limited environmental capacity - when thestandard evolution rules were modified, we observed a plateau ($n=0$) in thepower law in short time scale, again followed by $n\approx -2$ law for longertimes. The modified model uses birth rate controlled by the current populationinstead of the standard Verhulst death factor

DIVERGENT EVOLUTION PATHS OF DIFFERENT GENETIC FAMILIES IN THE PENNA MODEL