Title:Divergent evolution paths of different genetic families in the Penna model

Abstract: We present some results of simulations of population growth and evolution, using the standard asexual Penna model, with individuals characterized by a string of bits representing a genome containing some possible mutations. After about 20000 simulation steps, when only a few genetic families are still present from among rich variety of families at the beginning of the simulation game, strong peaks in mutation distribution functions are observed. This known effect is due to evolution rules with hereditary mechanism. The birth and death balance in the simulation game also leads to elimination of families specified by different genomes. Number of families $G(t)$ versus time $t$ follow the power 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, when only 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 that this discrepancy may be due to two different time scales in simulations - initial stages follow the $n\approx-1$ law, yet for large number of simulation steps we get $n\approx-2$, providing random initial population was sufficiently big to allow for still reliable statistical analysis. The $n\approx-1$ evolution stage seems to be associated with the Verhulst mechanism of population elimination due to the limited environmental capacity - when the standard evolution rules were modified, we observed a plateau ($n=0$) in the power law in short time scale, again followed by $n\approx -2$ law for longer times. The modified model uses birth rate controlled by the current population instead of the standard Verhulst death factor.