  Several populational networks present complex topologies when implemented in
evolutionary algorithms. A common feature of these topologies is the emergence
of a power law. Power law behavior with different scaling factors can also be
observed in genealogical networks, but we still can not satisfactorily describe
its dynamics or its relation to population evolution over time. In this paper,
we use an algorithm to measure the impact of individuals in several numerical
populations and study its dynamics of evolution through nonextensive
statistics. Like this, we show evidence that the observed emergence of power
law has a dynamic behavior over time. This dynamic development can be described
using a family of q-exponential distributions whose parameters are
time-dependent and follow a specific pattern. We also show evidence that
elitism significantly influences the power law scaling factors observed. These
results imply that the different power law shapes and deviations observed in
genealogical networks are static images of a time-dependent dynamic development
that can be satisfactorily described using q-exponential distributions.
