Power law dynamics in genealogical graphs

Abstract

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 cannot 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.