  We introduce a population dynamics model, where individual genomes are
represented by bit-strings. Selection is described by death probabilities which
depend on these genomes, and new individuals continuously replace the ones that
die, keeping the population constant. An offspring has the same genome as its
(randomly chosen) parent, except for a small amount of (also random) mutations.
Chance may thus generate a newborn with a genome that is better than that of
its parent, and the newborn will have a smaller death probability. When this
happens, this individual is a would-be founder of a new lineage. A new lineage
is considered created if its alive descendence grows above a certain previously
defined threshold. The time evolution of populations evolving under these rules
is followed by computer simulations and the probability densities of lineage
duration and size, among others, are computed. These densities show a
scale-free behaviour, in accordance with some conjectures in paleoevolution,
and suggesting a simple mechanism as explanation for the ubiquity of these
power-laws.
