  We investigate Eigen's model for the evolution of the genetic code of
microorganisms using a novel method based on population dynamics analysis. This
model, for a given number of offspring, determines long-term survival as a
function of the "genetic" information length and copy error probability. There
exists a maximum threshold for the quantity of information that can be
consistently preserved through the process of evolution within a population of
perfectly replicating sequences, meaning no errors are allowed. With our
formula, we expand upon the traditional error threshold formula of Eigen's
theory and introduce a new expression for general cases where the
self-reproduction process allows up to any integer number of copying errors per
digit per replication step.
