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Abstract
The occurrence of thresholds for error propagation in asexually replicating populations
is investigated by means of a simple birth and death model as well as by numerical
simulation. Previous results derived for infinite population sizes are extended to
finite populations. Here, replication has to be more accurate than in infinitely large
populations because the master sequence can be lost not only by accumulation of errors--similar
to the loss of wildtype through the operation of Muller's ratchet--but also by natural
fluctuations. An analytical expression is given which allows straight computation
of highly accurate values of error thresholds. The error threshold can be expanded
in a power series of the reciprocal square root of the population size and thus increases
with 1 square root of N in sufficiently large populations.