Error thresholds of replication in finite populations mutation frequencies and the onset of Muller's ratchet.

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.