Effects of Finite Population Size and Other Stochastic Phenomena in Molecular Evolution

Polynucleotide replication is visualized as a stochastic process. Adaptive selection leads to optimization of mean replication rates in ensembles of molecules. Due to the intrinsic dynamics of replication, populations become uniform also in the absence of differences in rate constants. We called this process “random selection” in order to distinguish from adaption. Random selection leads to random drift particularly in small populations. Sequence information is stable in replicating systems only if the process of replication is sufficiently accurate. We apply the theory of multitype branching processes and derive a stochastic error threshold for replication. In addition, this theory allows to study accumulation of fluctuations. The total population size may fluctuate strongly in an ensemble of replicating molecules, but relative frequencies of individual molecular species approach a “law of large numbers” in sufficiently large populations.

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