The two fundamental equations of quasispecies theory (243). The first equation describes the concentration of mutant i as a function of time, *x*_{i}(*t*), and accordingly, *x*_{k}(*t*) describes the concentration of mutant k. *A*_{i}, *D*_{i}, and *W*_{ik} are reaction rate parameters for the replication of i, for the degradation of i, and for the error-prone synthesis of i on k being the template, respectively. The factor *Q*_{i} expresses the fraction of correct replications producing i through copying of template i. Φ_{i} is a function which describes the flux of molecules as a consequence of the embedding of the replication-mutation system in some environment. In a simple flow reactor, Φ_{i} would be proportional to the concentration of i. This equation describes the dynamics of mutant generation within mutant spectra, as represented schematically in Fig. 2, 3, and 5. Extensions of the original equation have been developed, as described in references quoted in the text. The second equation is the error threshold relationship, in which ν_{max} is the maximum genetic complexity that can be maintained during replication, σ_{0} is the selectivity or superiority of the master sequence relative to the sequences of the mutant spectrum, and *q̄* is the average copying fidelity of the replicative system, with 1 − *q̄* being the average error rate per site and replication. The equation shows two important conditions: (i) the existence of a maximal sequence length ν_{max} for constant replication accuracy (left side) and (ii) the existence of a maximal error rate for constant sequence length (right side). Exceeding the limiting values leads to a breakdown of inheritance. The second case is of particular importance in virology since a drug-induced increase of the mutation rate may drive a virus population beyond the error threshold. This lies at the basis of lethal mutagenesis, depicted schematically in Fig. 12 and discussed in the text.

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