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Updated: May 14, 2026

Isolation of Fidelity Variants of RNA Viruses and Characterization of Virus Mutation Frequency
Published on: June 16, 2011
Virus replication as a phenotypic version of polynucleotide evolution
Fernando Antoneli1, Francisco Bosco, Diogo Castro
1Departamento de Informática em Saúde, Universidade Federal de São Paulo, São Paulo, SP, Brazil. fernando.antoneli@unifesp.br
Abstract:
In this paper, we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius et al. (Bull. Math. Biol. 46:239-262, 1985), in their study of polynucleotide evolution. By taking into account beneficial effects, we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model, which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull et al. (J. Virol. 18:2930-2939, 2007), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium", and transient. Finally, based on these quantitative results, we are able to draw some qualitative conclusions.
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