The optimal burst of mutation to create a phenotype.

Mutagenesis is commonly applied to genes and genomes to create novel variants with desired properties. This paper calculates the level of mutagenesis that maximizes the appearance of favorable mutants, assuming that the mutagenesis is applied in a single episode. The downside of mutagenesis is that a substantial fraction of mutations will destroy gene/genome function. The upside of mutagenesis is the production of beneficial mutations, but the desired phenotype may require that 1, 2 or more beneficial mutations be present simultaneously (the phenotype dimensionality). The optimum level of mutagenesis is sensitive to both properties. In the simplest model, the mutation optimum occurs when number of lethal equivalents per genome equals the phenotype dimensionality, a result first derived by Mundry and Gierer [1958. Production of mutations in tobacco mosaic virus by chemical treatment of its nucleic acid in vitro. Z. Vererbungsl. 89 (4), 614-630]. This level of mutation is shown to be an upper bound for the optimum in various extensions of the model, and the recovery of mutants is also reasonably tolerant to deviations from the optimum.