Numerous empirical studies show that stress of various kinds induces a state of hypermutation in bacteria via multiple mechanisms, but theoretical treatment of this intriguing phenomenon is lacking. We used deterministic and stochastic models to study the evolution of stress-induced hypermutation in infinite and finite-size populations of bacteria undergoing selection, mutation, and random genetic drift in constant environments and in changing ones. Our results suggest that if beneficial mutations occur, even rarely, then stress-induced hypermutation is advantageous for bacteria at both the individual and the population levels and that it is likely to evolve in populations of bacteria in a wide range of conditions because it is favored by selection. These results imply that mutations are not, as the current view holds, uniformly distributed in populations, but rather that mutations are more common in stressed individuals and populations. Because mutation is the raw material of evolution, these results have a profound impact on broad aspects of evolution and biology.
K E Y W O R D S :Mathematical models/simulations, population genetics, phenotypic plasticity, mutagenesis, genetic variation, evolvability.Hypermutation-an increase in the genomic mutation rate-is a surprising phenomenon, as most mutations are deleterious, so mutators (alleles that induce hypermutation) will usually be surrounded by poor genetic backgrounds and experience a decrease in fitness (Sturtevant 1937;Kimura and Maruyama 1966;Funchain et al. 2000;Montanari et al. 2007). Consequently, selection against mutator alleles should drive the mutation rate to its lower limit (Kimura 1967;Tröbner and Piechocki 1984;Liberman and Feldman 1986;Drake 1991; but also see Dawson 1998;Johnson 1999;Lynch 2010). However, mutations can also help individuals escape stress. Theory (Kimura 1967;Leigh 1970Leigh , 1973Ishii et al. 1989;Sniegowski et al. 2000) and evolutionary experiments in vivo (Gibson et al. 1970;Sniegowski et al. 1997;Oliver 2000;Giraud et al. 2001;Loh et al. 2010;Gentile et al. 2011) and in silico (Taddei et al. 1997;Tenaillon et al. 1999;Heo and Shakhnovich 2010) show that in maladapted populations and in changing environments, mutators can increase in frequency when they "hitchhike" with the beneficial mutations they generate, and therefore the mutation rate evolves to a significantly higher level than the one predicted in well-adapted populations at a mutation-selection balance. Nevertheless, after adaptation is complete and the balance is restored, mutators decrease in frequency due to accumulation of deleterious mutations (Taddei et al. 1997;Sniegowski et al. 1997;Denamur and Matic 2006), thereby restoring the population-wide mutation rate to a lower level.Most models of the evolution of the mutation rate consider only mutators that constitutively increase mutation rates (reviewed in [Sniegowski et al. 2000], but see below for exceptions). Here we focus on stress-induced mutators (SIMs)-alleles that increase the mutation rate in response to...