Optimal mutation rate

Figure 11. The error threshold of replication and mutation in genotype space. Asexually reproducing populations with sufficiently accurate replication and mutation, approach stationary mutant distributions which cover some region in sequence space. The condition of stationarity leads to a (genotypic) error threshold. In order to sustain a stable population the error rate has to be below an upper limit above which the population starts to drift randomly through sequence space. In case of selective neutrality, i.e. the case of equal replication rate constants, the superiority becomes unity, Om = 1, and then stationarity is bound to zero error rate, pmax = 0. Polynucleotide replication in nature is confined also by a lower physical limit which is the maximum accuracy which can be achieved with the given molecular machinery. As shown in the illustration, the fraction of mutants increases with increasing error rate. More mutants and hence more diversity in the population imply more variability in optimization. The choice of an optimal mutation rate depends on the environment. In constant environments populations with lower mutation rates do better, and hence they will approach the lower limit. In highly variable environments those populations which approach the error threshold as closely as possible have an advantage. This is observed for example with viruses, which have to cope with an immune system or other defence mechanisms of the host.

The quasispecies model defines an optimal mutation rate for evolving populations (Eigen et al., 1988). At the critical mutation rate pmml (referred to as the error threshold), the distribution becomes too broad for selection to withstand the dispersion and it wanders stochastically on the fitness landscape. The optimal mutation rate for evolvability should be as close to pm Crit as possible without exceeding it. Indeed, it was found that viral mutation rates are very close to pm m,. By assuming that the mutation probability is the same at each residue, the error threshold in terms of mutation rate pm ai, was derived as... 

Fig. 6. The optimal DNA mutation rate as determined from a model that incorporates one-body and two-body fitness contributions (similar to a spin glass). The genetic code is included in the model. The data are for a N = 50 protein. The fitness improvement is the maximum change in fitness averaged over 10,000 landscapes. To compare the relative location of the optima, the curves have been scaled such that the optima are at 1.0. (a) The optimum mutation rate for the uncoupled landscape as the number of mutants screened increases M= 1000 (O), 10,000 ( ), and 50,000 (A), (b) The optimal mutation rate as the landscape ruggedness increases. The number of coupling interactions is 75 (O), 25 ( ), and 0 (A). As the landscape ruggedness increases, the optimal mutation rate decreases. Reprinted from Voigt et ol. (2000a), with permission.

Mtihlenbein (1992) studied the optimal mutation rate for genetic algorithms. By using a Markov chain analysis, he found that the optimal mutation rate pm is... 

Van Nimwegen and Crutchfield (1999a) have constructed a theory for the optimization of evolutionary searches involving epochal dynamics. They showed that the destabilization of the epochs due to fluctuations in the finite population occurs near the optimal mutation rate and population size. Under these conditions, the epoch time is only constrained by the diffusion of the population to a neutral network boundary. Often the optimal parameters are very close to the region in which destabilization is an important effect. This emphasizes that, to utilize neutral evolution, it is important to tune the evolutionary parameters (such as mutation rate and population size) so that the time spent in an epoch is minimized without destabilizing the search. 

The optimal mutation rate is strongly influenced by the finite number of mutants that can be screened. A smooth fitness landscape implies that many mutations can be accumulated without disrupting the fitness. 

This has the effect of lowering the required library size to sample a higher mutation rate. As the sequence ascends the fitness landscape, the optimal mutation rate decreases as the probability of discovering improved mutations also decreases. Highly coupled regions require that many mutations be simultaneously made to generate a positive mutant. Therefore, positive mutations are discovered at uncoupled positions as the fitness of the parent increases. 

The optimal mutation rate depends on fitness of the parental sequence. For a sub-... 

It is possible to recombine any number of parent genes with the available methods, which raises the question of what is the optimal number. Similar to determining the optimal mutation rate for random mutagenesis, the answer will depend on the number of screened mutants and the additivity of the combined mutations. It could be advantageous to screen all the permutations of mutations from the parents. Assuming independent and additive recombination, the probability Pd that an offspring has d mutations is given by... 

Bak, T. Optimal Mutation Rates In Genetic Search. In Proceedings Of The fifth International Conference On Genetic Algorithms Forrest, S. Ed. Morgan Kaufmann Urbana-Champaign, 1993 pp 2-8. 

---