Optimal Mutation Rate Research Articles

SOME PROBLEMS WITH THE EVOLUTION OF SEX

During the last ten years John Maynard Smith and colleagues at the University of Sussex have reexplored some old models and developed new models for a variety of problems associated with genetic systems. These contributions have been collected together, expanded with some history and natural history, and presented as The Evolution of Sex. The first chapter provides a particularly lucid introduction to the problem beginning with the cost of producing males and proceeding to a discussion of the various long and short term advantages which have been attributed to sex and recombination. Maynard Smith also sketches out a possible model of the origin of sex, but emphasizes that the primary problem of the book is the maintenance of sex. Subsequent chapters (ten) follow the format of an introduction to the problem, the presentation of a model, and the discussion of selected biological observations. The major models or problems considered in these chapters are the flux of favorable or unfavorable mutations, parthenogenesis and evolutionary potential, selection for changes in the rate of recombination, sib-competition and unpredictable environments, recombination and hitch-hiking, hermaphroditism, anisogamy and sex ratio, sexual selection and optimal mutation rates. Maynard Smith's forte of making the steps by which conclusions emerge from assumptions followable for individuals without sophisticated knowledge is well represented in these chapters. Despite the positive features of the clear statement of the problem and understandable presentation of the models, many readers may feel that not much progress in understanding the origin and maintenance of sex has been made. This major fault is admitted by the author in the preface where he states, my mind is not made up and is not clear to me whether the short term selective forces I discuss are sufficient to account for the facts, or whether models of a qualitatively different kind are needed. While it is frequently more satisfying to finish a book with a focused theme, it is not just the lack of a theme which is disconcerting. The really discouraging thing about this book is that the diversity of the assumptions of the models and the flexible quantitative aspects of their predictions seem to offer no hope of

On the optimum mutation rate and optimum dose for practical mutation breeding

Optimum mutation rates for practical purpose were discussed based on the theoretically derived formulae, and mutagen doses giving the optimum mutation rates were estimated from the experiments reported hitherto. It was suggested that in cereal crops such as rice and barley, considerably low mutation rates as with the mutagen doses lower than 5 kR of λ or X rays and 2%·h of EMS are appropriate for obtaining directly applicable mutants. High mutation rates seem to be limited to the production of some rare breeding stocks.

A mathematical investigation of the induced mutation rate which is optimum for genetic improvement

Even if there is a high ratio of unfavorable to favorable mutations, there is still a finite probability that a favorable genotype will arise by mutation, if only favorable mutants happen to occur or if the effects of the favorable ones outweigh the effects of the unfavorable ones. The object of this investigation was to determine the mutation rate (termed the optimum mutation rate) that maximizes the probability of a favorable genotype. This was investigated for a diploid plant with pollen treatment followed by self-fertilization to essential homozygosity.The parameters considered are block (chromosome) number, number of loci per chromosome, ratio of favorable to unfavorable mutants, and amount of recombination (c). The exact ranges in the interval 0 ≤ c ≤ 0.5 have been obtained for the optimum mutation rate and the corresponding probability of obtaining an improved genotype.In later publications the effects of seed treatment and of random mating before self-fertilization are considered. It is found, and will be discussed in a later publication, that (1) seed treatment is better than pollen treatment, and (2) if the number of loci is sufficiently large the optimum dosage of the mutagen may be so small as to make artificial mutagenic treatment undesirable.

A Darwinian evolutionary system: I. Definition and basic properties

Biological evolution as conceived by the present synthetic theory of evolution is modelled by a mathematical system which consists of three arrays: the genotype and phenotype population and their environment, and four operators: selection, mutation, recombination, and alteration (describing the change of the environment by the population). An evolutionary process then could be represented as the cyclic iteration of these operations on the respective arrays. Some simple versions of this system were investigated by computer simulation. They exhibited the following properties. (i) Population fitness increased with the generation number. (ii) The evolutionary rate increased with variance of fitness. (iii) The evolutionary rate increased with the number of individuals, and decreased with the number of loci. (iv) The evolutionary rate increased with the selection pressure. (v) For a given system in a given state there existed an optimal mutation rate. (vi) Free recombination was optimal. (vii) The mutational load of fitness increased with the mutation rate, but was independent of the selection pressure; contrary to this, the mutational load of the population “morph” decreased with the selection pressure, i.e. one could compensate for the deleterious effect of mutation by strong selection. These rules applied to haploids with equal, unequal, non-epistatic, and epistatic gene effect, and also to diploids. It was found that epistatic gene effect for relatively low mutation rates slows down evolution, whereas unequal gene effect enhances it. Diploids were not found to be superior to haploids in evolutionary terms, except in the case of diploids with dominant gene action for very small population sizes. The results are discussed with regard to their applicability to the simulation of more complex evolutionary phenomena.

Natural Selection and Mutability

In sexual organisms, alleles increasing the mutation rate of the entire genome are invariably selected against, whereas in asexual organisms such "general mutators" are favored if they adjust the mutation rate closer to an optimum balancing the advantages of responsiveness to environmental change against those of a small mutational load. Unless very small selective pressures are effective, it seems that no mechanisms exist to establish optimum mutation rates in sexual organisms.

Zum Wirkungsmechanismus von 1-Nitroso-3-nitro-1-methylguanidin (NNMG) bei der Mutationsauslösung / The Mode of Action of 1-Nitroso-3-nitro-1-methyl-guanidine (NNMG) in Mutagenesis

1. The stability of NNMG with respect to pH was investigated. A maximum, with a half-life of 40 hours, was found in phosphate-citric acid buffer at pH 5. The stability decreases quickly with increasing concentration of hydroxyl ions. At the optimal mutation rate (pH 6, 37°, and shaking) the half-live is only 14,4 hours. 2. NNMG uptake (using labelled NNMG) and mutation rate in the range pH 3,5 — 8,0 show an optimum at pH 6,0/6,5 for both Escherichia coli B and the red ad- mutant E 188 of Saccharomyces cerevisiae. The pH-dependence of NNMG uptake and mutation rate is similar. 3. The methylation of nucleic acids by means of [3H]-methyl-NNMG or [14C] -methyl-NNMG in phosphate-citric acid at 37° while shaking increases with the growing concentration of hydroxyl ions. At the optimal mutation rate, however, NNMG methylates relatively poor. 4. Incorporation of radioactive NNMG into Escherichia coli B results in labelling of nucleic acids and proteins. The labelling of DNA shows an optimum at pH 6. The extent of methylation was found to be higher in vivo than in vitro. 5. In the presence of cysteine or β-mercaptoethanol nucleic acids are methylated more intensively than in the cysteine-free control experiment. After one hour the methylation was about twentyfold higher in the presence of cysteine or β-mercaptoethanol compared to the cysteine-free control experiment. The methylation in presence of SH-compounds shows a maximum at pH 6. The explanation of both a higher methylation rate and its optimum at pH 6 suggests the activation of methylation by means of sulphhydryl-groups.

On the evolutionary adjustment of spontaneous mutation rates

Evolutionary factors which tend to decrease the mutation rate through natural selection and those which tend to increase the mutation rate are discussed from the standpoint of population genetics. The author's theory of optimum mutation rate based on the principle of minimum genetic load is re-examined, assuming that mutation rate is adjusted in the course of evolution in such a way that the sum of mutational and substitutional load is minimized. Another hypothesis is also examined that only selection toward lowering the mutation rate is effective and the present mutation rate in each organism represents the physical or physiological limit that may be attained by natural selection.The possibility cannot be excluded that the spontaneous mutation rate is near the minimum that may be attained under the present mode of organization of the genetic material, and at the same time is not very far from the optimum in the sense of minimizing the genetic load.

Optimum mutation rate and degree of dominance as determined by the principle of minimum genetic load

It is demonstrated that by introducing what may be called the principle of minimum genetic load, the spontaneous mutation rate and the average degree of dominance of deleterious mutant genes may be derived theoretically from the total genetic damage and the rate of substitution of genes in horotelic evolution. The relations connecting these quantities may be expressed by a pair of equations: $$\left. \begin{gathered} \Sigma _\mu = \frac{{0 \cdot 3419E}}{{\bar h}}\left( {1 + 1 \cdot 720\bar h + ...} \right) \hfill \\ \bar h = 0 \cdot 6838\sqrt {\frac{E}{{2D}}} \left( {1 + 1 \cdot 018 \sqrt {\frac{E}{{2D}}} + ...} \right) \hfill \\ \end{gathered} \right\}$$ , where Σμ is the spontaneous mutation rate per gamete per generation,h is the average degree of dominance in fitness of deleterious mutant genes,D is the total mutational damage or approximately the rate of inbreeding depression in fitness per unit increase in the inbreeding coefficient andE is the rate of substitution of genes in horotelic evolution. The above formulae are sufficiently simple to be checked by observational data now available. The present result offers, as a byproduct, a new theory of dominance which can account for the partial dominance in fitness of the normal alleles of “recessive” deleterious genes.