The Maintenance of Single-Locus Polymorphism. IV. Models with Mutation from Existing Alleles

The ability of viability selection to maintain allelic polymorphism is investigated using a constructionist approach. In extensions to the models we have previously proposed, a population is bombarded with a series of mutations whose fitnesses in conjunction with other alleles are functions of the corresponding fitnesses with a particular allele, the parent allele, already in the population. Allele frequencies are iterated simultaneously, thus allowing alleles to be driven to extinction by selection. Such models allow very high levels of polymorphism to evolve: up to 38 alleles in one case. Alleles that are lethal as homozygotes can evolve to surprisingly high frequencies. The joint evolution of allele frequencies and viabilities highlights the necessity to consider more than the current morphology of a population. Comparisons are made with the neutral theory of evolution and it is suggested that failure to reject neutrality using the Ewens-Watterson test cannot be regarded as evidence for the neutral theory.     

Models of Frequency-Dependent Selection with Mutation from Parental Alleles

Frequency-dependent selection (FDS) remains a common heuristic explanation for the maintenance of genetic variation in natural populations. The pairwise-interaction model (PIM) is a well-studied general model of frequency-dependent selection, which assumes that a genotype’s fitness is a function of within-population intergenotypic interactions. Previous theoretical work indicated that this type of model is able to sustain large numbers of alleles at a single locus when it incorporates recurrent mutation. These studies, however, have ignored the impact of the distribution of fitness effects of new mutations on the dynamics and end results of polymorphism construction. We suggest that a natural way to model mutation would be to assume mutant fitness is related to the fitness of the parental allele, i.e., the existing allele from which the mutant arose. Here we examine the numbers and distributions of fitnesses and alleles produced by construction under the PIM with mutation from parental alleles and the impacts on such measures due to different methods of generating mutant fitnesses. We find that, in comparison with previous results, generating mutants from existing alleles lowers the average number of alleles likely to be observed in a system subject to FDS, but produces polymorphisms that are highly stable and have realistic allele-frequency distributions.     

Joint Frequencies of Alleles Determined by Separate Formulations for the Mating and Mutation Systems

A method to calculate joint gene frequencies, which are the probabilities that two neutral genes taken at random from a population have certain allelic states, is developed taking into account the effects of the mating system and the mutation scheme. We assume that the mutation rates are constant in the population and that the mating system does not depend on allelic states. Under either--the condition that mutation rates are symmetric or that the mating unit is large and the mutation rate is small--the general formula is represented by two terms, one for the mating system and the other for the mutation scheme. The term for the mating system is expressed using the coancestry coefficient in the infinite allele model, and the term for the mutation scheme is a function of the eigenvalues and the eigenvectors of the mutation matrix. Several examples are presented as applications of the method, including homozygosity in a stepping-stone model with a symmetric mutation scheme.     

Effects of Mutation on Selection Limits in Finite Populations with Multiple Alleles

The ultimate response to directional selection (i.e., the selection limit) under recurrent mutation is analyzed by a diffusion approximation for a population in which there are k possible alleles at a locus. The limit mainly depends on two scaled parameters S (= 4Ns sigma a) and theta (= 4Nu) and k, the number of alleles, where N is the effective population size, u is the mutation rate, s is the selection coefficient, and sigma 2a is the variance of allelic effects. When the selection pressure is weak (S less than or equal to 0.5), the limit is given approximately by 2S sigma a[1 - (1 + c2)/k]/(theta + 1) for additive effects of alleles, where c is the coefficient of variation of the mutation rates among alleles. For strong selection, other approximations are devised to analyze the limit in different parameter regions. The effect of mutation on selection limits largely relies on the potential of mutation to introduce new and better alleles into the population. This effect is, however, bounded under the present model. Unequal mutation rates among alleles tend to reduce the selection limit, and can have a substantial effect only for small numbers of alleles and weak selection. The selection limit decreases as the mutation rate increases.     

The Mutational Specificity of Two Escherichia Coli Dnae Antimutator Alleles as Determined from Laci Mutation Spectra

In a companion study we have described the isolation of a series of mutants of Escherichia coli that replicate their DNA with increased fidelity. These mutants carry a mutation in the dnaE gene, encoding the α (polymerase) subunit of DNA polymerase III holoenzyme, which is responsible for the faithful replication of the bacterial chromosome. The mutants were detected as suppressors of the high mutability of a mutL strain (defective in postreplicative mismatch correction), in which mutations may be considered to arise predominantly from errors of DNA replication. To investigate the specificity of these antimutator effects, we have analyzed spectra of forward mutations in the N-terminal part of the lacI gene (i(-d) mutations) for two of the mutL dnaE derivatives (dnaE911 and dnaE915), as well as the control mutL strain. DNA sequencing of over 600 mutants revealed that in the mutL background both antimutator alleles reduce specifically transition mutations (A·T -> G·C and G·C -> A·T). However, the two alleles behave differently in this respect. dnaE911 reduces A·T -> G·C more strongly than it does G·C -> A·T, whereas the reverse is true for dnaE915. Second, dnaE911 does not appear to affect either transversion or frameshift mutations, whereas dnaE915 displays a distinct mutator effect for both. This mutator effect of dnaE915 for frameshift mutations was confirmed by the frequency of reversion of the trpE9777 frameshift mutation. The discovery that dnaE antimutator alleles possess distinct specificities supports the notion that DNA polymerases discriminate against errors along multiple pathways and that these pathways can be influenced independently.     

Derivative Alleles of the Arabidopsis Gibberellin-Insensitive (gai) Mutation Confer a Wild-Type Phenotype

The gai mutation of Arabidopsis confers a dwarf phenotype resembling that of mutants defective in gibberellin (GA) biosynthesis. However, gai mutant plants differ from GA biosynthesis mutants because they fail to respond to exogenous GAs and accumulate endogenous GA species to higher (rather than lower) levels than found in wild-type controls. The gai mutation, therefore, identifies a gene that modulates the response of plant cells to GA. We have mapped gai with respect to visible and restriction fragment length polymorphism (RFLP) markers from chromosome 1. To observe the phenotype exhibited by individuals potentially lacking wild-type (GAI) function, we have also isolated novel irradiation-induced derivative alleles of gai. When homozygous, these alleles confer a revertant phenotype that is indistinguishable from the wild type. gai is a semidominant mutation that exerts its effects either because it is a gain-of-function mutation or because it is a loss-of-function or reduced-function mutation. The genetic and physiological properties of the derivative alleles are considered with reference to these alternative modes of dominance of gai. Because these alleles are potential deletion or rearrangement mutations, together with the closely linked RFLP markers identified in the linkage mapping experiments, they provide useful resources for the isolation of the gai locus via a map-based cloning approach.     

The Deterministic Behavior of Self-Incompatibility Alleles

For a system of n self-incompatibility alleles, neglecting mutation and random drift, it is shown that the completely symmetric equilibrium is locally stable, and any allelic frequency less than q = 1+a-(see PDF), where a = [2(n - 1)]^-1, will increase. For all n, q > (2n)^-1, but if n > > 1, q ≈ (2n)^-1.     

The Sampling Distribution of Disease-Associated Alleles

A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.     

Selection in Finite Populations with Multiple Alleles. III. Genetic Divergence with Centripetal Selection and Mutation

Natural selection for an intermediate level of gene or enzyme activity has been shown to lead to a high frequency of heterotic polymorphisms in populations subject to mutation and random genetic drift. The model assumes a symmetrical spectrum of mutational variation, with the majority of variants having only minor effects on the probability of survival. Each mutational event produces a variant which is novel to the population. Allelic effects are assumed to be additive on the scale of enzyme activity, heterosis arising whenever a heterozygote has a mean level of activity closer to optimal than that of other genotypes in the population.-A new measure of genetic divergence between populations is proposed, which is readily interpreted genetically, and increases approximately linearly with time under centripetal selection, drift and mutation. The parameter is closely related to the rate of accumulation of mutational changes in a cistron over an evolutionary time span.-A survey of published data concerning polymorphic loci in man and Drosophila suggests than an alternative model, based on the superiority of hybrid molecules, is not of general importance. Thirteen loci giving rise to hybrid zones on electrophoresis have a mean heterozygote frequency of 0.22 +/-.06, compared with a value of 0.23 +/-.04 for 16 loci classified as producing no hybrid enzyme.     

两对等位基因群体熵的性质

研究了两对等位基因群体熵的性质,并对位点多样度D与基因相对信息量多样度S′(G)进行了比较研究．结果表明,在遗传变异的度量上,位点多样度D与基因相对信息量多样度S′(G)具有一致性,且S′(G)还具有信息学内涵．     

The Distribution of Mutant Alleles in a Subdivided Population

The results are presented from a simulation study of the spatial distribution of mutant alleles in a subdivided population. Statistical measures of the spatial pattern are defined in such a way that the same quantities could be measured in a geographic survey of allele frequencies in natural populations. Two types of quantities are discussed in this paper: (1) the occupancy distribution provides information on the presence or absence of the mutant in different numbers of demes; and (2) the conditional frequency distribution provides information about the extent of local differentiation when the mutant is present in different numbers of demes. Properties of these distributions are found for different types of natural selection acting on the mutant. Some results are presented for the same statistical measures based on samples of individuals from a fraction of the total number of demes. The simulation results for intermediate levels of the migration rates are compared with analytic results obtained on the limits of high and low migration rates. The main conclusion is that these measures of the spatial distribution of mutants in a subdivided population have simple properties that could provide a new perspective on data from natural populations.