Genetic variability under mutation selection balance

A fundamental problem in evolutionary genetics is understanding how high levels of genetic variation in quantitative traits are maintained in natural populations. Variation is removed by the natural selection of individuals with optimal phenotypes and is recovered by mutation; however, previous analyses had indicated that a mutation-selection balance was insufficient to maintain observed levels of genetic variation in these traits. Using more general models, however, it has recently been shown that it is indeed a sufficient mechanism. These models can be used to explore other phenomena in evolutionary biology.     

The effects of demography and linkage on the estimation of selection and mutation parameters

We explore the effects of demography and linkage on a maximum-likelihood (ML) method for estimating selection and mutation parameters in a reversible mutation model. This method assumes free recombination between sites and a randomly mating population of constant size and uses information from both polymorphic and monomorphic sites in the sample. Two likelihood-ratio test statistics were constructed under this ML framework: LRTγ for detecting selection and LRTκ for detecting mutational bias. By carrying out extensive simulations, we obtain the following results. When mutations are neutral and population size is constant, LRTγ and LRTκ follow a chi-square distribution with 1 d.f. regardless of the level of linkage, as long as the mutation rate is not very high. In addition, LRTγ and LRTκ are relatively insensitive to demographic effects and selection at linked sites. We find that the ML estimators of the selection and mutation parameters are usually approximately unbiased and that LRTκ usually has good power to detect mutational bias. Finally, with a recombination rate that is typical for Drosophila, LRTγ has good power to detect weak selection acting on synonymous sites. These results suggest that the method should be useful under many different circumstances.     

Detecting positive selection from genome scans of linkage disequilibrium

Background

During the lifetime of a fermenter culture, the soil bacterium S. coelicolor undergoes a major metabolic switch from exponential growth to antibiotic production. We have studied gene expression patterns during this switch, using a specifically designed Affymetrix genechip and a high-resolution time-series of fermenter-grown samples.

Results

Surprisingly, we find that the metabolic switch actually consists of multiple finely orchestrated switching events. Strongly coherent clusters of genes show drastic changes in gene expression already many hours before the classically defined transition phase where the switch from primary to secondary metabolism was expected. The main switch in gene expression takes only 2 hours, and changes in antibiotic biosynthesis genes are delayed relative to the metabolic rearrangements. Furthermore, global variation in morphogenesis genes indicates an involvement of cell differentiation pathways in the decision phase leading up to the commitment to antibiotic biosynthesis.

Conclusions

Our study provides the first detailed insights into the complex sequence of early regulatory events during and preceding the major metabolic switch in S. coelicolor, which will form the starting point for future attempts at engineering antibiotic production in a biotechnological setting.     

The effect of recurrent mutation on the linkage disequilibrium under a selective sweep

A selective sweep describes the reduction of diversity due to strong positive selection. If the mutation rate to a selectively beneficial allele is sufficiently high, Pennings and Hermisson (Mol Biol Evol 23(5):1076–1084, 2006a) have shown, that it becomes likely, that a selective sweep is caused by several individuals. Such an event is called a soft sweep and the complementary event of a single origin of the beneficial allele, the classical case, a hard sweep. We give analytical expressions for the linkage disequilibrium (LD) between two neutral loci linked to the selected locus, depending on the recurrent mutation to the beneficial allele, measured by D and ${\widehat{\sigma_D^2}}$ , a quantity introduced by Ohta and Kimura (Genetics 63(1):229–238, 1969), and conclude that the LD-pattern of a soft sweep differs substantially from that of a hard sweep due to haplotype structure. The analytical results are compared with simulations.     

The effect of linkage on sample size determination for multiple trait selection

Sufficient sample sizes are needed in breeding programs to be confident, with a specified probability , of obtaining a specified number of plants of a desired genotype in segregating populations. We develop a method of determining the minimum sample size needed to produce, with specified probability , at least m individuals of a desired genotype. This method takes into consideration factors affecting differential selection of gametes, segregation at a single locus, and linkage among the loci of interest. We first consider the effects in the gametophyte (haploid level) of fitness and linkage on the frequencies of alleles at two linked loci, then at three or more linked loci. The probability of obtaining at least m successes, or occurrences of the desired allele, among n gametes is given by a formula based on the binomial distribution. This probability is affected by fitness and linkage through their impact on the probability that a single randomly chosen gamete is of the desired type. Using an extension of this approach, we examine the effects of the altered allelic frequencies on the likelihood of obtaining the desired genotype from a randomly chosen pair of gametes in the sporophyte (diploid level). A table and a figure show the sample size required to produce, with probability 0.95, m individuals of the desired g enotype or phenotype, as a function of m and the probability that a randomly selected individual is of the desired type.BU-1031-MC in the Technical Report Series of the Biometrics Unit, Cornell University, Ithaca, New York 14853     

The effect of selection on genetic balance when the population size is varying

It is known that a reformulation for variable population size of the classical Sewall Wright model for balance between two genotypes can lead, under some circumstances, to a situation of balanced polymorphism when there is no selection present. In this note it is shown that the presence of selection prohibits the possibility of balance and assures ultimate homozygosity with probability one.     

The balance between pleiotropic mutation and selection,when alleles have discrete effects

The theory of pleiotropic mutation and selection is investigated and developed for a large population of asexual organisms. Members of the population are subject to stabilising selection on Omega phenotypic characters, which each independently affect fitness. Pleiotropy is incorporated into the model by allowing each mutation to simultaneously affect all characters. To expose differences with continuous-allele models, the characters are taken to originate from discrete-effect alleles and thus have discrete genotypic effects. Each character can take the values nxDelta where n=0,+/-1,+/-2, em leader, and the splitting in character effects, Delta, is a parameter of the model. When the distribution of mutant effects is normally distributed around the parental value, and Delta is large, a "stepwise" model of mutation arises, where only adjacent trait effects are accessible from a single mutation. The present work is primarily concerned with the opposite limit, where Delta is small and many different trait effects are accessible from a single mutation.In contrast to what has been established for continuous-effect models, discrete-effect models do not yield a singular equilibrium distribution of genotypic effects for any value of Omega. Instead, for different values of Omega, the equilibrium frequencies of trait values have very different dependencies on Delta. For Omega=1 and 2, decreasing Delta broadens the width of the frequency distribution and hence increases the equilibrium level of polymorphism. For all sufficiently large values of Omega, however, decreasing Delta decreases the width of the frequency distribution and the equilibrium level of polymorphism. The connection with continuous trait models follows when the limit Delta-->0 is considered, and a singular probability density of trait values is obtained for all sufficiently large Omega.     

Genetic linkage and natural selection

The prevalence of recombination in eukaryotes poses one of the most puzzling questions in biology. The most compelling general explanation is that recombination facilitates selection by breaking down the negative associations generated by random drift (i.e. Hill–Robertson interference, HRI). I classify the effects of HRI owing to: deleterious mutation, balancing selection and selective sweeps on: neutral diversity, rates of adaptation and the mutation load. These effects are mediated primarily by the density of deleterious mutations and of selective sweeps. Sequence polymorphism and divergence suggest that these rates may be high enough to cause significant interference even in genomic regions of high recombination. However, neither seems able to generate enough variance in fitness to select strongly for high rates of recombination. It is plausible that spatial and temporal fluctuations in selection generate much more fitness variance, and hence selection for recombination, than can be explained by uniformly deleterious mutations or species-wide selective sweeps.     

Stabilizing selection and linkage disequilibrium

An approach to the investigation of the evolution of quantitative traits on the basis of analysis of two-locus marginal systems dynamics has been developed. It has been shown that under stabilizing selection the "quasi-stationary" state is quickly reached and maintained continuously. The "quasi-stationary" state is characterized by small changes in allele frequencies and by linkage disequilibrium that significantly decreases genotypic variance. Equations defining the role of linkage disequilibrium in the stationary state of mutation-selection balance are derived.     

Examining the effect of linkage disequilibrium on multipoint linkage analysis

Most linkage programs assume linkage equilibrium among multiple linked markers. This assumption may lead to bias for tightly linked markers where strong linkage disequilibrium (LD) exists. We used simulated data from Genetic Analysis Workshop 14 to examine the possible effect of LD on multipoint linkage analysis. Single-nucleotide polymorphism packets from a non-disease-related region that was generated with LD were used for both model-free and parametric linkage analyses. Results showed that high LD among markers can induce false-positive evidence of linkage for affected sib-pair analysis when parental data are missing. Bias can be eliminated with parental data and can be reduced when additional markers not in LD are included in the analyses.     

Human dental reduction: natural selection or the probable mutation effect

Dental reduction has been sufficiently widespread among human populations to render the phenomenon of reduced tooth size worthy of scientific explanation. One of the most controversial models invoked to explain structural reduction in organisms is referred to as the "probable mutation effect" (PME). According to this model, structures no longer functional owing to ecological or cultural changes will experience a relaxation of selection pressure, permitting an accumulation of mutations in the population that inevitably will result in the reduction in size or the loss of the concerned structure. Although the PME continues to be offered as a viable explanation of human dental reduction, it is based upon several premises that modern dental clinical experience fails to support. Known enzyme defects resulting from mutations, factors predisposing to dental infections, and the deleterious effects of teeth that are too large or too small reveal that the PME does not logically account for the reduction of tooth size. Given such information, this paper proposes models of dental reduction based upon natural selection, which, unlike the PME, are testable in both modern and archaeological populations. The integration of clinical and skeletal data permits a more thorough understanding of dental reduction in the hominid fossil record.     

Clone selection and the mutation rate

A statistical model for mutation and selection is formulated for organisms that reproduce by division. The mutation rate that optimizes the probability of clone survival is approximated using the theory of branching processes. However, it is shown by example that this optimizing mutation rate need not be the most advantageous mutation rate. The principle that selection favors those modifying features that optimize the probability of clone survival is thereby shown to be of limited applicability.