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.     

Identification of positive selection signatures in pigs by comparing linkage disequilibrium variances

Selection affects the patterns of linkage disequilibrium (LD) around the site of a beneficial allele with an increase in LD among the hitchhiking alleles. Comparing the differences in regional LD between pig populations could help to identify putative genomic regions with potential adaptations for economic traits. In this study, using Illumina Porcine SNP60K BeadChip genotyping data from 207 Chinese indigenous, 117 South American village and 408 Large White pigs, we estimated the variation of genome‐wide LD between populations using the varld program. The top 0.1% standardized VarLD scores were used as a criterion for all comparisons, and compared with LD blocks, a total of four selection signatures on Sus scrofa chromosome (SSC) 7, 9, 13 and 14 were identified in all populations. These signatures overlapped with quantitative trait loci for linoleic acid content, age at puberty, number of muscle fibers per unit area, hip structure and body weight traits in pigs. Among them, one of the signatures (56.5–56.6 Mb on SSC7) in Large White pigs harbored the ADAMTSL3 gene, which is known to affect body length. The findings of this study seem to point toward recent selection in different pig populations. Further investigations are encouraged to confirm the selection signatures detected by varld in the present study.     

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     

Upsetting the balance on sex selection

It is widely assumed that the strongest case for permitting non‐medical sex selection is where parents aim at family balance. This piece criticizes one representative attempt to justify sex selection for family balance. Kluge (2007) assumes that some couples may seek sex selection because they hold discriminatory values, but this need not impugn those who merely have preferences, without evaluative commitments, for a particular sex. This is disputed by those who see any sex selection as inherently sexist because it upholds stereotypes about the sexes. This article takes an alternative approach. I argue that, even if we accept that preference‐based selection is unobjectionable, a policy permitting selection for family balancing does a poor job of distinguishing between value‐based and preference‐based selection. If we wish to permit only preference‐based sex selection we should seek to identify parents’ motives. If we wish to justify a family balancing policy, other arguments are needed.     

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.     

Sexual selection and sex linkage

Some animal groups, such as birds, seem prone to extreme forms of sexual selection. One contributing factor may be sex linkage of genes affecting male displays and female preferences. Here we show that sex linkage can have substantial effects on the genetic correlation between these traits and consequently for Fisher's runaway and the good-genes mechanisms of sexual selection. Under some kinds of sex linkage (e.g. Z-linked preferences), a runaway is more likely than under autosomal inheritance, while under others (e.g., X-linked preferences and autosomal displays), the good-genes mechanism is particularly powerful. These theoretical results suggest empirical tests based on the comparative method.