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.     

The frequency of the perfect genotype in a population subject to pleiotropic mutation

We consider a large population of asexual organisms characterised by a number of quantitative traits that are subject to stabilising selection. Mutation is taken to act pleiotropically, with every mutation generally changing all of the traits under selection. We focus on the equilibrium distribution of the population, where mutation and selection are in balance. It has been previously established that the equilibrium distribution of genotypic effects may be anomalous, as it may contain a singular spike--a Dirac delta function--corresponding to a non-zero proportion of the population having exactly optimal genotypic values. In the present work, we present exact results for the case where three traits are under selection. These results give the equilibrium genetic variance of the population, and the proportion of the population that have the optimal genotype. This is achieved for two different spherically symmetric distributions of mutant effects. Additionally, a simple and robust numerical approach is also presented that allows the treatment of some other mutation distributions, where there are an arbitrary number of selected traits.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

A genome-wide scan for signatures of directional selection in domesticated pigs

Background

Animal domestication involved drastic phenotypic changes driven by strong artificial selection and also resulted in new populations of breeds, established by humans. This study aims to identify genes that show evidence of recent artificial selection during pig domestication.

Results

Whole-genome resequencing of 30 individual pigs from domesticated breeds, Landrace and Yorkshire, and 10 Asian wild boars at ~16-fold coverage was performed resulting in over 4.3 million SNPs for 19,990 genes. We constructed a comprehensive genome map of directional selection by detecting selective sweeps using an F_ST-based approach that detects directional selection in lineages leading to the domesticated breeds and using a haplotype-based test that detects ongoing selective sweeps within the breeds. We show that candidate genes under selection are significantly enriched for loci implicated in quantitative traits important to pig reproduction and production. The candidate gene with the strongest signals of directional selection belongs to group III of the metabolomics glutamate receptors, known to affect brain functions associated with eating behavior, suggesting that loci under strong selection include loci involved in behaviorial traits in domesticated pigs including tameness.

Conclusions

We show that a significant proportion of selection signatures coincide with loci that were previously inferred to affect phenotypic variation in pigs. We further identify functional enrichment related to behavior, such as signal transduction and neuronal activities, for those targets of selection during domestication in pigs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1330-x) contains supplementary material, which is available to authorized users.     

Assortative mating for a quantitative character

Phenotypic assortative mating is investigated for a character determined by additive loci without dominance and a stochastically independent environment. Conditional-expectation arguments are used to calculate the equilibrium values of the phenotypic variance and the correlation between sundry relatives. For the latter, it suffices to suppose that the regressions of an individual's genotype on his phenotype and of his phenotype on that of his mate are linear. For the former, linearity of the regression of the allelic effects on the phenotype is also posited. The biological implications of these assumptions are discussed.Supported by National Science Foundation Grant DEB81-03530     

Virtual mutation and directional evolution of anti-amoxicillin ScFv antibody for immunoassay of penicillins in milk

In this study, an anti-amoxicillin single chain variable fragment (ScFv) antibody was evolved by directional mutagenesis of a contact amino acid residue based on the analysis of virtual mutation. Comparison with its parental ScFv, the mutant showed highly improved affinity for 11 penicillins with up to 6-folds increased sensitivity. Then, its recognition mechanisms for the 11 drugs were studied by using molecular docking. Results showed that the mutant-penicillins intermolecular forces increased and the total binding energies decreased dramatically, which were responsible for the improvement of antibody sensitivity. The ScFv mutant was used to develop an indirect competitive enzyme linked immunosorbent assay for determination of the 11 drugs in milk. The limits of detection were in the range of 0.2–3.0 ng/mL, the crossreactivities were in the range of 31%–132%, and the recoveries from standards fortified blank milk were in the range of 65.7%–92.4%. This is the first study reporting the directional evolution of a ScFv antibody based on virtual mutation and the use of ScFv antibody for determination of penicillins in foods of animal origin.     

Long-term selection for a quantitative character in large replicate populations of Drosophila melanogaster

Summary Six replicate lines of Drosophila melanogaster, which had been selected for increased abdominal bristle number for more than 85 generations, were assayed by hierarchical analysis of variance and offspring on parent regression immediately after selection ceased, and by single-generation realised heritability after more than 25 generations of subsequent relaxed selection.Half-sib estimates of heritability in 5 lines were as high as in the base population and much higher than observed genetic gains would suggest, excluding lack of sufficient additive genetic variance as a cause of ineffective selection in these lines. Also, there was considerable diversity among the six lines in composition of phenotypic variability: in addition to differences in the additive genetic component, one or more of the components due to dominance, epistasis, sex-linkage or genotype-environment interaction appeared to be important in different lines.Even after relaxed selection, single-generation realised heritabilities in four lines were as high as in the base population. As a large proportion of total genetic gain must have been made by fixation of favourable alleles, the compensatory increase of genetic variability has been sought in a genetic model involving genes at low initial frequencies, enhancement of gene effects during selection and/or new mutations.     

Epistasis in a quantitative trait captured by a molecular model of transcription factor interactions

With technological advances in genetic mapping studies more of the genes and polymorphisms that underlie Quantitative Trait Loci (QTL) are now being identified. As the identities of these genes become known there is a growing need for an analysis framework that incorporates the molecular interactions affected by natural polymorphisms. As a step towards such a framework we present a molecular model of genetic variation in sporulation efficiency between natural isolates of the yeast, Saccharomyces cerevisiae. The model is based on the structure of the regulatory pathway that controls sporulation. The model captures the phenotypic variation between strains carrying different combinations of alleles at known QTL. Compared to a standard linear model the molecular model requires fewer free parameters, and has the advantage of generating quantitative hypotheses about the affinity of specific molecular interactions in different genetic backgrounds. Our analyses provide a concrete example of how the thermodynamic properties of protein-protein and protein-DNA interactions naturally give rise to epistasis, the non-linear relationship between genotype and phenotype. As more causative genes and polymorphisms underlying QTL are identified, thermodynamic analyses of quantitative traits may provide a useful framework for unraveling the complex relationship between genotype and phenotype.     

Testing the rare-alleles model of quantitative variation by artificial selection

The rare-alleles model of quantitative variation posits that a common allele (the ‘wild-type’) and one or more rare alleles segregate at each locus affecting a quantitative trait; a scenario predicted by several distinct evolutionary hypotheses. Single locus arguments suggest that artificial selection should substantially increase the genetic variance (Vg) if the rare-alleles model is accurate. This paper tests the ‘ΔVg prediction’ using a large artificial selection experiment on flower size of Mimulus guttatus. Vg for flower size does evolve, increasing with selection for larger flower while decreasing in the other direction. These data are consistent with a model in which flower size variation is caused by rare, partially dominant alleles. However, this explanation becomes increasingly tenuous when considered with other data (correlated responses to selection and the effects of inbreeding). A combination of modern (marker-based mapping) and classical (biometric) techniques will likely to be required to determine the distribution of allele frequencies at loci influencing quantitative traits.     

The causes of repeated genetic evolution

A general understanding of the evolutionary process is limited by the contingency of each evolutionary event, making it difficult, even retrospectively, to explain why things have unfolded the way they have. The repeated evolution of similar traits in organisms facing similar environmental conditions is a pervasive phenomenon, including for animal morphology, and is considered a strong evidence for adaptive evolution. Examples of repeated evolution of particular traits offer a unique opportunity to ask whether evolution has followed similar or different genetic paths. Case studies reveal that although multiple genetic paths were often possible to evolve a morphological trait, similar evolutionary trajectories have been followed repeatedly in independent lineages, suggesting that biases influence the course of genetic evolution. In the light of these examples we examine several factors influencing the genetic paths of adaptive evolution and in particular how the interplay between natural selection and genetic variations carves out predictable genetic trajectories of morphological evolution.     

An analytical model for the estimation of chromosome substitution effects in the offspring of individuals heterozygous at a segregating marker locus

Summary Use of marker genes for quantitative traits has been suggested as a supplement to selection for livestock species. Linkage relationships can be estimated by using data from offspring of a heterozygous parent, if offspring can be positively assigned segregation of one or the other of the marker alleles. In field data, some data on offspring can be characterized and used to estimate the difference in chromosome substitution effects, but other matings result in uncertain transfer of the marker alleles. In this study, an alternative estimation procedure is proposed that would allow incorporation of data on all offspring of a heterozygous parent, even those where chromosome segregation is ambiguous. If the frequency of the marker alleles is known in the population of mates of a heterozygous individual, the mean and variance of the heterozygous offspring can be used in a generalized leastsquares model to estimate the chromosome substitution effect. When gene frequencies are not known, maximum likelihood estimates can be obtained from the data for use in a conditional estimate. Monte Carlo simulations of data following the assumed genetic model were analyzed as proposed, and parameter estimates were characterized. Estimates of chromosome substitution effects were reasonable approximations of input values. Distributions of t-statistics testing the null hypothesis of no difference between marked chromosome segments were unbiased, with only slightly larger variance than expected. Addition of data from heterozygous offspring improved the efficiency of detection of chromosome substitution effects by more than four times when marker gene frequencies were low.     

A computational method to detect epistatic effects contributing to a quantitative trait

We develop a new computational method to detect epistatic effects that contribute to a complex quantitative trait. Rather than looking for epistatic effects that show statistical significance when considered in isolation, we search for a close approximation to the quantitative trait by a sum of epistatic effects. Our search algorithm consists of a sequence of random walks around the space of sums of epistatic effects. An important feature of our approach is that there is learning between random walks, i.e. the control mechanism that chooses steps in our random walks adapts to the experiences of earlier random walks. We test the effectiveness of our algorithms by applying them to synthetic datasets where the phenotype is a sum of epistatic effects plus normally distributed noise. Our test statistic is the rate of success that our methods achieve in identifying the underlying epistatic effects. We report on the effectiveness of our methods as we vary parameters that are intrinsic to the computation (length of random walks and degree of learning) as well as parameters that are extrinsic to the computation (number of markers, number of individuals, noise level, architecture of the epistatic effects).     

Speciation via habitat specialization: the evolution of reproductive isolation as a correlated character

Summary A diverse group of theoretical and empirical studies are integrated into a composite model of sympatric speciation via habitat specialization. It is shown that disruptive selection on a continuous distribution of habitat preference can lead to the evolution of prezygotic reproductive isolation as a correlated character. The form of selection eliminates the major theoretical objections to the process of sympatric speciation. The principal difference between this model and the allopatric model of speciation is that the initial barrier to gene flow between subpopulations is produced by the evolution of gaps in the phenotypic distribution of spatial/temporal habitat use, rather than an extrinsic geographical barrier.     

Inheritable nature of enological quantitative traits is demonstrated by meiotic segregation of industrial wine yeast strains

Wine yeast strains exhibit a wide variability in their technological properties. The large number of allelic variants and the high degree of heterozygosity explain this genetic variability found among the yeast flora. Furthermore, most enological traits are controlled by polygenic systems presenting complex interactions between the alleles. Taking this into account, we hypothesized that the meiotic segregation of such alleles from a given strain might generate a progeny population with very different technological properties. In this work, a population of 50 progeny clones derived from four industrial wine strains of Saccharomyces cerevisiae was characterized for three major enological traits: ethanol tolerance, volatile-acidity production and hydrogen sulphide production. For this purpose, reliable laboratory fermentation tests were developed in accordance with enological practice. A wide variability in the values of the various parameters was found among spore clones obtained after sporulation. Many clones presenting better aptitudes than the parental strains were obtained. Moreover, analysis of the progeny demonstrated that: (1) traits are in part inheritable; (2) traits are clearly polygenic; (3) broad relations of dominance/recessivity can be established. All these findings constitute an initial step for establishing breeding strategies for wine yeast improvement.     

Some additional results about polymorphisms in models of an additive quantitative trait under stabilizing selection

 The existence of two stable, symmetric (allelic frequency 0.5 in each locus) polymorphic states is demonstrated for a two-locus model of an additive quantitative trait under strong Gaussian selection. Linkage disequilibrium at one of the states is negative whereas it is positive at the other state. For a three-locus model, it is shown that in order to maintain a stable polymorphism in all three loci, selection must be sufficiently but not exces- sively strong relative to recombination. Also, positive linkage disequilibrium can be maintained in a three-locus model under stabilizing selection that is not very strong. Received 15 July 1995     

Directional mutation pressure,mutator mutations,and dynamics of molecular evolution

Using a general form of the directional mutation theory, this paper analyzes the effect of mutations in mutator genes on the G + C content of DNA, the frequency of substitution mutations, and evolutionary changes (cumulative mutations) under various degrees of selective constraints. Directional mutation theory predicts that when the mutational bias between A/T and G/C nucleotide pairs is equilibrated with the base composition of a neutral set of DNA nucleotides, the mutation frequency per gene will be much lower than the frequency immediately after the mutator mutation takes place. This prediction explains the wide variation of the DNA G + C content among unicellular organisms and possibly also the wide intragenomic heterogeneity of third codon positions for the genes of multicellular eukaryotes. The present analyses lead to several predictions that are not consistent with a number of the frequently held assumptions in the field of molecular evolution, including belief in a constant rate of evolution, symmetric branching of phylogenetic trees, the generality of higher mutation frequency for neutral sets of nucleotides, the notion that mutator mutations are generally deleterious because of their high mutation rates, and teleological explanations of DNA base composition. Presented at the NATO Advanced Research Workshop onGenome Organization and Evolution, Spetsai, Greece, 16–22 September 1992     

Sperm competition can drive a male-biased mutation rate

A pattern of male-biased mutation has been found in a wide range of species. The standard explanation for this bias is that there are greater numbers of mitotic cell divisions in the history of the average sperm, compared to the average egg, and that mutations typically result from errors made during replication. However, this fails to provide an ultimate evolutionary explanation for why the male germline would tolerate more mutations that are typically deleterious. One possibility is that if there is a tradeoff between producing large numbers of sperm and expending energetic resources in maintaining a lower mutation rate, sperm competition would select for males that produce larger numbers of sperm despite a higher resulting mutation rate. Here I describe a model that jointly considers the fitness consequences of deleterious mutation and mating success in the face of sperm competition. I show that a moderate level of sperm competition can account for the observation that the male germline tolerates a higher mutation rate than the female germline.     

Antibiotic resistance and the evolution of group-beneficial traits. II: a metapopulation model

Inspired by the evolution of antibiotic resistance in bacteria, we have developed a model that examines the evolution of "producers" (who secrete a substance that breaks down antibiotics) and non-producers. In a previous study, we found that frequency-dependent selection could favor an intermediate frequency of producers in a single, large population. Here we develop a metapopulation model that examines the evolution of producers and non-producers. Our results indicate that in a metapopulation with many groups, each of size N, the equilibrial frequency of producers decreases with group size. Even when N is high (e.g. 150 individuals/group), however, a significant frequency of producers is still predicted. We also found that the equilibrial frequency of producers increases as the minimum numbers of producers necessary to provide protection to non-producers increases. Lastly, increasing the benefit/cost ratio (b/c) for producers increases their equilibrial frequency.     

Insights from modeling protein evolution with context-dependent mutation and asymmetric amino acid selection

We develop an approximate maximum likelihood method to estimate flanking nucleotide context-dependent mutation rates and amino acid exchange-dependent selection in orthologous protein-coding sequences and use it to analyze genome-wide coding sequence alignments from mammals and yeast. Allowing context-dependent mutation provides a better fit to coding sequence data than simpler (context-independent or CpG "hotspot") models and significantly affects selection parameter estimates. Allowing asymmetric (nonreciprocal) selection on amino acid exchanges gives a better fit than simple dN/dS or symmetric selection models. Relative selection strength estimates from our models show good agreement with independent estimates derived from human disease-causing and engineered mutations. Selection strengths depend on local protein structure, showing expected biophysical trends in helical versus nonhelical regions and increased asymmetry on polar-hydrophobic exchanges with increased burial. The more stringent selection that has previously been observed for highly expressed proteins is primarily concentrated in buried regions, supporting the notion that such proteins are under stronger than average selection for stability. Our analyses indicate that a highly parameterized model of mutation and selection is computationally tractable and is a useful tool for exploring a variety of biological questions concerning protein and coding sequence evolution.