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.     

Deleterious mutation and the evolution of eusociality

Abstract.— Certain arguments concerning the evolution of eusociality form a classic example of the application of the principles of kin selection. These arguments center on the different degrees of relatedness of potential beneficiaries of an individual's efforts, for example a female's higher relatedness to her sisters than to her daughters in a haplodiploid system. This type of reasoning is insufficient to account for the evolution and maintainence of sexual reproduction, because parthenogenic females produce offspring that are more closely related to them than are offspring produced sexually. Among the forces invoked to explain sexual reproduction is deleterious mutation. This factor can be shown to favor eusociality as well, because siblings produced by helping carry fewer deleterious alleles on average than would offspring. The strength of this effect depends on the genomewide deleterious mutation rate, U, and on the selection coefficient, s, associated with deleterious alleles. For small s, the effect depends approximately on the product Us. This phenomenon illustrates that an assumption implicit in some analyses–that the relatedness of an individual to an actor is all that matters to its value to that actor–can fail for the evolution of eusociality as it does for the evolution of sex.     

Dynamics of a quantitative character subject only to stabilising selection

The implications of stabilising selection on a quantitative trait, in the absence of other evolutionary forces, are theoretically investigated in a randomly mating population. The dynamics of various statistics that describe the alleles contributing to the trait are determined and used to infer the behaviour of the trait. Dynamical solutions of the distribution of allelic effects and the distribution of the trait are found when all initial distributions of allelic effects are Gaussian and linkage disequilibria are neglected. Some results for the behaviour of the mean and the variance of genotypic effects of the population, when subject to a moving optimum, are derived. When the initial distributions of allelic effects are not Gaussian, but possess a small asymmetry, the mean and the variance of the allelic effects differ only slightly from the Gaussian results. By contrast, the third central moments of allelic effects, are, at all loci, strictly zero in the Gaussian case but are generally non-zero for non-symmetric initial distributions. To leading order in a quantitative measure of the asymmetry of the distribution, we determine the third central moment of allelic effects.     

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.     

Evolution of branched regulatory genetic pathways: directional selection on pleiotropic loci accelerates developmental system drift

Developmental systems are regulated by a web of interacting loci. One common and useful approach in studying the evolution of development is to focus on classes of interacting elements within these systems. Here, we use individual-based simulations to study the evolution of traits controlled by branched developmental pathways involving three loci, where one locus regulates two different traits. We examined the system under a variety of selective regimes. In the case where one branch was under stabilizing selection and the other under directional selection, we observed "developmental system drift": the trait under stabilizing selection showed little phenotypic change even though the loci underlying that trait showed considerable evolutionary divergence. This occurs because the pleiotropic locus responds to directional selection and compensatory mutants are then favored in the pathway under stabilizing selection. Though developmental system drift may be caused by other mechanisms, it seems likely that it is accelerated by the same underlying genetic mechanism as that producing the Dobzhansky-Muller incompatibilities that lead to speciation in both linear and branched pathways. We also discuss predictions of our model for developmental system drift and how different selective regimes affect probabilities of speciation in the branched pathway system.     

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     

Accumulation of deleterious mutations: additional Drosophila melanogaster estimates and a simulation of the effects of selection

We report an assay of egg-to-adult viability in full-sibling mutation accumulation (MA) lines derived from a completely homozygous population of Drosophila melanogaster and maintained for 210 generations. A simultaneous evaluation was also made of a large population derived from the same origin and maintained as a control for the same period. We also present computer simulations to explore the possible decline in viability of the control population due to mutation accumulation and the possible effect of selection within and between MA lines. For this purpose, we used two mutational models independent from the data analyzed and based on radically different assumptions. The first model implies a large number of mutations of small effect, whereas the second implies a much smaller number of mutations with much larger effects. The observed rate of decline in mean viability was very small but significant (0.077%). The rate of increase in among line variance (0.189 x 10(-3)) was similar to those obtained previously in the same lines. The simulation results indicated that a model of many mutations of small effect is incompatible with the evolution of the mean viability of the control and MA lines over generations, the distribution of line means after 210 generations of mutation accumulation, and the pattern of line extinction over generations. Basically, this model predicted a large drop in viability, both in the control and particularly the MA lines, that is not observed empirically. It also predicted a rate of line extinction too low in the early generations and too high in the later ones. In contrast, the model based on few mutations of large effect was generally consistent with all the observations.     

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 mutation matrix and the evolution of evolvability

Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, r(mu), the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at -1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.     

Fitness decline in spontaneous mutation accumulation lines of Caenorhabditis elegans with varying effective population sizes

The rate and fitness effects of new mutations have been investigated by mutation accumulation (MA) experiments in which organisms are maintained at a constant minimal population size to facilitate the accumulation of mutations with minimal efficacy of selection. We evolved 35 MA lines of Caenorhabditis elegans in parallel for 409 generations at three population sizes (N = 1, 10, and 100), representing the first spontaneous long-term MA experiment at varying population sizes with corresponding differences in the efficacy of selection. Productivity and survivorship in the N = 1 lines declined by 44% and 12%, respectively. The average effects of deleterious mutations in N = 1 lines are estimated to be 16.4% for productivity and 11.8% for survivorship. Larger populations (N = 10 and 100) did not suffer a significant decline in fitness traits despite a lengthy and sustained regime of consecutive bottlenecks exceeding 400 generations. Together, these results suggest that fitness decline in very small populations is dominated by mutations with large deleterious effects. It is possible that the MA lines at larger population sizes contain a load of cryptic deleterious mutations of small to moderate effects that would be revealed in more challenging environments.     

A method for estimating the effective number of loci affecting a quantitative character

A likelihood method is introduced that jointly estimates the number of loci and the additive effect of alleles that account for the genetic variance of a normally distributed quantitative character in a randomly mating population. The method assumes that measurements of the character are available from one or both parents and an arbitrary number of full siblings. The method uses the fact, first recognized by Karl Pearson in 1904, that the variance of a character among offspring depends on both the parental phenotypes and on the number of loci. Simulations show that the method performs well provided that data from a sufficient number of families (on the order of thousands) are available. This method assumes that the loci are in Hardy–Weinberg and linkage equilibrium but does not assume anything about the linkage relationships. It performs equally well if all loci are on the same non-recombining chromosome provided they are in linkage equilibrium. The method can be adapted to take account of loci already identified as being associated with the character of interest. In that case, the method estimates the number of loci not already known to affect the character. The method applied to measurements of crown–rump length in 281 family trios in a captive colony of African green monkeys (Chlorocebus aethiopus sabaeus) estimates the number of loci to be 112 and the additive effect to be 0.26 cm. A parametric bootstrap analysis shows that a rough confidence interval has a lower bound of 14 loci.     

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.     

Deleterious mutation in related species of the plant genus Amsinckia with contrasting mating systems

Theory for the evolution of modifiers of the rate of mutation suggests that a lower rate of mutation may evolve after the breakdown of mechanisms that enforce outcrossing. Mutation accumulation (MA) experiments were conducted to compare deleterious mutation parameters in two closely related species of the plant genus Amsinckia, a group that exhibits wide variation in the mating system. One of the two species studied (A. douglasiana) is predominantly outcrossed in natural populations, where as the other species (A. gloriosa) is predominantly self-pollinated. Progeny assays of flower number per plant from generation 1 lines (control) and generation 11 lines (MA treatment) were conducted in both species. Dry weight measurements of progeny from the control and MA treatment in A. douglasiana also were made. Estimation of mutation parameters was conducted using maximum likelihood under the assumption of a gamma distribution of mutational effects. The two species exhibited similar rates and effects of deleterious mutation affecting flower number. Estimates of mutation rate for dry weight in A. douglasiana are close to those for flower number. Overall, the estimates of mutation parameters observed in these species are intermediate within the range reported for fitness components in other eukaryotes. The results are discussed within the context of evolutionary change in deleterious mutation accompanying mating system evolution and with respect to previous estimates of mutation parameters based on assays of inbreeding depression and the assumption of mutation-selection equilibrium.     

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.