Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Molecular markers of nuclear restoration gene Rf1 in sunflower using bulked segregant analysis-RAPD

Restoration of cytoplasmic male sterility (CMS) in sunflower was demonstrated to be controlled by polygenes by analysing 982 effective crosses among 109 self-crossed lines and 16 CMS lines. Two self-crossed lines and one CMS line with distinct genotypes were applied to creation of segregating populations for DNA bulks of the target gene Rfl. Bulked DNA was prepared in order to investigate single gene Rfl and its gene marker among polygenic characters at the same genetic background. Using 80 10-mer operon primers, 620 RAPD reactions were carried out between fertile and sterile DNA bulks. In about 800 loci, primary results showed that 8 were related to the restoration genes. Furthermore. 2 were confirmed as RAPD markers for gene Rfl by examining 9 maintenance and 7 restoration lines. This method is the improvement for bulked segregant analysis[1] with which markers of single gene of target can be identified rapidly among polygenic characters.     

Effects of Pleiotropy on Predictions concerning Mutation-Selection Balance for Polygenic Traits

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.     

Quantitative trait loci affecting a courtship signal in Drosophila melanogaster

Courtship plays a major role in the sexual isolation of species, yet the genetics underlying courtship behaviour are poorly understood. Here we analyse quantitative trait loci (QTL) for a major component of courtship song in recombinant inbred lines derived from two laboratory strains of Drosophila melanogaster. The total variance among lines exceeds that between parental strains, and is broadly similar to that seen among geographic strains of the Cosmopolitan form of this species. Previous studies of the quantitative genetics of fly song have implied a polygenic additive inheritance with numerous genes spread throughout the genome. We find evidence for only three significant QTLs explaining 54% of the genetic variance in total. Thus there is evidence for a few large effect genes contributing to the genetic variance among lines. Interestingly, almost all of the candidate song genes previously described for D. melanogaster do not coincide with our QTLs.     

The Genetic Covariance between Characters Maintained by Pleiotropic Mutations

A statistical genetic model of a multivariate phenotype is derived to investigate the covariation of pleiotropic mutations with additive effects under the combined action of phenotypic selection, linkage and the mating system. Equilibrium formulas for large, randomly mating populations demonstrate that, when selection on polygenic variation is much smaller than twice the harmonic mean recombination rate between loci with interacting fitnesses, linkage disequilibrium is negligible and pleiotropy is the main cause of genetic correlations between characters. Under these conditions, approximate expressions for the dynamics of the genetic covariances due to pleiotropic mutations are obtained. Patterns of genetic covariance between characters and their evolution are discussed with reference to data on polygenic mutation, chromosomal organization and morphological integration.     

The Influence of the Mating System on the Maintenance of Genetic Variability in Polygenic Characters

The traditional models of the effect of assortative mating and inbreeding on the genetic variance of polygenic characters (Fisher 1918; Wright 1921) presume that there is no natural selection or mutation. In a large population, the genetic variance determined by additive genes may then increase by up to a factor of two with local inbreeding, and even more with assortative mating. The classical models are still used to interpret data from natural populations. But contrary to their assumptions, most metrical characters in natural populations are usually thought to be under a type of selection which depletes polygenic variation. Mutation is then necessary to maintain genetic variation. The present models show that with the additional features of mutation and selection, in a large population, the mating system has no influence on the amount of genetic variability maintained by additive genes.     

Spatial patterns in the distributions of polygenic characters

The spatial patterns in the mean and variance of a quantitative character that result from the interaction of spatially varying, optimizing selection and gene flow are considered. The model analyzed is an extension of those of Kimura (1965) and Lande (1976) for the distribution of a quantitative character maintained in a population by independent mutations. For weak selection, it is shown that there is only a small effect of gene flow on the variance of the character and that the mean value changes on a length scale that is large compared to the average dispersal distance. As in models of clines in allele frequencies, it is possible to define a “characteristic length” in terms of the average dispersal distance and strength of selection. The characteristic length is the smallest length scale environmental change to which the mean value of the character can significantly respond. It is also shown that, for weak selection, an asymmetry in dispersal can result in a significant shift in location of a cline. By considering an infinite linear cline in optimal values, it is shown that gene flow can increase the variance only when there is sufficient mixing in each generation of individuals from locations with different means. A model of selection in different niches is also considered. There is an increase in variance due to the effective weakening of the intensity of selection because of the differences in optimal values in different niches.The implications of the different models for maintenance of genetic polymorphism are discussed. Under some conditions gene flow can produce a significant increase in heterozygosity. It is also argued that spatial variation in selection on a polygenic character can be much more effective in increasing heterozygosity than temporal variation because of the potentially greater increase in phenotypic variance. The difference between some of the results for polygenic characters from those of similar models of one and two locus systems is accounted for by the fact that for normally distributed polygenic characters, changes in the variance are effectively decoupled from changes in the mean.     

Genotypic dispersion and covariance between relatives under linkage disequilibrium

A random mating diploid population under linkage disequilibrium is considered. In the case of two diallelic loci, the problem about condition and joint distributions of genotypes of relatives being in arbitrary genetic relations is solved. Formulae of the partitioning of genotypic variance and covariance between relatives with respect to a polygenic character are inferred (in the case of many characters - of genotypic covariance matrix).     

Genes and environment

Many quantitative characters depend on the action of a large number of genes and environmental factors. The mode of inheritance of these characters is polygenic. The phenotypic variance of the character is the sum of the components, thus the genetic and the environmental variances (VP = VG + VE). The degree of genetic determination VG/VP and VE/VP are difficult to estimate in man. The heritability a related coefficient to VG/VP can be estimated from the degree of ressemblance between relatives. The heritability is the additive genetique variance as a proportion of the phenotypic variance. Polygenic threshold inheritance can account for the familial non mendelian distribution of multifactorial diseases.     

Robust variance-components approach for assessing genetic linkage in pedigrees.

To assess evidence for genetic linkage from pedigrees, I developed a limited variance-components approach. In this method, variability among trait observations from individuals within pedigrees is expressed in terms of fixed effects from covariates and effects due to an unobservable trait-affecting major locus, random polygenic effects, and residual nongenetic variance. The effect attributable to a locus linked to a marker is a function of the additive and dominance components of variance of the locus, the recombination fraction, and the proportion of genes identical by descent at the marker locus for each pair of sibs. For unlinked loci, the polygenic variance component depends only on the relationship between the relative pair. Parameters can be estimated by either maximum-likelihood methods or quasi-likelihood methods. The forms of quasi-likelihood estimators are provided. Hypothesis tests derived from the maximum-likelihood approach are constructed by appeal to asymptotic theory. A simulation study showed that the size of likelihood-ratio tests was appropriate but that the monogenic component of variance was generally underestimated by the likelihood approach.     

Complex segregation analysis of dental morphological variants

A set of 20 morphological variants of the dental crowns and four characteristics of the jaws are tested for probable mode of inheritance using the complex segregation analysis method of Morton et al. (Am. J. Hum. Genet. 23:602-611, 1971). Models tested include three two-allele single-locus models (dominant, codominant, and recessive) and a model employing the polychotomized normal distribution of liability (an additive polygenic model), with transmissibility estimated via maximum likelihood. Most of the traits studied are observed using ordinal scales with several grades, and many are tested using more than one dichotomy of their scale. These multiple analyses allow for an examination of such factors as trait incidence on the results of the statistical analysis. The results of the analysis yield propositions of major genes for 13 of the 24 traits examined. Two traits give good evidence of being polygenic in origin. The remaining nine characters present methodological problems that do not allow for a definite conclusion on their mode of inheritance at this time. The ability to test varying levels of transmissibility in the polygenic model allows for an estimation of the percentage of trait variance determined by familial factors. Estimates of transmissibility for all characters examined range from 0 to 1, with a mean of 0.36. These findings may suggest a large environmental role in the development of dental crown morphology. However, the possibility exists that difficulties in the ability to classify the expression of certain traits consistently result in overestimates of the environmental influences on the development of those characters.     

COMPARISON OF NON‐GAUSSIAN QUANTITATIVE GENETIC MODELS FOR MIGRATION AND STABILIZING SELECTION

The balance between stabilizing selection and migration of maladapted individuals has formerly been modeled using a variety of quantitative genetic models of increasing complexity, including models based on a constant expressed genetic variance and models based on normality. The infinitesimal model can accommodate nonnormality and a nonconstant genetic variance as a result of linkage disequilibrium. It can be seen as a parsimonious one‐parameter model that approximates the underlying genetic details well when a large number of loci are involved. Here, the performance of this model is compared to several more realistic explicit multilocus models, with either two, several or a large number of alleles per locus with unequal effect sizes. Predictions for the deviation of the population mean from the optimum are highly similar across the different models, so that the non‐Gaussian infinitesimal model forms a good approximation. It does, however, generally estimate a higher genetic variance than the multilocus models, with the difference decreasing with an increasing number of loci. The difference between multilocus models depends more strongly on the effective number of loci, accounting for relative contributions of loci to the variance, than on the number of alleles per locus.     

Genetic Markers and Quantitative Genetic Variation in Medicago Truncatula (Leguminosae): A Comparative Analysis of Population Structure

Two populations of the selfing annual Medicago truncatula Gaertn. (Leguminoseae), each subdivided into three subpopulations, were studied for both metric traits (quantitative characters) and genetic markers (random amplified polymorphic DNA and one morphological, single-locus marker). Hierarchical analyses of variance components show that (1) populations are more differentiated for quantitative characters than for marker loci, (2) the contribution of both within and among subpopulations components of variance to overall genetic variance of these characters is reduced as compared to markers, and (3) at the population level, within population structure is slightly but not significantly larger for markers than for quantitative traits. Under the hypothesis that most markers are neutral, such comparisons may be used to make hypotheses about the strength and heterogeneity of natural selection in the face of genetic drift and gene flow. We thus suggest that in these populations, quantitative characters are under strong divergent selection among populations, and that gene flow is restricted among populations and subpopulations.     

Using the mixed model for interval mapping of quantitative trait loci in outbred line crosses

Interval mapping by simple regression is a powerful method for the detection of quantitative trait loci (QTLs) in line crosses such as F2 populations. Due to the ease of computation of the regression approach, relatively complex models with multiple fixed effects, interactions between QTLs or between QTLs and fixed effects can easily be accommodated. However, polygenic effects, which are not targeted in QTL analysis, cannot be treated as random effects in a least squares analysis. In a cross between true inbred lines this is of no consequence, as the polygenic effect contributes just to the residual variance. In a cross between outbred lines, however, if a trait has high polygenic heritability, the additive polygenic effect has a large influence on variation in the population. Here we extend the fixed model for the regression interval mapping method to a mixed model using an animal model. This makes it possible to use not only the observations from progeny (e.g. F2), but also those from the parents (F1) to evaluate QTLs and polygenic effects. We show how the animal model using parental observations can be applied to an outbred cross and so increase the power and accuracy of QTL analysis. Three estimation methods, i.e. regression and an animal model either with or without parental observations, are applied to simulated data. The animal model using parental observations is shown to have advantages in estimating QTL position and additive genotypic value, especially when the polygenic heritability is large and the number of progeny per parent is small.     

QTL analysis of leaf morphological characters in a Quercus robur full-sib family (Q. robur × Q. robur ssp. slavonica)

The distinction between white oak species (section Quercus sensu stricto ) is largely based on leaf morphological characters. There is, however, considerable within-species variation and no single species-diagnostic character, possibly due to phenotypic plasticity and/or underlying genetic variation. The aim of the present study was to identify quantitative trait loci (QTL) underlying the high within-species variation for leaf morphological characters in an F₁ full-sib family derived from a cross between Q. robur and Q. robur ssp. slavonica . In accordance with an earlier QTL mapping study in an intraspecific Q. robur full-sib family, polygenic inheritance was detected for leaf morphological characters that are used to discriminate between the species Quercus robur and Q. petraea . QTLs were distributed over ten linkage groups, showed a moderate effect in terms of phenotypic variance explained (PVE) in the mapping pedigree (3.6–9.6%), but accounted for a considerable amount of the parental differences. Co-localisation of QTLs on the same linkage group in different genetic backgrounds was found for the number and percentage of intercalary veins (NV, PV) on linkage group 3 and for NV on linkage group 5, revealing a high congruence in the relative QTL positions. The generally low correspondence of the other QTLs in the different mapping pedigrees may be an effect of the genetic background and of the environment. In conclusion, leaf morphological characters were found to be under polygenic control, and a comparison to earlier published results led to the identification of two QTLs that were stable across different genetic backgrounds.     

QTL analysis of leaf morphological characters in a Quercus robur full-sib family (Q. robur x Q. robur ssp. slavonica)

The distinction between white oak species (section Quercus sensu stricto) is largely based on leaf morphological characters. There is, however, considerable within-species variation and no single species-diagnostic character, possibly due to phenotypic plasticity and/or underlying genetic variation. The aim of the present study was to identify quantitative trait loci (QTL) underlying the high within-species variation for leaf morphological characters in an F(1) full-sib family derived from a cross between Q. robur and Q. robur ssp. slavonica. In accordance with an earlier QTL mapping study in an intraspecific Q. robur full-sib family, polygenic inheritance was detected for leaf morphological characters that are used to discriminate between the species Quercus robur and Q. petraea. QTLs were distributed over ten linkage groups, showed a moderate effect in terms of phenotypic variance explained (PVE) in the mapping pedigree (3.6-9.6%), but accounted for a considerable amount of the parental differences. Co-localisation of QTLs on the same linkage group in different genetic backgrounds was found for the number and percentage of intercalary veins (NV, PV) on linkage group 3 and for NV on linkage group 5, revealing a high congruence in the relative QTL positions. The generally low correspondence of the other QTLs in the different mapping pedigrees may be an effect of the genetic background and of the environment. In conclusion, leaf morphological characters were found to be under polygenic control, and a comparison to earlier published results led to the identification of two QTLs that were stable across different genetic backgrounds.     

Pleiotropic Stabilizing Selection Limits the Number of Polymorphic Loci to at Most the Number of Characters

We demonstrate that, in a model incorporating weak Gaussian stabilizing selection on n additively determined characters, at most n loci are polymorphic at a stable equilibrium. The number of characters is defined to be the number of independent components in the Gaussian selection scheme. We also assume linkage equilibrium, and that either the number of loci is large enough that the phenotypic distribution in the population can be approximated as multivariate Gaussian or that selection is weak enough that the mean fitness of the population can be approximated using only the mean and the variance of the characters in the population. Our results appear to rule out antagonistic pleiotropy without epistasis as a major force in maintaining additive genetic variation in a uniform environment. However, they are consistent with the maintenance of variability by genotype-environment interaction if a trait in different environments corresponds to different characters and the number of different environments exceeds the number of polymorphic loci that affect the trait.     

Linkage and the Maintenance of Heritable Variation by Mutation-Selection Balance

The role of linkage in influencing heritable variation maintained through a balance between mutation and stabilizing selection is investigated for two different models. In both cases one trait is considered and the interactions within and between loci are assumed to be additive. Contrary to most earlier investigations of this problem no a priori assumptions on the distribution of genotypic values are imposed. For a deterministic two-locus two-allele model with recombination and mutation, related to the symmetric viability model, a complete nonlinear analysis is performed. It is shown that, depending on the recombination rate, multiple stable equilibria may coexist. The equilibrium genetic and genic variances are calculated. For a polygenic trait in a finite population with a possible continuum of allelic effects a simulation study is performed. In both models the equilibrium genetic and genic variances are roughly equal to the house-of-cards prediction or its finite population counterpart as long as the recombination rate is not extremely low. However, negative linkage disequilibrium builds up. If the loci are very closely linked the equilibrium additive genetic variance is slightly lower than the house-of-cards prediction, but the genic variance is much higher. Depending on whether the parameters are in favor of the house-of-cards or the Gaussian approximation, different behavior of the genetic system occurs with respect to linkage.     

Integration of Random Forest with population‐based outlier analyses provides insight on the genomic basis and evolution of run timing in Chinook salmon (Oncorhynchus tshawytscha)

Anadromous Chinook salmon populations vary in the period of river entry at the initiation of adult freshwater migration, facilitating optimal arrival at natal spawning. Run timing is a polygenic trait that shows evidence of rapid parallel evolution in some lineages, signifying a key role for this phenotype in the ecological divergence between populations. Studying the genetic basis of local adaptation in quantitative traits is often impractical in wild populations. Therefore, we used a novel approach, Random Forest, to detect markers linked to run timing across 14 populations from contrasting environments in the Columbia River and Puget Sound, USA. The approach permits detection of loci of small effect on the phenotype. Divergence between populations at these loci was then examined using both principle component analysis and F_ST outlier analyses, to determine whether shared genetic changes resulted in similar phenotypes across different lineages. Sequencing of 9107 RAD markers in 414 individuals identified 33 predictor loci explaining 79.2% of trait variance. Discriminant analysis of principal components of the predictors revealed both shared and unique evolutionary pathways in the trait across different lineages, characterized by minor allele frequency changes. However, genome mapping of predictor loci also identified positional overlap with two genomic outlier regions, consistent with selection on loci of large effect. Therefore, the results suggest selective sweeps on few loci and minor changes in loci that were detected by this study. Use of a polygenic framework has provided initial insight into how divergence in a trait has occurred in the wild.