Fine mapping of multiple QTL using combined linkage and linkage disequilibrium mapping – A comparison of single QTL and multi QTL methods

Two previously described QTL mapping methods, which combine linkage analysis (LA) and linkage disequilibrium analysis (LD), were compared for their ability to detect and map multiple QTL. The methods were tested on five different simulated data sets in which the exact QTL positions were known. Every simulated data set contained two QTL, but the distances between these QTL were varied from 15 to 150 cM. The results show that the single QTL mapping method (LDLA) gave good results as long as the distance between the QTL was large (> 90 cM). When the distance between the QTL was reduced, the single QTL method had problems positioning the two QTL and tended to position only one QTL, i.e. a "ghost" QTL, in between the two real QTL positions. The multi QTL mapping method (MP-LDLA) gave good results for all evaluated distances between the QTL. For the large distances between the QTL (> 90 cM) the single QTL method more often positioned the QTL in the correct marker bracket, but considering the broader likelihood peaks of the single point method it could be argued that the multi QTL method was more precise. Since the distances were reduced the multi QTL method was clearly more accurate than the single QTL method. The two methods combine well, and together provide a good tool to position single or multiple QTL in practical situations, where the number of QTL and their positions are unknown.     

Detection of multiple QTL with epistatic effects under a mixed inheritance model in an outbred population

A quantitative trait depends on multiple quantitative trait loci (QTL) and on the interaction between two or more QTL, named epistasis. Several methods to detect multiple QTL in various types of design have been proposed, but most of these are based on the assumption that each QTL works independently and epistasis has not been explored sufficiently. The objective of the study was to propose an integrated method to detect multiple QTL with epistases using Bayesian inference via a Markov chain Monte Carlo (MCMC) algorithm. Since the mixed inheritance model is assumed and the deterministic algorithm to calculate the probabilities of QTL genotypes is incorporated in the method, this can be applied to an outbred population such as livestock. Additionally, we treated a pair of QTL as one variable in the Reversible jump Markov chain Monte Carlo (RJMCMC) algorithm so that two QTL were able to be simultaneously added into or deleted from a model. As a result, both of the QTL can be detected, not only in cases where either of the two QTL has main effects and they have epistatic effects between each other, but also in cases where neither of the two QTL has main effects but they have epistatic effects. The method will help ascertain the complicated structure of quantitative traits.     

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulæ for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.     

Targeted resequencing of a genomic region influencing tameness and aggression reveals multiple signals of positive selection

The identification of the causative genetic variants in quantitative trait loci (QTL) influencing phenotypic traits is challenging, especially in crosses between outbred strains. We have previously identified several QTL influencing tameness and aggression in a cross between two lines of wild-derived, outbred rats (Rattus norvegicus) selected for their behavior towards humans. Here, we use targeted sequence capture and massively parallel sequencing of all genes in the strongest QTL in the founder animals of the cross. We identify many novel sequence variants, several of which are potentially functionally relevant. The QTL contains several regions where either the tame or the aggressive founders contain no sequence variation, and two regions where alternative haplotypes are fixed between the founders. A re-analysis of the QTL signal showed that the causative site is likely to be fixed among the tame founder animals, but that several causative alleles may segregate among the aggressive founder animals. Using a formal test for the detection of positive selection, we find 10 putative positively selected regions, some of which are close to genes known to influence behavior. Together, these results show that the QTL is probably not caused by a single selected site, but may instead represent the joint effects of several sites that were targets of polygenic selection.     

侧翼标记基因型方差组分随不同选择强度的变化

从实际角度看,选择在用于标记-QTL连锁分析的实验群体中是较普遍存在的。为获得QTL位置及其效应的无偏估计,有必要研究选择对连锁分析实验所造成的影响。该文在侧翼标记情况下利用广泛使用的半同胞设计提出了3种方差组分,即标记组间方差、组内多基因方差和组内重组方差及其构成。着重从理论上研究了各方差组分在不同选择强度下的变化规律,阐明了选择对各方差组分的效应。结果表明,各方差组分对选择强度的变化很敏感。随着选择强度的增加,所有方差组分都以二次曲线方式有不同程度的下降。比较而言,标记组间方差组分下降最快,标记组内多基因方差下降较慢,组内重组方差下降最慢。这意味着QTL连锁分析功效的降低。所以在实际群体中应采取必要措施尽量避免选择的发生,从而消除选择对QTL连锁分析的负面效应。     

Prediction of identity by descent probabilities from marker-haplotypes

The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.     

High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F2 and Advanced Intercross Mice

Genetic influences on anxiety disorders are well documented; however, the specific genes underlying these disorders remain largely unknown. To identify quantitative trait loci (QTL) for conditioned fear and open field behavior, we used an F₂ intercross (n = 490) and a 34th-generation advanced intercross line (AIL) (n = 687) from the LG/J and SM/J inbred mouse strains. The F₂ provided strong support for several QTL, but within wide chromosomal regions. The AIL yielded much narrower QTL, but the results were less statistically significant, despite the larger number of mice. Simultaneous analysis of the F₂ and AIL provided strong support for QTL and within much narrower regions. We used a linear mixed-model approach, implemented in the program QTLRel, to correct for possible confounding due to familial relatedness. Because we recorded the full pedigree, we were able to empirically compare two ways of accounting for relatedness: using the pedigree to estimate kinship coefficients and using genetic marker estimates of “realized relatedness.” QTL mapping using the marker-based estimates yielded more support for QTL, but only when we excluded the chromosome being scanned from the marker-based relatedness estimates. We used a forward model selection procedure to assess evidence for multiple QTL on the same chromosome. Overall, we identified 12 significant loci for behaviors in the open field and 12 significant loci for conditioned fear behaviors. Our approach implements multiple advances to integrated analysis of F₂ and AILs that provide both power and precision, while maintaining the advantages of using only two inbred strains to map QTL.     

Modular Skeletal Evolution in Sticklebacks Is Controlled by Additive and Clustered Quantitative Trait Loci

Understanding the genetic architecture of evolutionary change remains a long-standing goal in biology. In vertebrates, skeletal evolution has contributed greatly to adaptation in body form and function in response to changing ecological variables like diet and predation. Here we use genome-wide linkage mapping in threespine stickleback fish to investigate the genetic architecture of evolved changes in many armor and trophic traits. We identify >100 quantitative trait loci (QTL) controlling the pattern of serially repeating skeletal elements, including gill rakers, teeth, branchial bones, jaws, median fin spines, and vertebrae. We use this large collection of QTL to address long-standing questions about the anatomical specificity, genetic dominance, and genomic clustering of loci controlling skeletal differences in evolving populations. We find that most QTL (76%) that influence serially repeating skeletal elements have anatomically regional effects. In addition, most QTL (71%) have at least partially additive effects, regardless of whether the QTL controls evolved loss or gain of skeletal elements. Finally, many QTL with high LOD scores cluster on chromosomes 4, 20, and 21. These results identify a modular system that can control highly specific aspects of skeletal form. Because of the general additivity and genomic clustering of major QTL, concerted changes in both protective armor and trophic traits may occur when sticklebacks inherit either marine or freshwater alleles at linked or possible “supergene” regions of the stickleback genome. Further study of these regions will help identify the molecular basis of both modular and coordinated changes in the vertebrate skeleton.     

A comparison of bivariate and univariate QTL mapping in livestock populations

This study presents a multivariate, variance component-based QTL mapping model implemented via restricted maximum likelihood (REML). The method was applied to investigate bivariate and univariate QTL mapping analyses, using simulated data. Specifically, we report results on the statistical power to detect a QTL and on the precision of parameter estimates using univariate and bivariate approaches. The model and methodology were also applied to study the effectiveness of partitioning the overall genetic correlation between two traits into a component due to many genes of small effect, and one due to the QTL. It is shown that when the QTL has a pleiotropic effect on two traits, a bivariate analysis leads to a higher statistical power of detecting the QTL and to a more precise estimate of the QTL''s map position, in particular in the case when the QTL has a small effect on the trait. The increase in power is most marked in cases where the contributions of the QTL and of the polygenic components to the genetic correlation have opposite signs. The bivariate REML analysis can successfully partition the two components contributing to the genetic correlation between traits.     

Methods for multiple-marker mapping of quantitative trait loci in half-sib populations

In this paper we consider the detection of individual loci controlling quantitative traits of interest (quantitative trait loci or QTLs) in the large half-sib family structure found in some species. Two simple approaches using multiple markers are proposed, one using least squares and the other maximum likelihood. These methods are intended to provide a relatively fast screening of the entire genome to pinpoint regions of interest for further investigation. They are compared with a more traditional single-marker least-squares approach. The use of multiple markers is shown to increase power and has the advantage of providing an estimate for the location of the QTL. The maximum-likelihood and the least-squares approaches using multiple markers give similar power and estimates for the QTL location, although the likelihood approach also provides estimates of the QTL effect and sire heterozygote frequency. A number of assumptions have been made in order to make the likelihood calculations feasible, however, and computationally it is still more demanding than the least-squares approach. The least-squares approach using multiple markers provides a fast method that can easily be extended to include additional effects.     

Changes in Variance Components of Flanking Marker Genotypes Under Varying Selection Intensities

Selection is practically ubiquitous during marker-QTL linkage analysis with an experimental population. Thus, it is necessary to investigate the impacts of selection upon linkage analyses in order to obtain unbiased estimates of QTL position and effect. In this article, by exploiting flanking markers through the widely applied half-sib design, we have developed the structures of three variance components, i.e., variance component between marker genotypes, polygenic variance component and recombinant variance component within marker genotypes. Changes in these variance components under varying selection intensities were investigated in this study to formulate the effects of selection on various variance components. Results showed clearly that all variance components presented were quite sensitive to changes in selection intensity. As selection intensity increased, all variance components declined by differing extents in a quadratic fashion. Comparatively speaking, the variance between marker genotypes decreased most drastically, followed by the polygenic variance within marker genotypes and then the recombinant variance within marker genotypes, which suggested a decrease of power for QTL linkage analysis. Therefore, steps should be taken to avoid as much as possible the presence of selection in real populations, so as to further eliminate the negative effects of selection on QTL linkage analysis.     

Bayesian QTL mapping using skewed Student-t distributions

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.     

Estimation of Effects of Quantitative Trait Loci in Large Complex Pedigrees

A method was derived to estimate effects of quantitative trait loci (QTL) using incomplete genotype information in large outbreeding populations with complex pedigrees. The method accounts for background genes by estimating polygenic effects. The basic equations used are very similar to the usual linear mixed model equations for polygenic models, and segregation analysis was used to estimate the probabilities of the QTL genotypes for each animal. Method R was used to estimate the polygenic heritability simultaneously with the QTL effects. Also, initial allele frequencies were estimated. The method was tested in a simulated data set of 10,000 animals evenly distributed over 10 generations, where 0, 400 or 10,000 animals were genotyped for a candidate gene. In the absence of selection, the bias of the QTL estimates was <2%. Selection biased the estimate of the Aa genotype slightly, when zero animals were genotyped. Estimates of the polygenic heritability were 0.251 and 0.257, in absence and presence of selection, respectively, while the simulated value was 0.25. Although not tested in this study, marker information could be accommodated by adjusting the transmission probabilities of the genotypes from parent to offspring according to the marker information. This renders a QTL mapping study in large multi-generation pedigrees possible.     

Estimation of genetic variance contributed by a quantitative trait locus: correcting the bias associated with significance tests

The Beavis effect in quantitative trait locus (QTL) mapping describes a phenomenon that the estimated effect size of a statistically significant QTL (measured by the QTL variance) is greater than the true effect size of the QTL if the sample size is not sufficiently large. This is a typical example of the Winners’ curse applied to molecular quantitative genetics. Theoretical evaluation and correction for the Winners’ curse have been studied for interval mapping. However, similar technologies have not been available for current models of QTL mapping and genome-wide association studies where a polygene is often included in the linear mixed models to control the genetic background effect. In this study, we developed the theory of the Beavis effect in a linear mixed model using a truncated noncentral Chi-square distribution. We equated the observed Wald test statistic of a significant QTL to the expectation of a truncated noncentral Chi-square distribution to obtain a bias-corrected estimate of the QTL variance. The results are validated from replicated Monte Carlo simulation experiments. We applied the new method to the grain width (GW) trait of a rice population consisting of 524 homozygous varieties with over 300 k single nucleotide polymorphism markers. Two loci were identified and the estimated QTL heritability were corrected for the Beavis effect. Bias correction for the larger QTL on chromosome 5 (GW5) with an estimated heritability of 12% did not change the QTL heritability due to the extremely large test score and estimated QTL effect. The smaller QTL on chromosome 9 (GW9) had an estimated QTL heritability of 9% reduced to 6% after the bias-correction.     

On the detection of imprinted quantitative trait loci in line crosses: effect of linkage disequilibrium

Imprinted quantitative trait loci (QTL) are commonly reported in studies using line-cross designs, especially in livestock species. It was previously shown that such parent-of-origin effects might result from the nonfixation of QTL alleles in one or both parental lines, rather than from genuine molecular parental imprinting. We herein demonstrate that if linkage disequilibrium exists between marker loci and nonfixed QTL, spurious detection of pseudo-imprinting is increased by an additional 40–80% in scenarios mimicking typical livestock situations. This is due to the fact that imprinting can be tested only in F₂ offspring whose sire and dam have distinct marker genotypes. In the case of linkage disequilibrium between markers and QTL, such parents have a higher chance to have distinct QTL genotypes as well, thus resulting in distinct padumnal and madumnal allele substitution effects, i.e., QTL pseudo-imprinting.     

A New Simple Method for Improving QTL Mapping Under Selective Genotyping

The selective genotyping approach, where only individuals from the high and low extremes of the trait distribution are selected for genotyping and the remaining individuals are not genotyped, has been known as a cost-saving strategy to reduce genotyping work and can still maintain nearly equivalent efficiency to complete genotyping in QTL mapping. We propose a novel and simple statistical method based on the normal mixture model for selective genotyping when both genotyped and ungenotyped individuals are fitted in the model for QTL analysis. Compared to the existing methods, the main feature of our model is that we first provide a simple way for obtaining the distribution of QTL genotypes for the ungenotyped individuals and then use it, rather than the population distribution of QTL genotypes as in the existing methods, to fit the ungenotyped individuals in model construction. Another feature is that the proposed method is developed on the basis of a multiple-QTL model and has a simple estimation procedure similar to that for complete genotyping. As a result, the proposed method has the ability to provide better QTL resolution, analyze QTL epistasis, and tackle multiple QTL problem under selective genotyping. In addition, a truncated normal mixture model based on a multiple-QTL model is developed when only the genotyped individuals are considered in the analysis, so that the two different types of models can be compared and investigated in selective genotyping. The issue in determining threshold values for selective genotyping in QTL mapping is also discussed. Simulation studies are performed to evaluate the proposed methods, compare the different models, and study the QTL mapping properties in selective genotyping. The results show that the proposed method can provide greater QTL detection power and facilitate QTL mapping for selective genotyping. Also, selective genotyping using larger genotyping proportions may provide roughly equivalent power to complete genotyping and that using smaller genotyping proportions has difficulties doing so. The R code of our proposed method is available on http://www.stat.sinica.edu.tw/chkao/.     

Mapping species differences for adventitious rooting in a <Emphasis Type="Italic">Corymbia torelliana</Emphasis> × <Emphasis Type="Italic">Corymbia citriodora</Emphasis> subspecies <Emphasis Type="Italic">variegata</Emphasis> hybrid

Quantitative trait loci (QTL) detection was carried out for adventitious rooting and associated propagation traits in a second-generation outbred Corymbia torelliana × Corymbia citriodora subspecies variegata hybrid family (n = 186). The parental species of this cross are divergent in their capacity to develop roots adventitiously on stem cuttings and their propensity to form lignotubers. For the ten traits studied, there was one or two QTL detected, with some QTL explaining large amounts of phenotypic variation (e.g. 66% for one QTL for percentage rooting), suggesting that major effects influence rooting in this cross. Collocation of QTL for many strongly genetically correlated rooting traits to a single region on linkage group 12 suggested pleiotropy. A three locus model was most parsimonious for linkage group 12, however, as differences in QTL position and lower genetic correlations suggested separate loci for each of the traits of shoot production and root initiation. Species differences were thought to be the major source of phenotypic variation for some rooting rate and root quality traits because of the major QTL effects and up to 59-fold larger homospecific deviations (attributed to species differences) relative to heterospecific deviations (attributed to standing variation within species) evident at some QTL for these traits. A large homospecific/heterospecific ratio at major QTL suggested that the gene action evident in one cross may be indicative of gene action more broadly in hybrids between these species for some traits.     

The Use of Multiple Markers in a Bayesian Method for Mapping Quantitative Trait Loci

Information on multiple linked genetic markers was used in a Bayesian method for the statistical mapping of quantitative trait loci (QTL). Bayesian parameter estimation and hypothesis testing were implemented via Markov chain Monte Carlo algorithms. Variables sampled were the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage or nonlinkage, and the parameters. The parameter vector included allele frequencies at the markers and the QTL, map distances of the markers and the QTL, QTL substitution effect, and polygenic and residual variances. The criterion for QTL detection was the marginal posterior probability of a QTL being located on the chromosome carrying the markers. The method was evaluated empirically by analyzing simulated granddaughter designs consisting of 2000 sons, 20 related sires, and their ancestors.     

Postzygotic isolation involves strong mitochondrial and sex-specific effects in Tigriopus californicus,a species lacking heteromorphic sex chromosomes

Detailed studies of the genetics of speciation have focused on a few model systems, particularly Drosophila. The copepod Tigriopus californicus offers an alternative that differs from standard animal models in that it lacks heteromorphic chromosomes (instead, sex determination is polygenic) and has reduced opportunities for sexual conflict, because females mate only once. Quantitative trait loci (QTL) mapping was conducted on reciprocal F₂ hybrids between two strongly differentiated populations, using a saturated linkage map spanning all 12 autosomes and the mitochondrion. By comparing sexes, a possible sex ratio distorter was found but no sex chromosomes. Although studies of standard models often find an excess of hybrid male sterility factors, we found no QTL for sterility and multiple QTL for hybrid viability (indicated by non-Mendelian adult ratios) and other characters. Viability problems were found to be stronger in males, but the usual explanations for weaker hybrid males (sex chromosomes, sensitivity of spermatogenesis, sexual selection) cannot fully account for these male viability problems. Instead, higher metabolic rates may amplify deleterious effects in males. Although many studies of standard speciation models find the strongest genetic incompatibilities to be nuclear–nuclear (specifically X chromosome–autosome), we found the strongest deleterious interaction in this system was mito–nuclear. Consistent with the snowball theory of incompatibility accumulation, we found that trigenic interactions in this highly divergent cross were substantially more frequent (>6 × ) than digenic interactions. This alternative system thus allows important comparisons to studies of the genetics of reproductive isolation in more standard model systems.