Comparison of three multitrait methods for QTL detection

A comparison of power and accuracy of estimation of position and QTL effects of three multitrait methods and one single trait method for QTL detection was carried out on simulated data, taking into account the mixture of full and half-sib families. One multitrait method was based on a multivariate function as the penetrance function (MV). The two other multitrait methods were based on univariate analysis of linear combination(s) (LC) of the traits. One was obtained by a principal component analysis (PCA) performed on the phenotypic data. The second was based on a discriminate analysis (DA). It calculates a LC of the traits at each position, maximising the ratio between the genetic and the residual variabilities due to the putative QTL. Due to its number of parameters, MV was less powerful and accurate than the other methods. In general, DA better detected QTL, but it had lower accuracy for the QTL effect estimation when the detection power was low, due to higher bias than the other methods. In this case, PCA was better. Otherwise, PCA was slightly less powerful and accurate than DA. Compared to the single trait method, power can be improved by 30% to 100% with multitrait methods.     

Power of three multitrait methods for QTL detection in crossbred populations

The multitrait detections of QTL applied to a mixture of full- and half-sib families require specific strategies. Indeed, the number of parameters estimated by the multivariate methods is excessive compared with the size of the population. Thus, only multitrait methods based on a univariate analysis of a linear combination (LC) of the traits can be extensively performed. We compared three strategies to obtain the LC of the traits. Two linear transformations were performed on the overall population. The last one was performed within each half-sib family. Their powers were compared on simulated data depending on the frequency of the two QTL alleles in each of the grand parental populations of an intercross design. The transformations from the whole population did not lead to a large loss of power even though the frequency of the QTL alleles was similar in the two grand parental populations. In these cases, applying the within-sire family transformation improved the detection when the number of progeny per sire was greater than 100.     

Selective genotyping for QTL detection using sib pair analysis in outbred populations with hierarchical structures

A simulation study illustrates the effects of the inclusion of half-sib pairs as well as the effects of selective genotyping on the power of detection and the parameter estimates in a sib pair analysis of data from an outbred population. The power of QTL detection obtained from samples of sib pairs selected according to their within family variance or according to the mean within family variance within half sib family was compared and contrasted with the power obtained when only full sib pair analysis was used. There was an increase in power (4–16%) and decrease in the bias of parameter estimates with the use of half-sib information. These improvements in power and parameter estimates depended on the number of the half sib pairs (half sib family size). Almost the same power as that obtained using all the available sib pairs could be achieved by selecting only 50–60% the animals. The most effective method was to select both full and half sib pairs on the basis of high within full sib family variance for the trait in question. The QTL position estimates were in general slightly biased towards the center of the chromosome and the QTL variance estimates were biased upwards, there being quite large differences in bias depending on the selection method.     

A comprehensive analysis of QTL for abdominal fat and breast muscle weights on chicken chromosome 5 using a multivariate approach

Quantitative trait loci (QTL) influencing the weight of abdominal fat (AF) and of breast muscle (BM) were detected on chicken chromosome 5 (GGA5) using two successive F₂ crosses between two divergently selected 'Fat' and 'Lean' INRA broiler lines. Based on these results, the aim of the present study was to identify the number, location and effects of these putative QTL by performing multitrait and multi-QTL analyses of the whole available data set. Data concerned 1186 F₂ offspring produced by 10 F₁ sires and 85 F₁ dams. AF and BM traits were measured on F₂ animals at slaughter, at 8 (first cross) or 9 (second cross) weeks of age. The F₀, F₁ and F₂ birds were genotyped for 11 microsatellite markers evenly spaced along GGA5. Before QTL detection, phenotypes were adjusted for the fixed effects of sex, F₂ design, hatching group within the design, and for body weight as a covariable. Univariate analyses confirmed the QTL segregation for AF and BM on GGA5 in male offspring, but not in female offspring. Analyses of male offspring data using multitrait and linked-QTL models led us to conclude the presence of two QTL on the distal part of GGA5, each controlling one trait. Linked QTL models were applied after correction of phenotypic values for the effects of these distal QTL. Several QTL for AF and BM were then discovered in the central region of GGA5, splitting one large QTL region for AF into several distinct QTL. Neither the 'Fat' nor the 'Lean' line appeared to be fixed for any QTL genotype. These results have important implications for prospective fine mapping studies and for the identification of underlying genes and causal mutations.     

Mapping multiple QTL of different effects: comparison of a simple sequential testing strategy and multiple QTL mapping

The aim of this study was to explore, by computer simulation, the mapping of QTLs in a realistic but complex situation of many (linked) QTLs with different effects, and to compare two QTL mapping methods. A novel method to dissect genetic variation on multiple chromosomes using molecular markers in backcross and F₂ populations derived from inbred lines was suggested, and its properties tested using simulations. The rationale for this sequential testing method was to explicitly test for alternative genetic models. The method consists of a series of four basic statistical tests to decide whether variance was due to a single QTL, two QTLs, multiple QTLs, or polygenes, starting with a test to detect genetic variance associated with a particular chromosome. The method was able to distinguish between different QTL configurations, in that the probability to `detect' the correct model was high, varying from 0.75 to 1. For example, for a backcross population of 200 and an overall heritability of 50%, in 78% of replicates a polygenic model was detected when that was the underlying true model. To test the method for multiple chromosomes, QTLs were simulated on 10 chromosomes, following a geometric series of allele effects, assuming positive alleles were in coupling in the founder lines For these simulations, the sequential testing method was compared to the established Multiple QTL Mapping (MQM) method. For a backcross population of 400 individuals, power to detect genetic variance was low with both methods when the heritability was 0.40. For example, the power to detect genetic variation on a chromosome on which 6 QTLs explained 12.6% of the genetic variance, was less than 60% for both methods. For a large heritability (0.90), the power of MQM to detect genetic variance and to dissect QTL configurations was generally better, due to the simultaneous fitting of markers on all chromosomes. It is concluded that when testing different QTL configurations on a single chromosome using the sequential testing procedure, regions of other chromosomes which explain a significant amount of variation should be fitted in the model of analysis. This study reinforces the need for large experiments in plants and other species if the aim of a genome scan is to dissect quantitative genetic variation.     

Detection and parameter estimation for quantitative trait loci using regression models and multiple markers

A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.     

Merino sheep: a further look at quantitative trait loci for wool production

A quantitative trait loci (QTL) analysis of wool traits from experimental half-sib data of Merino sheep is presented. A total of 617 animals distributed in 10 families were genotyped for 36 microsatellite markers on four ovine chromosomes OAR1, OAR3, OAR4 and OAR11. The markers covering OAR3 and OAR11 were densely spaced, at an average distance of 2.8 and 1.2 cM, respectively. Body weight and wool traits were measured at first and second shearing. Analyses were conducted under three hypotheses: (i) a single QTL controlling a single trait (for multimarker regression models); (ii) two linked QTLs controlling a single trait (using maximum likelihood techniques) and (iii) a single QTL controlling more than one trait (also using maximum likelihood techniques). One QTL was identified for several wool traits on OAR1 (average curvature of fibre at first and second shearing, and clean wool yield measured at second shearing) and on OAR11 (weight and staple strength at first shearing, and coefficient of variation of fibre diameter at second shearing). In addition, one QTL was detected on OAR4 affecting weight measured at second shearing. The results of the single trait method and the two-QTL hypotheses showed an additional QTL segregating on OAR11 (for greasy fleece weight at first shearing and clean wool yield trait at second shearing). Pleiotropic QTLs (controlling more than one trait) were found on OAR1 (clean wool yield, average curvature of fibre, clean and greasy fleece weightand staple length, all measured at second shearing).     

Power of QTL detection by either fixed or random models in half-sib designs

The aim of this study was to compare the variance component approach for QTL linkage mapping in half-sib designs to the simple regression method. Empirical power was determined by Monte Carlo simulation in granddaughter designs. The factors studied (base values in parentheses) included the number of sires (5) and sons per sire (80), ratio of QTL variance to total genetic variance (λ = 0.1), marker spacing (10 cM), and QTL allele frequency (0.5). A single bi-allelic QTL and six equally spaced markers with six alleles each were simulated. Empirical power using the regression method was 0.80, 0.92 and 0.98 for 5, 10, and 20 sires, respectively, versus 0.88, 0.98 and 0.99 using the variance component method. Power was 0.74, 0.80, 0.93, and 0.95 using regression versus 0.77, 0.88, 0.94, and 0.97 using the variance component method for QTL variance ratios (λ) of 0.05, 0.1, 0.2, and 0.3, respectively. Power was 0.79, 0.85, 0.80 and 0.87 using regression versus 0.80, 0.86, 0.88, and 0.85 using the variance component method for QTL allele frequencies of 0.1, 0.3, 0.5, and 0.8, respectively. The log₁₀ of type I error profiles were quite flat at close marker spacing (1 cM), confirming the inability to fine-map QTL by linkage analysis in half-sib designs. The variance component method showed slightly more potential than the regression method in QTL mapping.     

Use of maternal information for QTL detection in a (grand)daughter design

In a (grand)daughter design, maternal information is often neglected because the number of progeny per dam is limited. The number of dams per maternal grandsire (MGS), however, could be large enough to contribute to QTL detection. But dams and MGS usually are not genotyped, there are two recombination opportunities between the MGS and the progeny, and at a given location, only half the progeny receive a MGS chromosomal segment. A 3-step procedure was developed to estimate: (1) the marker phenotypes probabilities of the MGS; (2) the probability of each possible MGS haplotype; (3) the probabilities that the progeny receives either the first, or second MGS segment, or a maternal grandam segment. These probabilities were used for QTL detection in a linear model including the effects of sire, MGS, paternal QTL, MGS QTL and maternal grandam QTL. Including the grandam QTL effect makes it possible to detect QTL in the grandam population, even when MGS are not informative. The detection power, studied by simulation, was rather high, provided that MGS family size was greater than 50. Using maternal information in the French dairy cattle granddaughter design made it possible to detect 23 additional QTL genomewise significant.     

植物数量性状变异的分子基础与QTL克隆研究进展

探讨数量性状变异规律以便对其进行遗传操纵一直是植物遗传学的一个重要领域。DNA分子标记和QTL作图技术的发展以及拟南芥和水稻全基因组测序的完成极大地促进了植物数量性状分子基础的研究。现已克隆了拟南芥ED1、水稻Hdl、玉米Tb1、番茄fw2．2和Brii9-2-5等控制目标数量性状的基因。数量性状表型变异不仅源于多个数量性状基因（QTL）的分离．而且还受到内外环境的修饰。QTL等位基因变异与孟德尔基因变异具有类似的分子基础,即基因表达或蛋白质功能发生改变。通过分析已克隆的植物QTL的变异特征及分子基础,讨论了植物QTL克隆技术策略,并对QTL研究所面临的挑战和应用前景进行了展望。     

Identification of chromosomal regions associated with growth and carcass traits in an F3 full sib intercross line originating from a cross of chicken lines divergently selected on body weight

An F₃ resource population originating from a cross between two divergently selected lines for high (D+ line) or low (D− line) body weight at 8-weeks of age (BW55) was generated and used for Quantitative Trait Locus (QTL) mapping. From an initial cross of two founder F₀ animals from D(+) and D(−) lines, progeny were randomly intercrossed over two generations following a full sib intercross line (FSIL) design. One hundred and seventy-five genome-wide polymorphic markers were employed in the DNA pooling and selective genotyping of F₃ to identify markers with significant effects on BW55. Fifty-three markers on GGA2, 5 and 11 were then genotyped in the whole F₃ population of 503 birds, where interval mapping with GridQTL software was employed. Eighteen QTL for body weight, carcass traits and some internal organ weights were identified. On GGA2, a comparison between 2-QTL vs. 1-QTL analysis revealed two separate QTL regions for body, feet, breast muscle and carcass weight. Given co-localization of QTL for some highly correlated traits, we concluded that there were 11 distinct QTL mapped. Four QTL localized to already mapped QTL from other studies, but seven QTL have not been previously reported and are hence novel and unique to our selection line. This study provides a low resolution QTL map for various traits and establishes a genetic resource for future fine-mapping and positional cloning in the advanced FSIL generations.     

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.     

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.     

应用二种定位法比较不同世代水稻产量性状QTL的检测结果

应用珍汕97B／密阳46的F2和重组自交系（RIL）群体,建立RFLP连锁图,检测控制稻谷产量及其5个构成因子的QTL。结果表明,具有较大加性效应者,能同时在F2和RIL群体中检测到。而且,在重组自交系群体中,发现设重复的表型鉴定与基于单株的表型鉴定,对效应较高的QTL的检测影响不大。     

Sensitive detection of sequence similarity using combinatorial pattern discovery: a challenging study of two distantly related protein families

We investigate the performance of combinatorial pattern discovery to detect remote sequence similarities in terms of both biological accuracy and computational efficiency for a pair of distantly related families, as a case study. The two families represent the cupredoxins and multicopper oxidases, both containing blue copper-binding domains. These families present a challenging case due to low sequence similarity, different local structure, and variable sequence conservation at their copper-binding active sites. In this study, we investigate a new approach for automatically identifying weak sequence similarities that is based on combinatorial pattern discovery. We compare its performance with a traditional, HMM-based scheme and obtain estimates for sensitivity and specificity of the two approaches. Our analysis suggests that pattern discovery methods can be substantially more sensitive in detecting remote protein relationships while at the same time guaranteeing high specificity.     

Overview of QTL detection in plants and tests for synergistic epistatic interactions

Improvements in the usefulness of QTL analysis arise from better statistical methods applied to the problem, ability to analyze more complex mating designs, and the fitting of less simplified genetic models. Here we review the advantages of different plant mating designs in QTL analysis and conclude that diallel designs have several favorable properties. We then turn to the detection of systematic genome-wide synergistic epistasis. This form of epistasis has important implications from evolutionary (maintenance of sexual reproduction and concealment of cryptic genetic variation) and practical perspectives (response to pyramided favorable alleles). We develop two methods for detecting systematic synergistic epistasis, one based on analyzing interactions between locus effects and predicted individual genotypic values and one based on analyzing pairwise locus interactions. Using the first method we detect synergistic epistasis in a barley and a wheat dataset but not in a maize dataset. We fail to detect synergistic epistasis with the second method. We discuss our results in the light of theoretical questions concerning the mechanisms of synergistic epistasis.     

Linkage and association studies of QTL for nuclear families by mixed models

The transmission disequilibrium test (TDT) has been utilized to test the linkage and association between a genetic trait locus and a marker. Spielman et al. (1993) introduced TDT to test linkage between a qualitative trait and a marker in the presence of association. In the presence of linkage, TDT can be applied to test for association for fine mapping (Martin et al., 1997; Spielman and Ewens, 1996). In recent years, extensive research has been carried out on the TDT between a quantitative trait and a marker locus (Allison, 1997; Fan et al., 2002; George et al., 1999; Rabinowitz, 1997; Xiong et al., 1998; Zhu and Elston, 2000, 2001). The original TDT for both qualitative and quantitative traits requires unrelated offspring of heterozygous parents for analysis, and much research has been carried out to extend it to fit for different settings. For nuclear families with multiple offspring, one approach is to treat each child independently for analysis. Obviously, this may not be a valid method since offspring of one family are related to each other. Another approach is to select one offspring randomly from each family for analysis. However, with this method much information may be lost. Martin et al. (1997, 2000) constructed useful statistical tests to analyse the data for qualitative traits. In this paper, we propose to use mixed models to analyse sample data of nuclear families with multiple offspring for quantitative traits according to the models in Amos (1994). The method uses data of all offspring by taking into account their trait mean and variance-covariance structures, which contain all the effects of major gene locus, polygenic loci and environment. A test statistic based on mixed models is shown to be more powerful than the test statistic proposed by George et al. (1999) under moderate disequilibrium for nuclear families. Moreover, it has higher power than the TDT statistic which is constructed by randomly choosing a single offspring from each nuclear family.     

Toward positional cloning of Vgt1, a QTL controlling the transition from the vegetative to the reproductive phase in maize

Vgt1 (Vegetative to generative transition 1) is a quantitative trait locus (QTL) for flowering time in maize (Zea mays L.). Vgt1 was initially mapped in a ca. 5-cM interval on chromosome bin 8.05, using a set of near-isogenic lines (NILs) in the genetic background of the late dent line N28, with the earliness allele introgressed from the early variety Gaspé Flint. A new large mapping population was produced by crossing N28 and one early NIL with a ca. 6-cM long Gaspé Flint introgression at the Vgt1 region. Using PCR-based assays at markers flanking Vgt1, 69 segmental NILs homozygous for independent crossovers near the QTL were developed. When the NILs were tested in replicated field trials for days to pollen shed (DPS) and plant node number (ND), the QTL followed a Mendelian segregation. Using bulk segregant analysis and AFLP profiling, 17 AFLP markers linked to the QTL region were identified. Statistical analysis indicated a substantial coincidence of the effects of Vgt1 on both DPS and ND. Vgt1 was mapped at ca. 0.3 cM from an AFLP marker. As compared to DPS, the higher heritability of ND allowed for a more accurate assessment of the effects of Vgt1. The feasibility of the positional cloning of Vgt1 is discussed.     

Estimation of the contribution of quantitative trait loci (QTL) to the variance of a quantitative trait by means of genetic markers

The estimation of the contribution of an individual quantitative trait locus (QTL) to the variance of a quantitative trait is considered in the framework of an analysis of variance (ANOVA). ANOVA mean squares expectations which are appropriate to the specific case of QTL mapping experiments are derived. These expectations allow the specificities associated with the limited number of genotypes at a given locus to be taken into account. Discrepancies with classical expectations are particularly important for two-class experiments (backcross, recombinant inbred lines, doubled haploid populations) and F₂ populations. The result allows us firstly to reconsider the power of experiments (i.e. the probability of detecting a QTL with a given contribution to the variance of the trait). It illustrates that the use of classical formulae for mean squares expectations leads to a strong underestimation of the power of the experiments. Secondly, from the observed mean squares it is possible to estimate directly the variance associated with a locus and the fraction of the total variance associated to this locus (r _l ² ). When compared to other methods, the values estimated using this method are unbiased. Considering unbiased estimators increases in importance when (1) the experimental size is limited; (2) the number of genotypes at the locus of interest is large; and (3) the fraction of the variation associated with this locus is small. Finally, specific mean squares expectations allows us to propose a simple analytical method by which to estimate the confidence interval of r _l ² . This point is particularly important since results indicate that 95% confidence intervals for r _l ² can be rather wide:2–23% for a 10% estimate and 8–34% for a 20% estimate if 100 individuals are considered.     

Trait-based analyses for the detection of linkage between marker loci and quantitative trait loci in crosses between inbred lines

Summary Methods are presented for determining linkage between a marker locus and a nearby locus affecting a quantitative trait (quantitative trait locus=QTL), based on changes in the marker allele frequencies in selection lines derived from the F-2 of a cross between inbred lines, or in the high and low phenotypic classes of an F-2 or BC population. The power of such trait-based (TB) analyses was evaluated and compared with that of methods for determining linkage based on the mean quantitative trait value of marker genotypes in F-2 or BC populations [marker-based (MB) analyses]. TB analyses can be utilized for marker-QTL linkage determination in situations where the MB analysis is not applicable, including analysis of polygenic resistance traits where only a part of the population survives exposure to the Stressor and analysis of marker-allele frequency changes in selection lines. TB analyses may be a useful alternative to MB analyses when interest is centered on a single quantitative trait only and costs of scoring for markers are high compared with costs of raising and obtaining quantitative trait information on F-2 or BC individuals. In this case, a TB analysis will enable equivalent power to be obtained with fewer individuals scored for the marker, but more individuals scored for the quantitative trait. MB analyses remain the method of choice when more than one quantitative trait is to be analyzed in a given population.Contribution from the ARO, Bet Dagan, Israel. No. 1698-E, 1986 series