Mapping quantitative trait loci for binary trait in the F2:3 design

In the analysis of inheritance of quantitative traits with low heritability, an F_2:3 design that genotypes plants in F₂ and phenotypes plants in F_2:3 progeny is often used in plant genetics. Although statistical approaches for mapping quantitative trait loci (QTL) in the F_2:3 design have been well developed, those for binary traits of biological interest and economic importance are seldom addressed. In this study, an attempt was made to map binary trait loci (BTL) in the F_2:3 design. The fundamental idea was: the F₂ plants were genotyped, all phenotypic values of each F_2:3 progeny were measured for binary trait, and these binary trait values and the marker genotype informations were used to detect BTL under the penetrance and liability models. The proposed method was verified by a series of Monte-Carlo simulation experiments. These results showed that maximum likelihood approaches under the penetrance and liability models provide accurate estimates for the effects and the locations of BTL with high statistical power, even under of low heritability. Moreover, the penetrance model is as efficient as the liability model, and the F_2:3 design is more efficient than classical F₂ design, even though only a single progeny is collected from each F_2:3 family. With the maximum likelihood approaches under the penetrance and the liability models developed in this study, we can map binary traits as we can do for quantitative trait in the F_2:3 design.     

Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny

In plants and laboratory animals, QTL mapping is commonly performed using F(2) or BC individuals derived from the cross of two inbred lines. Typical QTL mapping statistics assume that each F(2) individual is genotyped for the markers and phenotyped for the trait. For plant traits with low heritability, it has been suggested to use the average phenotypic values of F(3) progeny derived from selfing F(2) plants in place of the F(2) phenotype itself. All F(3) progeny derived from the same F(2) plant belong to the same F(2:3) family, denoted by F(2:3). If the size of each F(2:3) family (the number of F(3) progeny) is sufficiently large, the average value of the family will represent the genotypic value of the F(2) plant, and thus the power of QTL mapping may be significantly increased. The strategy of using F(2) marker genotypes and F(3) average phenotypes for QTL mapping in plants is quite similar to the daughter design of QTL mapping in dairy cattle. We study the fundamental principle of the plant version of the daughter design and develop a new statistical method to map QTL under this F(2:3) strategy. We also propose to combine both the F(2) phenotypes and the F(2:3) average phenotypes to further increase the power of QTL mapping. The statistical method developed in this study differs from published ones in that the new method fully takes advantage of the mixture distribution for F(2:3) families of heterozygous F(2) plants. Incorporation of this new information has significantly increased the statistical power of QTL detection relative to the classical F(2) design, even if only a single F(3) progeny is collected from each F(2:3) family. The mixture model is developed on the basis of a single-QTL model and implemented via the EM algorithm. Substantial computer simulation was conducted to demonstrate the improved efficiency of the mixture model. Extension of the mixture model to multiple QTL analysis is developed using a Bayesian approach. The computer program performing the Bayesian analysis of the simulated data is available to users for real data analysis.     

Mendelian Factors Underlying Quantitative Traits in Tomato: Comparison across Species, Generations, and Environments

As part of ongoing studies regarding the genetic basis of quantitative variation in phenotype, we have determined the chromosomal locations of quantitative trait loci (QTLs) affecting fruit size, soluble solids concentration, and pH, in a cross between the domestic tomato (Lycopersicon esculentum Mill.) and a closely-related wild species, L. cheesmanii. Using a RFLP map of the tomato genome, we compared the inheritance patterns of polymorphisms in 350 F2 individuals with phenotypes scored in three different ways: (1) from the F2 progeny themselves, grown near Davis, California; (2) from F3 families obtained by selfing each F2 individual, grown near Gilroy, California (F3-CA); and (3) from equivalent F3 families grown near Rehovot, Israel (F3-IS). Maximum likelihood methods were used to estimate the approximate chromosomal locations, phenotypic effects (both additive effects and dominance deviations), and gene action of QTLs underlying phenotypic variation in each of these three environments. A total of 29 putative QTLs were detected in the three environments. These QTLs were distributed over 11 of the 12 chromosomes, accounted for 4.7-42.0% of the phenotypic variance in a trait, and showed different types of gene action. Among these 29 QTLs, 4 were detected in all three environments, 10 in two environments, and 15 in only a single environment. The two California environments were most similar, sharing 11/25 (44%) QTLs, while the Israel environment was quite different, sharing 7/20 (35%) and 5/26 (19%) QTLs with the respective California environments. One major goal of QTL mapping is to predict, with maximum accuracy, which individuals will produce progeny showing particular phenotypes. Traditionally, the phenotype of an individual alone has been used to predict the phenotype of its progeny. Our results suggested that, for a trait with low heritability (soluble solids), the phenotype of F3 progeny could be predicted more accurately from the genotype of the F2 parent at QTLs than from the phenotype of the F2 individual. For a trait with intermediate heritability (fruit pH), QTL genotype and observed phenotype were about equally effective at predicting progeny phenotype. For a trait with high heritability (mass per fruit), knowing the QTL genotype of an individual added little if any predictive value, to simply knowing the phenotype. The QTLs mapped in the L. esculentum X L. cheesmanii F2 appear to be at similar locations to many of those mapped in a previous cross with a different wild tomato (L. chmielewskii).(ABSTRACT TRUNCATED AT 400 WORDS)     

Enhanced efficiency of quantitative trait loci mapping analysis based on multivariate complexes of quantitative traits

An approach to increase the efficiency of mapping quantitative trait loci (QTL) was proposed earlier by the authors on the basis of bivariate analysis of correlated traits. The power of QTL detection using the log-likelihood ratio (LOD scores) grows proportionally to the broad sense heritability. We found that this relationship holds also for correlated traits, so that an increased bivariate heritability implicates a higher LOD score, higher detection power, and better mapping resolution. However, the increased number of parameters to be estimated complicates the application of this approach when a large number of traits are considered simultaneously. Here we present a multivariate generalization of our previous two-trait QTL analysis. The proposed multivariate analogue of QTL contribution to the broad-sense heritability based on interval-specific calculation of eigenvalues and eigenvectors of the residual covariance matrix allows prediction of the expected QTL detection power and mapping resolution for any subset of the initial multivariate trait complex. Permutation technique allows chromosome-wise testing of significance for the whole trait complex and the significance of the contribution of individual traits owing to: (a) their correlation with other traits, (b) dependence on the chromosome in question, and (c) both a and b. An example of application of the proposed method on a real data set of 11 traits from an experiment performed on an F(2)/F(3) mapping population of tetraploid wheat (Triticum durum x T. dicoccoides) is provided.     

QTL mapping of complex binary traits in an advanced intercross line

An advanced intercross line (AIL) is an easier and more cost-effective approach compared to recombinant inbred lines for fine mapping of quantitative trait loci (QTL) identified by F(2) designs. In an AIL, a complex binary trait can be mapped through analysis of either continuously distributed proxy traits for the liability of the binary trait or the liability itself, the latter presenting the greater statistical challenge. In another work, we successfully applied both approaches in an AIL to fine map previously identified QTL underlying anatomical parameters of the cardiac inter-atrial septum including patent foramen ovale. Here, we describe the statistical methods that we used to analyse complex binary traits in our AIL design. This is achieved using a likelihood-based method, with the expectation-maximisation algorithm allowing use of standard logistic regression methods for model fitting.     

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.     

Power of quantitative trait locus mapping for polygenic binary traits using generalized and regression interval mapping in multi-family half-sib designs

A generalized interval mapping (GIM) method to map quantitative trait loci (QTL) for binary polygenic traits in a multi-family half-sib design is developed based on threshold theory and implemented using a Newton-Raphson algorithm. Statistical power and bias of QTL mapping for binary traits by GIM is compared with linear regression interval mapping (RIM) using simulation. Data on 20 paternal half-sib families were simulated with two genetic markers that bracketed an additive QTL. Data simulated and analysed were: (1) data on the underlying normally distributed liability (NDL) scale, (2) binary data created by truncating NDL data based on three thresholds yielding data sets with three different incidences, and (3) NDL data with polygenic and QTL effects reduced by a proportion equal to the ratio of the heritabilities on the binary versus NDL scale (reduced-NDL). Binary data were simulated with and without systematic environmental (herd) effects in an unbalanced design. GIM and RIM gave similar power to detect the QTL and similar estimates of QTL location, effects and variances. Presence of fixed effects caused differences in bias between RIM and GIM, where GIM showed smaller bias which was affected less by incidence. The original NDL data had higher power and lower bias in QTL parameter estimates than binary and reduced-NDL data. RIM for reduced-NDL and binary data gave similar power and estimates of QTL parameters, indicating that the impact of the binary nature of data on QTL analysis is equivalent to its impact on heritability.     

Does fructan have a functional role in physiological traits? Investigation by quantitative trait locus mapping

* The role of fructan in growth and drought-stress responses of perennial ryegrass (Lolium perenne) was investigated in an F(2) mapping family that segregates for carbohydrate metabolism. * A quantitative trait locus approach was used to compare the genetic control of traits. * Growth and drought-stress traits were extremely variable within the family. Most traits had high broad-sense heritability. Quantitative trait loci (QTL) were identified for most traits; the maximum number of QTL per trait was four. Between 11% and 75% of total phenotypic variation was explained. Few growth-trait QTL coincided with previously identified fructan QTL. A cluster of drought-trait QTL was close to two previously identified regions of the genome with tiller base fructan QTL in repulsion. * The high sugar parent contributed few alleles that increased 'reserve-driven' growth or performance during drought-stress. Correlation of growth and drought-stress traits with fructan content was low and increasing fructan content per se would not appear to improve drought resistance. Complex patterns of carbohydrate partitioning and metabolism within the cell may explain contradictory relationships between carbohydrate content and growth/stress-resistance traits.     

Multiple-interval mapping for ordinal traits

Many statistical methods have been developed to map multiple quantitative trait loci (QTL) in experimental cross populations. Among these methods, multiple-interval mapping (MIM) can map QTL with epistasis simultaneously. However, the previous implementation of MIM is for continuously distributed traits. In this study we extend MIM to ordinal traits on the basis of a threshold model. The method inherits the properties and advantages of MIM and can fit a model of multiple QTL effects and epistasis on the underlying liability score. We study a number of statistical issues associated with the method, such as the efficiency and stability of maximization and model selection. We also use computer simulation to study the performance of the method and compare it to other alternative approaches. The method has been implemented in QTL Cartographer to facilitate its general usage for QTL mapping data analysis on binary and ordinal traits.     

A Sequential Quantitative Trait Locus Fine-Mapping Strategy Using Recombinant-Derived Progeny

A thorough understanding of the quantitative trait loci(QTLs)that underlie agronomically important traits in crops would greatly increase agricultural productivity.Although advances have been made in QTL cloning,the majority of QTLs remain unknown because of their low heritability and minor contributions to phenotypic performance.Here we summarize the key advantages and disadvantages of current QTL fine-mapping methodologies,and then introduce a sequential QTL fine-mapping strategy based on both genotypes and phenotypes of progeny derived from recombinants.With this mapping strategy,experimental errors could be dramatically diminished so as to reveal the authentic genetic effect of target QTLs.The number of progeny required to detect QTLs atvarious R~2 values was calculated,and the backcross generation suitable to start QTL fine-mapping was also estimated.This mapping strategy has proved to be very powerful in narrowing down QTL regions,particularly minor-effect QTLs,as revealed by fine-mapping of various resistance QTLs in maize.Application of this sequential QTL mapping strategy should accelerate cloning of agronomically important QTLs,which is currently a substantial challenge in crops.     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

离散性状QTL区间定位的最大似然方法

采用最大似然区间定位法对阈模型与一般线性模型的QTL定位效率进行了比较,并对影响离散性状QTL检测效率的主要因素（QTL效应、性状的遗传力和表型发生率）进行了模拟研究,实验设计为多个家系的女儿设计．资源群体大小为500头。研究结果表明：在QTL参数估计及检验功效方面,阈模型方法具有较大的优势,对离散性状QTL定位的效率明显高于LM（Linear Model）方法,定位的准确性也较高。另外,性状遗传力、QTL效应的大小和性状表型发生率对QTL定位的准确度也有直接的影响,随着性状遗传力和表型发生率的提高,随着QTL效应的增大,QTL定位的效率也进一步提高。     

Mapping quantitative trait Loci underlying fitness-related traits in a free-living sheep population

We searched for quantitative trait loci (QTL) underlying fitness-related traits in a free-living pedigree of 588 Soay sheep in which a genetic map using 251 markers with an average spacing of 15 cM had been established previously. Traits examined included birth date and weight, considered both as maternal and offspring traits, foreleg length, hindleg length, and body weight measured on animals in August and jaw length and metacarpal length measured on cleaned skeletal material. In some cases the data were split to consider different age classes separately, yielding a total of 15 traits studied. Genetic and environmental components of phenotypic variance were estimated for each trait and, for those traits showing nonzero heritability (N= 12), a QTL search was conducted by comparing a polygenic model with a model including a putative QTL. Support for a QTL at genome-wide significance was found on chromosome 11 for jaw length; suggestive QTL were found on chromosomes 2 and 5 (for birth date as a trait of the lamb), 8 (birth weight as a trait of the lamb), and 15 (adult hindleg length). We discuss the prospects for refining estimates of QTL position and effect size in the study population, and for QTL searches in free-living pedigrees in general.     

基于F3种子的胚乳性状QTL区间定位

文章提出了包括胚乳效应和母体效应的胚乳性状QTL定位的统计方法,该方法的实验设计是分子标记基因型信息来自F2母体植株和F3种子胚(或植株),胚乳性状表型值来自F3单粒种子胚乳,称之为两步等级设计。同时,用计算机全面模拟以验证该模型的可行性,模拟结果表明,只要群体足够大,该模型能较有效地进行胚乳性状QTL定位并精确地估计出胚乳QTL的各种遗传效应和母体效应。     

Detection of quantitative trait loci for teat number and female reproductive traits in Meishan × Large White F2 pigs

A quantitative trait locus (QTL) analysis of female reproductive data from a three-generation experimental cross between Meishan (MS) and Large White (LW) pig breeds is presented. Six F1 boars and 23 F1 sows, progeny of six LW boars and six MS sows, produced 573 F2 females and 530 F2 males. Six traits, i.e. teat number (TN), age at puberty (AP), ovulation rate (OR), weight at mating (WTM), number of viable embryos (NVE) and embryo survival (ES) at 30 days of gestation were analysed. Animals were genotyped for a total of 137 markers covering the entire porcine genome. Analyses were carried out based on interval mapping methods, using a line-cross (LC) regression and a half-full sib (HFS) maximum likelihood test. Genome-wide (GW) highly significant (P < 0.001) QTL were detected for WTM on SSC 7 and for AP on SSC 13. They explained, respectively, 14.5% and 8.9% of the trait phenotypic variance. Other GW significant (P < 0.05) QTL were detected for TN on SSC 3, 7, 8, 16 and 17, for OR on SSC 4 and 5, and for ES on SSC 9. Two additional chromosome-wide significant (P < 0.05) QTL were detected for TN, three for WTM, four for AP, three for OR, three for NVE and two for ES. With the exception of the two above-mentioned loci, the QTL explained from 1.2% to 4.6% of trait phenotypic variance. QTL alleles were in most cases not fixed in the grand-parental populations and Meishan alleles were not systematically associated with higher reproductive performance.     

Genetic characterisation of seed yield and fertility traits in perennial ryegrass (<Emphasis Type="Italic">Lolium perenne</Emphasis> L.)

Seed yield is a trait of major interest for the key grassland species Lolium perenne L. An F2 mapping population of perennial ryegrass (VrnA), recently characterised for vernalisation response, was assessed in a glasshouse for traits related to seed yield based on a lattice design with four replications over 2 years. The traits heading date, plant height, length of panicles, number of panicles per plant, seed yield per panicle, flag leaf length, flag leaf width and seed yield per plant revealed repeatabilities ranging from 41 to 76% and a considerable amount of genetic variation in the VrnA population. Path analysis partitioned the direct and indirect effects of seed yield components on seed yield per plant. Seed yield per panicle showed the highest effect on total seed yield. The adjusted mean values of each trait and a genetic linkage map consisting of 97 anonymous and 85 gene associated DNA markers were used for quantitative trait loci (QTL) analysis. Of particular interest were two QTL on linkage group (LG) 1 and LG 2, explaining 41 and 18%, respectively, of the observed phenotypic variation for the trait seed yield per panicle. Both QTL co-located with two major QTL for total seed yield per plant possibly representing the S and Z loci of the gametophytic self incompatibility (SI) system of perennial ryegrass. The diversity of SI alleles in mapping parents and the degree of heterozygosity at SI loci in the full sib progeny determines the interference of self incompatibility with seed production.     

Genetic analysis of sunflower domestication

Quantitative trait loci (QTL) controlling phenotypic differences between cultivated sunflower and its wild progenitor were investigated in an F(3) mapping population. Composite interval mapping revealed the presence of 78 QTL affecting the 18 quantitative traits of interest, with 2-10 QTL per trait. Each QTL explained 3.0-68.0% of the phenotypic variance, although only 4 (corresponding to 3 of 18 traits) had effects >25%. Overall, 51 of the 78 QTL produced phenotypic effects in the expected direction, and for 13 of 18 traits the majority of QTL had the expected effect. Despite being distributed across 15 of the 17 linkage groups, there was a substantial amount of clustering among QTL controlling different traits. In several cases, regions influencing multiple traits harbored QTL with antagonistic effects, producing a cultivar-like phenotype for some traits and a wild-like phenotype for others. On the basis of the directionality of QTL, strong directional selection for increased achene size appears to have played a central role in sunflower domestication. None of the other traits show similar evidence of selection. The occurrence of numerous wild alleles with cultivar-like effects, combined with the lack of major QTL, suggests that sunflower was readily domesticated.     

Mapping single-locus and epistatic quantitative trait loci for plant architectural traits in chrysanthemum

Plant architecture is important for chrysanthemum cultivation and breeding. To determine the genetic basis of plant architectural traits in chrysanthemum, a population of 142 F1 plants derived from a cross between the creeping ground-cover chrysanthemum cultivar Yuhualuoying and the erect potted cultivar Aoyunhanxiao was used to detect quantitative trait loci (QTL) associated with plant height, plant width, inter-node length and flower neck length. The broad-sense heritability h _B ² for the four plant architectural traits ranged from 0.33 to 0.83, and transgressive segregation was observed. Single-locus QTL analysis revealed a total of five QTL, accounting for 6.0?C16.1% of the phenotypic variation. Additionally, 11 pairs of epistatic QTL were identified, explaining 3.5?C14.5% of the phenotypic variations. The majority of the interactions detected occurred between background loci. These results indicate that both additive and epistatic effects contribute to phenotypic variation in the plant architecture of chrysanthemum. It is expected that the identified markers associated with the additive QTL and epistatic QTL detected in this study will be of importance in future breeding programs to develop chrysanthemum cultivars exhibiting desirable plant architecture.     

Genetic basis of sex-specific color pattern variation in Drosophila malerkotliana

Pigmentation is a rapidly evolving trait that can play important roles in mimicry, sexual selection, thermoregulation, and other adaptive processes in many groups of animals. In Drosophila, pigmentation can differ dramatically among closely related taxa, presenting a good opportunity to dissect the genetic changes underlying species divergence. In this report, we investigate the genetic basis of color pattern variation between two allopatric subspecies of Drosophila malerkotliana, a widespread member of the ananassae species subgroup. In D. malerkotliana malerkotliana, the last three abdominal segments are darkly pigmented in males but not in females, while in D. malerkotliana pallens both sexes lack dark pigmentation. Composite interval mapping in F(2) hybrid progeny shows that this difference is largely controlled by three quantitative trait loci (QTL) located on the 2L chromosome arm, which is homologous to the 3R of D. melanogaster (Muller element E). Using highly recombinant introgression strains produced by repeated backcrossing and phenotypic selection, we show that these QTL do not correspond to any of the candidate genes known to be involved in pigment patterning and synthesis in Drosophila. These results, in combination with similar analyses in other Drosophila species, indicate that different genetic and molecular changes are responsible for the evolution of similar phenotypic traits in different lineages. This feature makes Drosophila color patterns a powerful model for investigating how the genetic basis of trait evolution is influenced by the intrinsic organization of regulatory pathways controlling the development of these traits.     

The Nature of Genetic Variation for Complex Traits Revealed by GWAS and Regional Heritability Mapping Analyses

We use computer simulations to investigate the amount of genetic variation for complex traits that can be revealed by single-SNP genome-wide association studies (GWAS) or regional heritability mapping (RHM) analyses based on full genome sequence data or SNP chips. We model a large population subject to mutation, recombination, selection, and drift, assuming a pleiotropic model of mutations sampled from a bivariate distribution of effects of mutations on a quantitative trait and fitness. The pleiotropic model investigated, in contrast to previous models, implies that common mutations of large effect are responsible for most of the genetic variation for quantitative traits, except when the trait is fitness itself. We show that GWAS applied to the full sequence increases the number of QTL detected by as much as 50% compared to the number found with SNP chips but only modestly increases the amount of additive genetic variance explained. Even with full sequence data, the total amount of additive variance explained is generally below 50%. Using RHM on the full sequence data, a slightly larger number of QTL are detected than by GWAS if the same probability threshold is assumed, but these QTL explain a slightly smaller amount of genetic variance. Our results also suggest that most of the missing heritability is due to the inability to detect variants of moderate effect (∼0.03–0.3 phenotypic SDs) segregating at substantial frequencies. Very rare variants, which are more difficult to detect by GWAS, are expected to contribute little genetic variation, so their eventual detection is less relevant for resolving the missing heritability problem.