A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

The power of identity-by-state methods for linkage analysis.

The affected-sib-pair method has been widely utilized for mapping. This methodology is aimed at mapping complex traits which have been observed to be familial but for which Mendelian segregation, even after allowing for partial penetrance, is not apparent. Indications of linkage are based on the observation of nonrandom segregation at a marker locus in two affected siblings. We extend this methodology to more distant genetic relationships and examine the power of identity-by-state methods for mapping when marker information is only available on pairs of affected relatives. The power depends on the polymorphism of the marker, the probability of identity by descent at the trait locus, and the recombination fraction between the trait and the marker loci.     

Molecular-Marker-Facilitated Investigations of Quantitative-Trait Loci in Maize. I. Numbers, Genomic Distribution and Types of Gene Action

Individual genetic factors which underlie variation in quantitative traits of maize were investigated in each of two F2 populations by examining the mean trait expressions of genotypic classes at each of 17-20 segregating marker loci. It was demonstrated that the trait expression of marker locus classes could be interpreted in terms of genetic behavior at linked quantitative trait loci (QTLs). For each of 82 traits evaluated, QTLs were detected and located to genomic sites. The numbers of detected factors varied according to trait, with the average trait significantly influenced by almost two-thirds of the marked genomic sites. Most of the detected associations between marker loci and quantitative traits were highly significant, and could have been detected with fewer than the 1800-1900 plants evaluated in each population. The cumulative, simple effects of marker-linked regions of the genome explained between 8 and 40% of the phenotypic variation for a subset of 25 traits evaluated. Single marker loci accounted for between 0.3% and 16% of the phenotypic variation of traits. Individual plant heterozygosity, as measured by marker loci, was significantly associated with variation in many traits. The apparent types of gene action at the QTLs varied both among traits and between loci for given traits, although overdominance appeared frequently, especially for yield-related traits. The prevalence of apparent overdominance may reflect the effects of multiple QTLs within individual marker-linked regions, a situation which would tend to result in overestimation of dominance. Digenic epistasis did not appear to be important in determining the expression of the quantitative traits evaluated. Examination of the effects of marked regions on the expression of pairs of traits suggests that genomic regions vary in the direction and magnitudes of their effects on trait correlations, perhaps providing a means of selecting to dissociate some correlated traits. Marker-facilitated investigations appear to provide a powerful means of examining aspects of the genetic control of quantitative traits. Modifications of the methods employed herein will allow examination of the stability of individual gene effects in varying genetic backgrounds and environments.     

Mapping Quantitative Trait Loci for Complex Binary Diseases Using Line Crosses

A composite interval gene mapping procedure for complex binary disease traits is proposed in this paper. The binary trait of interest is assumed to be controlled by an underlying liability that is normally distributed. The liability is treated as a typical quantitative character and thus described by the usual quantitative genetics model. Translation from the liability into a binary (disease) phenotype is through the physiological threshold model. Logistic regression analysis is employed to estimate the effects and locations of putative quantitative trait loci (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). Simulation studies show that properties of this mapping procedure mimic those of the composite interval mapping for normally distributed data. Potential utilization of the QTL mapping procedure for resolving alternative genetic models (e.g., single- or two-trait-locus model) is discussed.     

Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

Many binary phenotypes do not follow a classical Mendelian inheritance pattern. Interaction between genetic and environmental factors is thought to contribute to the incomplete penetrance phenomena often observed in these complex binary traits. Several two-locus models for penetrance have been proposed to aid the genetic dissection of binary traits. Such models assume linear genetic effects of both loci in different mathematical scales of penetrance, resembling the analytical framework of quantitative traits. However, changes in phenotypic scale are difficult to envisage in binary traits and limited genetic interpretation is extractable from current modeling of penetrance. To overcome this limitation, we derived an allelic penetrance approach that attributes incomplete penetrance to the stochastic expression of the alleles controlling the phenotype, the genetic background and environmental factors. We applied this approach to formulate dominance and recessiveness in a single diallelic locus and to model different genetic mechanisms for the joint action of two diallelic loci. We fit the models to data on the genetic susceptibility of mice following infections with Listeria monocytogenes and Plasmodium berghei. These models gain in genetic interpretation, because they specify the alleles that are responsible for the genetic (inter)action and their genetic nature (dominant or recessive), and predict genotypic combinations determining the phenotype. Further, we show via computer simulations that the proposed models produce penetrance patterns not captured by traditional two-locus models. This approach provides a new analysis framework for dissecting mechanisms of interlocus joint action in binary traits using genetic crosses.     

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.     

An improved procedure of mapping a quantitative trait locus via the EM algorithm using posterior probabilities

Mapping a locus controlling a quantitative genetic trait (e.g. blood pressure) to a specific genomic region is of considerable contemporary interest. Data on the quantitative trait under consideration and several codominant genetic markers with known genomic locations are collected from members of families and statistically analysed to estimate the recombination fraction, θ, between the putative quantitative trait locus and a genetic marker. One of the major complications in estimating θ for a quantitative trait in humans is the lack of haplotype information on members of families. We have devised a computationally simple two-stage method of estimation of θ in the absence of haplotypic information using the expectation-maximization (EM) algorithm. In the first stage, parameters of the quantitative trait locus (QTL) are estimated on the basis of data of a sample of unrelated individuals and a Bayes’s rule is used to classify each parent into a QTL genotypic class. In the second stage, we have proposed an EM algorithm for obtaining the maximum-likelihood estimate of θ based on data of informative families (which are identified upon inferring parental QTL genotypes performed in the first stage). The purpose of this paper is to investigate whether, instead of using genotypically ‘classified’ data of parents, the use of posterior probabilities of QT genotypes of parents at the second stage yields better estimators. We show, using simulated data, that the proposed procedure using posterior probabilities is statistically more efficient than our earlier classification procedure, although it is computationally heavier.     

Genetic Mapping and Genomic Selection Using Recombination Breakpoint Data

The correct models for quantitative trait locus mapping are the ones that simultaneously include all significant genetic effects. Such models are difficult to handle for high marker density. Improving statistical methods for high-dimensional data appears to have reached a plateau. Alternative approaches must be explored to break the bottleneck of genomic data analysis. The fact that all markers are located in a few chromosomes of the genome leads to linkage disequilibrium among markers. This suggests that dimension reduction can also be achieved through data manipulation. High-density markers are used to infer recombination breakpoints, which then facilitate construction of bins. The bins are treated as new synthetic markers. The number of bins is always a manageable number, on the order of a few thousand. Using the bin data of a recombinant inbred line population of rice, we demonstrated genetic mapping, using all bins in a simultaneous manner. To facilitate genomic selection, we developed a method to create user-defined (artificial) bins, in which breakpoints are allowed within bins. Using eight traits of rice, we showed that artificial bin data analysis often improves the predictability compared with natural bin data analysis. Of the eight traits, three showed high predictability, two had intermediate predictability, and two had low predictability. A binary trait with a known gene had predictability near perfect. Genetic mapping using bin data points to a new direction of genomic data analysis.     

Application of the false discovery rate to quantitative trait loci interval mapping with multiple traits

Controlling the false discovery rate (FDR) has been proposed as an alternative to controlling the genome-wise error rate (GWER) for detecting quantitative trait loci (QTL) in genome scans. The objective here was to implement FDR in the context of regression interval mapping for multiple traits. Data on five traits from an F2 swine breed cross were used. FDR was implemented using tests at every 1 cM (FDR1) and using tests with the highest test statistic for each marker interval (FDRm). For the latter, a method was developed to predict comparison-wise error rates. At low error rates, FDR1 behaved erratically; FDRm was more stable but gave similar significance thresholds and number of QTL detected. At the same error rate, methods to control FDR gave less stringent significance thresholds and more QTL detected than methods to control GWER. Although testing across traits had limited impact on FDR, single-trait testing was recommended because there is no theoretical reason to pool tests across traits for FDR. FDR based on FDRm was recommended for QTL detection in interval mapping because it provides significance tests that are meaningful, yet not overly stringent, such that a more complete picture of QTL is revealed.     

Fine mapping quantitative trait loci affecting milk production traits on bovine chromosome 6 in a Chinese Holstein population

To fine map the previously detected quantitative trait loci （QTLs） affecting milk production traits on bovine chromosome 6 （BTA6）, 15 microsatellite markers situated within an interval of 14.3 cM spanning from BMS690 to BM4528 were selected and 918 daughters of 8 sires were genotyped. Two mapping approaches, haplotype sharing based LD mapping and single marker regression mapping, were used to analyze the data. Both approaches revealed a quantitative trait locus （QTL） with significant effects on milk yield, fat yield and protein yield located in the segment flanked by markers BMS483 and MNB209, which spans a genetic distance of 0.6 cM and a physical distance of 1.5 Mb. In addition, the single marker regression mapping also revealed a QTL affecting fat percentage and protein percentage at marker DIK2291. Our fine mapping work will facilitate the cloning of candidate genes underlying the QTLs for milk production traits.     

QTL analysis of yield and seed number in Citrus

Amount, regularity and low seed content of the crop are important properties of scion citrus cultivars. The genetic control of these traits was studied in a progeny derived from the cross Citrus volkameriana×Poncirus trifoliata using molecular marker analysis. Since the traits were not normally distributed, the Kruskal-Wallis non-parametric test was used for quantitative trait loci (QTLs) detection. Most of the QTLs detected correspond to the trait ”number of fruits per tree”, in agreement with its known physiological complexity. Related traits (fruit number, fruit size and seed number) are controlled by QTLs some of which are located in the same genomic regions, suggesting that undesired associations could be broken to some degree by recombination. QTL analysis over years revealed important effects of genotype-by-environment interaction on QTL detection. This result agrees with the differences found for the trait means among years, which was found to be related, among other causes, to the alternate bearing of some genotypes and the amount of rain before harvest. Received: 1 October 1999 / Accepted: 2 December 1999     

Evidence for genetic heterogeneity in hereditary hydronephrosis caused by pelvi-ureteric junction obstruction,with one locus assigned to chromosome 6p

Summary Hereditary hydronephrosis (MIM 143400) is an autosomal dominant trait that causes unilateral or bilateral pelvi-ureteric junction (PUJ) obstruction. Linkage analysis was undertaken in 5 families with hereditary PUJ obstruction using the major histocompatibility complex locus as a test marker. The data as a whole supported a hereditary hydronephrosis locus on 6p. Maximal lod scores were 3.090 at a recombination fraction of 0.1 with full penetrance, and 2.486 at a recombination fraction of 0.1 with a penetrance of 90%. However, analysis of two point lod scores using the HOMOG program revealed significant evidence for genetic heterogeneity with one locus on 6p in 4 of the families, and a different locus in one family. After exclusion of this unlinked family, two point analysis gave a maximal lod score of 3.9 at a recombination fraction of 0.05 with full penetrance, and 4.2 at a recombination fraction of 0.0 with 90% penetrance. These data support the assignment of one of the loci for hereditary hydronephrosis to chromosome 6p.     

Verification of marker–trait associations in biparental winter barley (<Emphasis Type="Italic">Hordeum vulgare</Emphasis> L.) DH populations

In previous genome-wide association studies, marker–trait associations for grain yield and additional traits of agronomic importance were identified in the German winter barley (Hordeum vulgare L.) breeding gene pool. In the present study, seven doubled haploid populations segregating for the relevant alleles at the associated loci were used to get information whether these marker–trait associations can be verified in biparental populations and reliably used in applied barley breeding. The doubled haploid populations were phenotyped in field trials at two to five locations each in 1 year and genotyped by 40 trait-associated single nucleotide polymorphisms using an Illumina VeraCode GoldenGate assay. Large phenotypic variation was observed for all traits within at least one doubled haploid population. For 19 out of 58 marker–trait associations tested, the phenotypic means of both marker classes were significantly (p ≤ 0.005) different, thus confirming the association of the respective marker and the quantitative trait locus detected. For example, doubled haploid lines derived from a cross of ‘Malta’ × ‘Goldmine’ carrying different marker alleles differed by 0.41 t/ha in mean grain yield. The 19 (out of 58) marker–trait associations verified correspond to 10 (out of 27) genomic regions. Markers that were verified to be associated with a quantitative trait locus can be implemented directly in winter barley breeding for the selection of parental lines and marker-assisted pedigree selection.     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Molecular mapping of qualitative and quantitative loci for resistance to Leptosphaeria maculans causing blackleg disease in canola (Brassica napus L.)

Blackleg, caused by Leptosphaeria maculans, is one of the most important diseases of oilseed and vegetable crucifiers worldwide. The present study describes (1) the construction of a genetic linkage map, comprising 255 markers, based upon simple sequence repeats (SSR), sequence-related amplified polymorphism, sequence tagged sites, and EST-SSRs and (2) the localization of qualitative (race-specific) and quantitative (race non-specific) trait loci controlling blackleg resistance in a doubled-haploid population derived from the Australian canola (Brassica napus L.) cultivars Skipton and Ag-Spectrum using the whole-genome average interval mapping approach. Marker regression analyses revealed that at least 14 genomic regions with LOD ≥ 2.0 were associated with qualitative and quantitative blackleg resistance, explaining 4.6-88.9 % of genotypic variation. A major qualitative locus, designated RlmSkipton (Rlm4), was mapped on chromosome A7, within 0.8 cM of the SSR marker Xbrms075. Alignment of the molecular markers underlying this QTL region with the genome sequence data of B. rapa L. suggests that RlmSkipton is located approximately 80 kb from the Xbrms075 locus. Molecular marker-RlmSkipton linkage was further validated in an F(2) population from Skipton/Ag-Spectrum. Our results show that SSR markers linked to consistent genomic regions are suitable for enrichment of favourable alleles for blackleg resistance in canola breeding programs.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Genetic Control of the Leaf Angle and Leaf Orientation Value as Revealed by Ultra-High Density Maps in Three Connected Maize Populations

Plant architecture is a key factor for high productivity maize because ideal plant architecture with an erect leaf angle and optimum leaf orientation value allow for more efficient light capture during photosynthesis and better wind circulation under dense planting conditions. To extend our understanding of the genetic mechanisms involved in leaf-related traits, three connected recombination inbred line (RIL) populations including 538 RILs were genotyped by genotyping-by-sequencing (GBS) method and phenotyped for the leaf angle and related traits in six environments. We conducted single population quantitative trait locus (QTL) mapping and joint linkage analysis based on high-density recombination bin maps constructed from GBS genotype data. A total of 45 QTLs with phenotypic effects ranging from 1.2% to 29.2% were detected for four leaf architecture traits by using joint linkage mapping across the three populations. All the QTLs identified for each trait could explain approximately 60% of the phenotypic variance. Four QTLs were located on small genomic regions where candidate genes were found. Genomic predictions from a genomic best linear unbiased prediction (GBLUP) model explained 45±9% to 68±8% of the variation in the remaining RILs for the four traits. These results extend our understanding of the genetics of leaf traits and can be used in genomic prediction to accelerate plant architecture improvement.     

A Minimum Distance Estimation Approach to Estimate the Recombination Fraction from a Marker Locus in Robust Linkage Analysis for Quantitative Traits

OLSON and WIJSMAN (1993) have proposed a robust linkage analysis between quantitative traits and a marker locus using all relative pairs. We extend their work to estimate the recombination fraction using a two-step procedure. In the first step Generalised Estimating Equations are solved. After robust linkage analysis minimum distance estimation is applied in the second step. Our approach requires a single codominant marker locus only. The relevant parameters of the genetic model can also be estimated by this method in the presence of linkage. We illustrate our approach by simulations.     

QTL analysis of white blood cell, platelet and red blood cell-related traits in an F2 intercross between Landrace and Korean native pigs

Haematological traits play important roles in disease resistance and defence functions. The objective of this study was to locate quantitative trait loci (QTL) and the associated positional candidate genes influencing haematological traits in an F₂ intercross between Landrace and Korean native pigs. Eight blood‐related traits (six erythrocyte traits, one leucocyte trait and one platelet trait) were measured in 816 F₂ progeny. All experimental animals were genotyped with 173 informative microsatellite markers located throughout the pig genome. We report that nine chromosomes harboured QTL for the baseline blood parameters: genomic regions on SSC 1, 4, 5, 6, 8, 9, 11, 13 and 17. Eight of twenty identified QTL reached genome‐wide significance. In addition, we evaluated the KIT locus, an obvious candidate gene locus affecting variation in blood‐related traits. Using dense single nucleotide polymorphism marker data on SSC 8 and the marker‐assisted association test, the strong association of the KIT locus with blood phenotypes was confirmed. In conclusion, our study identified both previously reported and novel QTL affecting baseline haematological parameters in pigs. Additionally, the positional candidate genes identified here could play an important role in elucidating the genetic architecture of haematological phenotype variation in swine and in humans.     

A semiparametric approach for composite functional mapping of dynamic quantitative traits

Functional mapping has emerged as a powerful tool for mapping quantitative trait loci (QTL) that control developmental patterns of complex dynamic traits. Original functional mapping has been constructed within the context of simple interval mapping, without consideration of separate multiple linked QTL for a dynamic trait. In this article, we present a statistical framework for mapping QTL that affect dynamic traits by capitalizing on the strengths of functional mapping and composite interval mapping. Within this so-called composite functional-mapping framework, functional mapping models the time-dependent genetic effects of a QTL tested within a marker interval using a biologically meaningful parametric function, whereas composite interval mapping models the time-dependent genetic effects of the markers outside the test interval to control the genome background using a flexible nonparametric approach based on Legendre polynomials. Such a semiparametric framework was formulated by a maximum-likelihood model and implemented with the EM algorithm, allowing for the estimation and the test of the mathematical parameters that define the QTL effects and the regression coefficients of the Legendre polynomials that describe the marker effects. Simulation studies were performed to investigate the statistical behavior of composite functional mapping and compare its advantage in separating multiple linked QTL as compared to functional mapping. We used the new mapping approach to analyze a genetic mapping example in rice, leading to the identification of multiple QTL, some of which are linked on the same chromosome, that control the developmental trajectory of leaf age.