A quantitative genetics model for viability selection

Viability selection will change gene frequencies of loci controlling fitness. Consequently, the frequencies of marker loci linked to the viability loci will also change. In genetic mapping, the change of marker allelic frequencies is reflected by the departure from Mendelian segregation ratio. The non-Mendelian segregation of markers has been used to map viability loci along the genome. However, current methods have not been able to detect the amount of selection (s) and the degree of dominance (h) simultaneously. We developed a method to detect both s and h using an F2 mating design under the classical fitness model. We also developed a quantitative genetics model for viability selection by proposing a continuous liability controlling the viability of individuals. With the liability model, mapping viability loci has been formulated as mapping quantitative trait loci. As a result, nongenetic systematic environmental effects can be easily incorporated into the model and subsequently separated from the genetic effects of the viability loci. The quantitative genetic model has been verified with a series of Monte Carlo simulation experiments.     

The Contribution of Quantitative Trait Loci and Neutral Marker Loci to the Genetic Variances and Covariances among Quantitative Traits in Random Mating Populations

Using Cockerham's approach of orthogonal scales, we develop genetic models for the effect of an arbitrary number of multiallelic quantitative trait loci (QTLs) or neutral marker loci (NMLs) upon any number of quantitative traits. These models allow the unbiased estimation of the contributions of a set of marker loci to the additive and dominance variances and covariances among traits in a random mating population. The method has been applied to an analysis of allozyme and quantitative data from the European oyster. The contribution of a set of marker loci may either be real, when the markers are actually QTLs, or apparent, when they are NMLs that are in linkage disequilibrium with hidden QTLs. Our results show that the additive and dominance variances contributed by a set of NMLs are always minimum estimates of the corresponding variances contributed by the associated QTLs. In contrast, the apparent contribution of the NMLs to the additive and dominance covariances between two traits may be larger than, equal to or lower than the actual contributions of the QTLs. We also derive an expression for the expected variance explained by the correlation between a quantitative trait and multilocus heterozygosity. This correlation explains only a part of the genetic variance contributed by the markers, i.e., in general, a combination of additive and dominance variances and, thus, provides only very limited information relative to the method supplied here.     

Mapping quantitative trait loci underlying triploid endosperm traits

Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue in cereals. Endosperm tissue determines the grain quality of cereals. Improving grain quality is one of the important breeding objectives in cereals. However, current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. In this paper, we derive for the first time the conditional probabilities of F(3) endosperm QTL genotypes given different flanking marker genotypes in F(2) plants. Using these probabilities, we develop a multiple linear regression method implemented via the iteratively reweighted least-squares (IRWLS) algorithm and a maximum likelihood method (ML) implemented via the expectation-maximization (EM) algorithm to map QTL underlying endosperm traits. We use the mean value of endosperm traits of F(3) seeds as the dependent variable and the expectations of genotypic indicators for additive and dominance effect of a putative QTL flanked by a pair of markers as independent variables for IRWLS mapping. However, if an endosperm trait is measured quantitatively using a single endosperm sample, the ML mapping method can be used to separate the two dominance effects. Efficiency of the methods is verified through extensive Monte Carlo simulation studies. Results of simulation show that the proposed methods provide accurate estimates of both the QTL effects and locations with very high statistical power. With these methods, we are now ready to map endosperm traits, as we can for regular quantitative trait under diploid control.     

Linkage analysis of quantitative traits in an interspecific cross of tomato (lycopersicon esculentum x lycopersicon pimpinellifolium) by means of genetic markers

Linkage relationships between loci affecting quantitative traits (QTL) and marker loci were examined in an interspecific cross between Lycopersicon esculentum and Lycopersicon pimpinellifolium. Parental lines differed for six morphological markers and for four electrophoretic markers. Almost 1700 F-2 plants were scored with respect to the genetic markers and also with respect to 18 quantitative traits. Major genes affecting the quantitative traits were not found, but out of 180 possible marker x trait combinations, 85 showed significant quantitative effects associated with the genetic markers. The average marker-associated main effect was on the order of 6% of the mean value of the trait. Most of the main effects were apparently due to linkage of QTL to the marker loci rather than to pleiotropy. Fourteen of the traits showed at least one highly significant effect of opposite sign to the overall difference between the parental lines, demonstrating the ability of this design to uncover cryptic genetic variation. Significant variance and skewness effects on the quantitative traits were found to be associated with the genetic markers, suggesting the possible presence of loci affecting the variance and shape of quantitative trait distribution in a population. Most marker-associated quantitative effects showed some degree of dominance, generally in the direction of the L. pimpinellifolium parent. When the significant marker-associated effects were examined in pairs, 12% showed significant interaction effects. The results of this study illustrate the potential usefulness of this type of analysis for the detailed genetic investigation of quantitative trait variation in suitably marked populations.     

Comparing linkage disequilibrium-based methods for fine mapping quantitative trait loci

Recently, a method for fine mapping quantitative trait loci (QTL) using linkage disequilibrium was proposed to map QTL by modeling covariance between individuals, due to identical-by-descent (IBD) QTL alleles, on the basis of the similarity of their marker haplotypes under an assumed population history. In the work presented here, the advantage of using marker haplotype information for fine mapping QTL was studied by comparing the IBD-based method with 10 markers to regression on a single marker, a pair of markers, or a two-locus haplotype under alternative population histories. When 10 markers were genotyped, the IBD-based method estimated the position of the QTL more accurately than did single-marker regression in all populations. When 20 markers were genotyped for regression, as single-marker methods do not require knowledge of haplotypes, the mapping accuracy of regression in all populations was similar to or greater than that of the IBD-based method using 10 markers. Thus for populations similar to those simulated here, the IBD-based method is comparable to single-marker regression analysis for fine mapping QTL.     

GENETIC BASIS OF INBREEDING DEPRESSION IN ARABIS PETRAEA

Inbreeding depression may be caused by (partially) recessive or overdominant gene action. The relative evolutionary importance of these two modes has been debated; the former mode is emphasized in the “dominance hypothesis,” the latter in the “overdominance hypothesis.” We analyzed the genetic basis of inbreeding depression in the self-incompatible herb Arabis petraea (L.) Lam.: In the selfed progeny of twelve parental plants, we studied the proportion of chlorophyll-deficient seedlings, the genotypic distributions of marker genes, and associations of marker genotypes with viability and quantitative traits. Early components of fitness were examined by scoring seed size, germination time, and early growth rate and by observing the proportion of chlorophyll-deficient seedlings. Later components of fitness, flowering, and root and aboveground biomass were also measured. Marker genotypes of young seedlings were scored for 11 enzyme loci and three microsatellite markers. We found a high proportion (about 70%) of families with chlorophyll-deficient seedlings, indicating a high mutational load. We found six significant deviations from 1:2:1 ratio at marker loci of 60 tests in seedlings, with three of these significant at the experimentwide level. Deviations from the expected ratio were assumed to be due to linked viability loci. A graphical and a Bayesian method were used to distinguish between the overdominance and dominance hypotheses. Most of the deviant segregation ratios suggested overdominance instead of recessivity of the deleterious allele. Neither the early (seed size, germination time, or early growth trait) nor the late quantitative traits (flowering, and root and aboveground biomass) showed significant linkage to markers at the experimentwide level. Presence of significant associations between markers and early viability, but lack thereof for quantitative traits expressed late, suggests either that there may be relatively low inbreeding depression in later life stages or that individual quantitative trait loci may have smaller effects than loci contributing to early viability.     

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.     

A MARKER-BASED METHOD FOR INFERENCES ABOUT QUANTITATIVE INHERITANCE IN NATURAL POPULATIONS

A marker-based method for studying quantitative genetic characters in natural populations is presented and evaluated. The method involves regressing quantitative trait similarity on marker-estimated relatedness between individuals. A procedure is first given for estimating the narrow sense heritability and additive genetic correlations among traits, incorporating shared environments. Estimation of the actual variance of relatedness is required for heritability, but not for genetic correlations. The approach is then extended to include isolation by distance of environments, dominance, and shared levels of inbreeding. Investigations of statistical properties show that good estimates do not require great marker polymorphism, but rather require significant variation of actual relatedness; optimal allocation generally favors sampling many individuals at the expense of assaying fewer marker loci; when relatedness declines with physical distance, it is optimal to restrict comparisons to within a certain distance; the power to estimate shared environments and inbreeding effects is reasonable, but estimates of dominance variance may be difficult under certain patterns of relationship; and any linkage of markers to quantitative trait loci does not cause significant problems. This marker-based method makes possible studies with long-lived organisms or with organisms difficult to culture, and opens the possibility that quantitative trait expression in natural environments can be analyzed in an unmanipulative way.     

A Random Model Approach to Interval Mapping of Quantitative Trait Loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.     

A model for marker-assisted selection among single crosses with multiple genetic markers

 Trait means of marker genotypes are often inconsistent across experiments, thereby hindering the use of regression techniques in marker-assisted selection. Best linear unbiased prediction based on trait and marker data (TM-BLUP) does not require prior information on the mean effects associated with specific marker genotypes and, consequently, may be useful in applied breeding programs. The objective of this paper is to present a flanking-marker, TM-BLUP model that is applicable to interpopulation single crosses that characterize maize (Zea mays L.) breeding programs. The performance of a single cross is modeled as the sum of testcross additive and dominance effects at unmarked quantitative trait loci (QTL) and at marked QTL (MQTL). The TM-BLUP model requires information on the recombination frequencies between flanking markers and the MQTL and on MQTL variances. A tabular method is presented for calculating the conditional probability that MQTL alleles in two inbreds are identical by descent given the observed marker genotypes (G ^k _obs) at the kth MQTL. Information on identity by descent of MQTL alleles can then be used to calculate the conditional covariance of MQTL effects between single crosses given G ^k _obs. The inverse of the covariance matrix for dominance effects at unmarked QTL and MQTL can be written directly from the inverse of the covariance matrices of the corresponding testcross additive effects. In practice, the computations required in TM-BLUP may be prohibitive. The computational requirements may be reduced with simplified TM-BLUP models wherein dominance effects at MQTL are excluded, only the single crosses that have been tested are included, or information is pooled across several MQTL. Received: 22 June 1997 / Accepted: 25 February 1998     

A classical setting for associations between markers and loci affecting quantitative traits

We examine the relationships between a genetic marker and a locus affecting a quantitative trait by decomposing the genetic effects of the marker locus into additive and dominance effects under a classical genetic model. We discuss the structure of the associations between the marker and the trait locus, paying attention to non-random union of gametes, multiple alleles at the marker and trait loci, and non-additivity of allelic effects at the trait locus. We consider that this greater-than-usual level of generality leads to additional insights, in a way reminiscent of Cockerham's decomposition of genetic variance into five terms: three terms in addition to the usual additive and dominance terms. Using our framework, we examine several common tests of association between a marker and a trait.     

A two-stage variable-stringency semiparametric method for mapping quantitative-trait loci with the use of genomewide-scan data on sib pairs

Genomewide scans for mapping loci have proved to be extremely powerful and popular. We present a semiparametric method of mapping a quantitative-trait locus (QTL) or QTLs with the use of sib-pair data generated from a two-stage genomic scan. In a two-stage genomic scan, either the entire genome or a large portion of the genome is saturated with low-density markers at the first stage. At the second stage, the intervals that are identified as probable locations of the trait loci, by means of analysis of data from the first stage, are then saturated with higher-density markers. These data are then analyzed for fine mapping of the loci. Our statistical strategy for analysis of data from the first stage is a low-stringency method based on the rank correlation of squared trait-difference values of the sib pairs and the estimated identity-by-descent scores at the marker loci. We suggest the use of a low-stringency method at the first stage, to save on computational time and to avoid missing any marker interval that may contain the trait loci. For analysis of data from the second stage, we have developed a high-stringency nonparametric-regression approach, using the kernel-smoothing technique. Through extensive simulations, we show that this approach is more powerful than is a currently used method for mapping QTLs by use of sib pairs, particularly in the presence of dominance and epistatic effects at the trait loci.     

Stochastic search variable selection for identifying multiple quantitative trait loci

In this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.     

Interactions between markers can be caused by the dominance effect of quantitative trait loci

F₂ populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive composite-interval QTL mapping (ICIM) for F₂ populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F₂ population.     

Marker-assisted selection using ridge regression

In cross between inbred lines, linear regression can be used to estimate the correlation of markers with a trait of interest; these marker effects then allow marker assisted selection (MAS) for quantitative traits. Usually a subset of markers to include in the model must be selected: no completely satisfactory method of doing this exists. We show that replacing this selection of markers by ridge regression can improve the mean response to selection and reduce the variability of selection response.     

High-resolution association mapping of quantitative trait loci: a population-based approach

In this article, population-based regression models are proposed for high-resolution linkage disequilibrium mapping of quantitative trait loci (QTL). Two regression models, the "genotype effect model" and the "additive effect model," are proposed to model the association between the markers and the trait locus. The marker can be either diallelic or multiallelic. If only one marker is used, the method is similar to a classical setting by Nielsen and Weir, and the additive effect model is equivalent to the haplotype trend regression (HTR) method by Zaykin et al. If two/multiple marker data with phase ambiguity are used in the analysis, the proposed models can be used to analyze the data directly. By analytical formulas, we show that the genotype effect model can be used to model the additive and dominance effects simultaneously; the additive effect model takes care of the additive effect only. On the basis of the two models, F-test statistics are proposed to test association between the QTL and markers. By a simulation study, we show that the two models have reasonable type I error rates for a data set of moderate sample size. The noncentrality parameter approximations of F-test statistics are derived to make power calculation and comparison. By a simulation study, it is found that the noncentrality parameter approximations of F-test statistics work very well. Using the noncentrality parameter approximations, we compare the power of the two models with that of the HTR. In addition, a simulation study is performed to make a comparison on the basis of the haplotype frequencies of 10 SNPs of angiotensin-1 converting enzyme (ACE) genes.     

Pleiotropic effects on mandibular morphology I. Developmental morphological integration and differential dominance

Pleiotropy refers to a single genetic locus that affects more than one phenotypic trait. Pleiotropic effects of genetic loci are thought to play an important role in evolution, reflecting functional and developmental relationships among phenotypes. In a previous study, we examined pleiotropic effects displayed by quantitative trait loci (QTLs) on murine mandibular morphology in relation to mandibular structure and function. In replicating most of our previous QTLs and increasing our sample size, this study strengthens and extends our earlier results. As in our previous study, we find that QTL effects tend to be restricted to developmentally or functionally related traits. In addition, we examine patterns of differential dominance for pleiotropic QTL effects. Differential dominance occurs when dominance patterns for a single locus vary among traits. We find that multivariate overdominance is a common and substantial phenomenon, and may potentially provide an explanation for the persistence of heterozygosity in natural populations.     

QTL analysis: a simple ‘marker-regression’ approach

A method to locate quantitative trait loci (QTL) on a chromosome and to estimate their additive and dominance effects is described. It applies to generations derived from an F₁ by selfing or backcrossing and to doubled haploid lines, given that marker genotype information (RFLP, RAPD, etc.) and quantitative trait data are available. The method involves regressing the additive difference between marker genotype means at a locus against a function of the recombination frequency between that locus and a putative QTL. A QTL is located, as by other regression methods, at that point where the residual mean square is minimised. The estimates of location and gene effects are consistent and as reliable as conventional flanking-marker methods. Further applications include the ability to test for the presence of two, or more, linked QTL and to compare different crosses for the presence of common QTL. Furthermore, the technique is straightforward and may be programmed using standard pc-based statistical software.     

雄性不交换条件下F2群体区间标记——QTL定位的相关方法（英文）

提出了雄性不交换条件下F2群体区间标记定位QTL的相关方法,并且对其适用的条件进行了讨论,通过对分子区间标记进行赋值,计算在无交叉干涉条件下分子标记与表型值的简单相关系数,并在此基础上进行连锁检验,在特定条件下可以估计数量性状座位（QTL）与分子标记座位间的连锁值。