More about quantitative trait locus mapping with diallel designs

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.     

Biometric-genetic analysis of genotype dissimilarity in diallel crosses of spring wheat

A new biometric-genetic model and parameters described in [1] have been used for analysis of pair dissimilarity between spring wheat cultivars and F1 hybrids obtained by diallel crossing. The dissimilarity between the reactions of different genotypes estimated by a growth trait (plant height) served as a metric. The mode of inheritance of dissimilarity has been determined, and the cultivars that are the most dissimilar in allelic composition have been detected.     

Analysis of quantitative trait loci using hybrid pedigrees: quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral chi(2) distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are original data for the analysis of a quantitative trait.     

Biometric-genetic analysis of genotype dissimilarity in diallel crosses of spring wheat

A new biometric-genetic model and parameters described in [2] have been used for analysis of pair dissimilarity between spring wheat cultivars and F₁ hybrids obtained by diallel crossing. The dissimilarity between shape of the reactions of different genotypes estimated by a growth trait (plant height) served as a metric. The mode of inheritance of dissimilarity has been determined, and the cultivars that are the most dissimilar in allelic composition have been detected.     

A score test for the linkage analysis of qualitative and quantitative traits based on identity by descent data from sib-pairs

We propose a general likelihood-based approach to the linkage analysis of qualitative and quantitative traits using identity by descent (IBD) data from sib-pairs. We consider the likelihood of IBD data conditional on phenotypes and test the null hypothesis of no linkage between a marker locus and a gene influencing the trait using a score test in the recombination fraction theta between the two loci. This method unifies the linkage analysis of qualitative and quantitative traits into a single inferential framework, yielding a simple and intuitive test statistic. Conditioning on phenotypes avoids unrealistic random sampling assumptions and allows sib-pairs from differing ascertainment mechanisms to be incorporated into a single likelihood analysis. In particular, it allows the selection of sib-pairs based on their trait values and the analysis of only those pairs having the most informative phenotypes. The score test is based on the full likelihood, i.e. the likelihood based on all phenotype data rather than just differences of sib-pair phenotypes. Considering only phenotype differences, as in Haseman and Elston (1972) and Kruglyak and Lander (1995), may result in important losses in power. The linkage score test is derived under general genetic models for the trait, which may include multiple unlinked genes. Population genetic assumptions, such as random mating or linkage equilibrium at the trait loci, are not required. This score test is thus particularly promising for the analysis of complex human traits. The score statistic readily extends to accommodate incomplete IBD data at the test locus, by using the hidden Markov model implemented in the programs MAPMAKER/SIBS and GENEHUNTER (Kruglyak and Lander, 1995; Kruglyak et al., 1996). Preliminary simulation studies indicate that the linkage score test generally matches or outperforms the Haseman-Elston test, the largest gains in power being for selected samples of sib-pairs with extreme phenotypes.     

A blocking Gibbs sampling method to detect major genes with phenotypic data from a diallel mating

Diallel mating is a frequently used design for estimating the additive and dominance genetic (polygenic) effects involved in quantitative traits observed in the half- and full-sib progenies generated in plant breeding programmes. Gibbs sampling has been used for making statistical inferences for a mixed-inheritance model (MIM) that includes both major genes and polygenes. However, using this approach it has not been possible to incorporate the genetic properties of major genes with the additive and dominance polygenic effects in a diallel mating population. A parent block Gibbs sampling method was developed in this study to make statistical inferences about the major gene and polygenic effects on quantitative traits for progenies derived from a half-diallel mating design. Using simulated data sets with different major and polygenic effects, the proposed method accurately estimated the major and polygenic effects of quantitative traits, and possible genotypes of parents and progenies. The impact of specifying different prior distributions was examined and was found to have little effect on inference on the posterior distribution. This approach was applied to an experimental data set of Loblolly pine (Pinus taeda L.) derived from a 6-parent half-diallel mating. The result indicated that there might be a recessive major gene affecting height growth in this diallel population.     

Analysis of quantitative trait loci using hybrid pedigrees: Quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral x ² distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are initial data for the analysis of a quantitative trait.     

Modeling effect of homo- or heterozygosity on animal growth intensity

A model has been developed that describes the dependence of a quantitative selective trait on the animal homo- and heterozygosity for the genes that control the biochemical reaction rate (isoenzyme systems). The model includes any cases of gene control of a quantitative trait and is applicable to real, genetically heterogeneous populations. The results of testing the model show that it can be used for identifying the genes involved in additive polygenic determination of quantitative commercially valuable traits.     

Mapping quantitative trait loci controlling silking date in a diallel cross among four lines of maize

 We describe and apply an interval mapping method for quantitative trait locus (QTL) detection using F₃ and testcross progenies derived from F₂ populations obtained from a diallel cross among four elite lines of maize. Linear model-based procedures were used for the test and estimation of putative QTL effects together with genetic interactions including epistasis. We mapped QTL associated with silking date and explored their genetic effects. Ten QTL were detected, and these explained more than 40% of the phenotypic variance. Most of these QTL had consistent and stable effects among genetic backgrounds and did not show significant epistasis. QTL-by-environment interaction was important for four QTL and was essentially due to changes in magnitude of allelic effects. These results show the efficiency of our method in several genetic situations as well as the power of the diallel design in detecting QTL simultaneously over several populations. Received: 2 September 1996 / Accepted: 20 December 1996     

Detecting the undetected: estimating the total number of loci underlying a quantitative trait

Recent studies have begun to reveal the genes underlying quantitative trait differences between closely related populations. Not all quantitative trait loci (QTL) are, however, equally likely to be detected. QTL studies involve a limited number of crosses, individuals, and genetic markers and, as a result, often have little power to detect genetic factors of small to moderate effects. In this article, we develop an estimator for the total number of fixed genetic differences between two parental lines. Like the Castle-Wright estimator, which is based on the observed segregation variance in classical crossbreeding experiments, our QTL-based estimator requires that a distribution be specified for the expected effect sizes of the underlying loci. We use this expected distribution and the observed mean and minimum effect size of the detected QTL in a likelihood model to estimate the total number of loci underlying the trait difference. We then test the QTL-based estimator and the Castle-Wright estimator in Monte Carlo simulations. When the assumptions of the simulations match those of the model, both estimators perform well on average. The 95% confidence limits of the Castle-Wright estimator, however, often excluded the true number of underlying loci, while the confidence limits for the QTL-based estimator typically included the true value approximately 95% of the time. Furthermore, we found that the QTL-based estimator was less sensitive to dominance and to allelic effects of opposite sign than the Castle-Wright estimator. We therefore suggest that the QTL-based estimator be used to assess how many loci may have been missed in QTL studies.     

Estimation of variance components of quantitative traits in inbred populations

Use of variance-component estimation for mapping of quantitative-trait loci in humans is a subject of great current interest. When only trait values, not genotypic information, are considered, variance-component estimation can also be used to estimate heritability of a quantitative trait. Inbred pedigrees present special challenges for variance-component estimation. First, there are more variance components to be estimated in the inbred case, even for a relatively simple model including additive, dominance, and environmental effects. Second, more identity coefficients need to be calculated from an inbred pedigree in order to perform the estimation, and these are computationally more difficult to obtain in the inbred than in the outbred case. As a result, inbreeding effects have generally been ignored in practice. We describe here the calculation of identity coefficients and estimation of variance components of quantitative traits in large inbred pedigrees, using the example of HDL in the Hutterites. We use a multivariate normal model for the genetic effects, extending the central-limit theorem of Lange to allow for both inbreeding and dominance under the assumptions of our variance-component model. We use simulated examples to give an indication of under what conditions one has the power to detect the additional variance components and to examine their impact on variance-component estimation. We discuss the implications for mapping and heritability estimation by use of variance components in inbred populations.     

Predicting response to selection on a quantitative trait: a comparison between models for mixed-mating populations

Two different theoretical frameworks have been developed to predict response to selection in a mixed mating population (in which reproduction occurs by a mixture of outcrossing and self-fertilization). The genotypic covariance model (GCM) and the structured linear model (SLM) rely on the same assumptions regarding quantitative trait inheritance, but use different genetic summary statistics. Here, we demonstrate the algebraic relationships between the various genetic metrics used in each theory. This is accomplished by reformulating the GCM in terms of the Wright-Kempthorne equation. We use stochastic simulations to investigate the relative accuracy of each theory for a range of selfing rates. The SLM is generally more accurate than the GCM, the most pronounced differences emerging in simulations with inbreeding depression for fitness. In fact, with strong inbreeding depression and high selfing rates, evolution can occur opposite the direction predicted by the GCM. The simulations also indicate that direct application of random mating models to partially selfing populations can produce very inaccurate predictions if quantitative trait loci exhibit dominance.     

多维功能作图在胡杨幼苗生长QTL的应用

功能作图框架能够表征复杂动态性状背后的数量性状位点(Quantitative trait locus, QTL)或核苷酸。此前,功能作图广泛应用于单个性状或两个性状的QTL定位当中,多个相关性状功能作图的研究相对匮乏。本研究通过对SAD(Structured antedependence)模型进一步推导,得到在多个性状时用于拟合时间相关协方差矩阵的结构化模型,并使用胡杨(Populus euphratica Oliv.)340个F₁代群体的4个生长相关性状以及模拟实验对多维功能作图模型进行测试。结果显示,共定位出173个显著位点,分布于除4、9、10、15、16以外的染色体。功能注释涉及参与叶绿体早期发育、生长素横向运输、提高植物非生物胁迫耐受性以及作为跨膜运输系统开关等生物学过程的32个基因。     

Sensory bias as an explanation for the evolution of mate preferences

The sensory bias model of sexual selection posits that female mating preferences are by-products of natural selection on sensory systems. Although sensory bias was proposed 20 years ago, its critical assumptions remain untested. This paradox arises because sensory bias has been used to explain two different phenomena. First, it has been used as a hypothesis about signal design, that is, that males evolve traits that stimulate female sensory systems. Second, sensory bias has been used as a hypothesis for the evolution of female preference itself, that is, to explain why females exhibit particular preferences. We focus on this second facet. First, we clarify the unique features of sensory bias relative to the alternative models by considering each in the same quantitative genetic framework. The key assumptions of sensory bias are that natural selection is the predominant evolutionary mechanism that affects preference and that sexual selection on preferences is quantitatively negligible. We describe four studies that would test these assumptions and review what we can and cannot infer about sensory bias from existing studies. We suggest that the importance of sensory bias as an explanation for the evolution of female preferences remains to be determined.     

The Use of Combining Ability Analysis to Identify Elite Parents for Artemisia annua F1 Hybrid Production

Artemisia annua is an important medicinal crop used for the production of the anti-malarial compound artemisinin. In order to assist in the production of affordable high quality artemisinin we have carried out an A. annua breeding programme aimed at improving artemisinin concentration and biomass. Here we report on a combining ability analysis of a diallel cross to identify robust parental lines for hybrid breeding. The parental lines were selected based on a range of phenotypic traits to encourage heterosis. The general combining ability (GCA) values for the diallel parental lines correlated to the positive alleles of quantitative trait loci (QTL) in the same parents indicating the presence of beneficial alleles that contribute to parental performance. Hybrids generated from crossing specific parental lines with good GCA were identified as having an increase in both artemisinin concentration and biomass when grown either in glasshouse or experimental field trials and compared to controls. This study demonstrates that combining ability as determined by a diallel cross can be used to identify elite parents for the production of improved A. annua hybrids. Furthermore, the selection of material for breeding using this approach was found to be consistent with our QTL-based molecular breeding approach.     

Genetic mapping of developmental instability: design, model and algorithm

Developmental instability or noise, defined as the phenotypic imprecision of an organism in the face of internal or external stochastic disturbances, has been thought to play an important role in shaping evolutionary processes and patterns. The genetic studies of developmental instability have been based on fluctuating asymmetry (FA) that measures random differences between the left and the right sides of bilateral traits. In this article, we frame an experimental design characterized by a spatial autocorrelation structure for determining the genetic control of developmental instability for those traits that cannot be bilaterally measured. This design allows the residual environmental variance of a quantitative trait to be dissolved into two components due to permanent and random environmental factors. The degree of developmental instability is quantified by the relative proportion of the random residual variance to the total residual variance. We formulate a mixture model to estimate and test the genetic effects of quantitative trait loci (QTL) on the developmental instability of the trait. The genetic parameters including the QTL position, the QTL effects, and spatial autocorrelations are estimated by implementing the EM algorithm within the mixture model framework. Simulation studies were performed to investigate the statistical behavior of the model. A live example for poplar trees was used to map the QTL that control root length growth and its developmental instability from cuttings in water culture.     

Using mating designs to uncover QTL and the genetic architecture of complex traits

Analysis of quantitative trait loci (QTL) affecting complex traits is often pursued in single-cross experiments. For most purposes, including breeding, some assessment is desired of the generalizability of the QTL findings and of the overall genetic architecture of the trait. Single-cross experiments provide a poor basis for these purposes, as comparison across experiments is hampered by segregation of different allelic combinations among different parents and by context-dependent effects of QTL. To overcome this problem, we combined the benefits of QTL analysis (to identify genomic regions affecting trait variation) and classic diallel analysis (to obtain insight into the general inheritance of the trait) by analyzing multiple mapping families that are connected via shared parents. We first provide a theoretical derivation of main (general combining ability (GCA)) and interaction (specific combining ability (SCA)) effects on F(2) family means relative to variance components in a randomly mating reference population. Then, using computer simulations to generate F(2) families derived from 10 inbred parents in different partial-diallel designs, we show that QTL can be detected and that the residual among-family variance can be analyzed. Standard diallel analysis methods are applied in order to reveal the presence and mode of action (in terms of GCA and SCA) of undetected polygenes. Given a fixed experiment size (total number of individuals), we demonstrate that QTL detection and estimation of the genetic architecture of polygenic effects are competing goals, which should be explicitly accounted for in the experimental design. Our approach provides a general strategy for exploring the genetic architecture, as well as the QTL underlying variation in quantitative traits.     

Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods

In recent years, three related methods have been used to model the phenotypic dynamics of traits under the influence of natural selection. The first is based on an approximation to quantitative genetic recursion equations for sexual populations. The second is based on evolution in asexual lineages with mutation-generated variation. The third method finds an evolutionarily stable set of phenotypes for species characterized by a given set of fitness functions, assuming that the mode of reproduction places no constraints on the number of distinct types that can be maintained in the population. The three methods share the property that the rate of change of a trait within a homogeneous population is approximately proportional to the individual fitness gradient. The methods differ in assumptions about the potential magnitude of phenotypic differences in mutant forms, and in their assumptions about the probability that invasion or speciation occurs when a species has a stable, yet invadable phenotype. Determining the range of applicability of the different methods is important for assessing the validity of optimization methods in predicting the evolutionary outcome of ecological interactions. Methods based on quantitative genetic models predict that fitness minimizing traits will often be evolutionarily stable over significant time periods, while other approaches suggest this is likely to be rare. A more detailed study of cases of disruptive selection might reveal whether fitness-minimizing traits occur frequently in natural communities.     

Detecting epistatic genetic variance with a clonally replicated design: models for lowvs high-order nonallelic interaction

A quantitative genetic model, that uses known family structure with clonal replicates to separate genetic variance into its additive, dominance and epistatic components, is available in the current literature. Making use of offspring testing, this model is based on the theory that components of variance from the linear model of an experimental design may be expressed in terms of expected covariances among relatives. However, if interactions between a pair of quantitative trait loci (QTLs) explain a large proportion of the total epistasis, it will seriously overestimate the additive and dominance variances but underestimate the epistatic variance. In the present paper, a new model is developed to manipulate this problem by combining parental and offspring material into the same test. Under the condition described above, the new model can provide an accurate estimate for additive x additive variances. Also, its accuracy in estimating dominance and total epistatic variances is much greater than the accuracy of the previous model. However, if there is obvious evidence showing the major contribution of high-order interactions, especially among 4QTLs, to the total epistasis, the previous model is more appropriate to partition the genetic variance for a quantitative trait. The re-analysis of an example from a factorial mating design in poplar shows large differences in estimating variance components between the new and previous models when two different assumptions (lowvs high-order epistatic interactions) are used. The new model will be an alternative to estimating the mode of quantitative inheritance for species, especially for longlived, predominantly outcrossing forest trees, that can be clonally replicated.     

Power to detect higher-order epistatic interactions in a metabolic pathway using a new mapping strategy

Epistatic interactions among quantitative trait loci (QTL) contribute substantially to the variation in complex traits. The main objectives of this study were to (i) compare three- vs. four-step genome scans to identify three-way epistatic interactions among QTL belonging to a metabolic pathway, (ii) investigate by computer simulations the power and proportion of false positives (PFP) for detecting three-way interactions among QTL in recombinant inbred line (RIL) populations derived from a nested mating design, and (iii) compare these estimates to those obtained for detecting three-way interactions among QTL in RIL populations derived from diallel and different partial diallel mating designs. The single-nucleotide polymorphism haplotype data of B73 and 25 diverse maize inbreds were used to simulate the production of various RIL populations. Compared to the three-step genome scan, the power to detect three-way interactions was higher with the four-step genome scan. Higher power to detect three-way interactions was observed for RILs derived from optimally allocated distance-based designs than from nested designs or diallel designs. The power and PFP to detect three-way interactions using a nested design with 5000 RILs were for both the 4-QTL and the 12-QTL scenario of a magnitude that seems promising for their identification.