远交群体动态性状基因定位的似然分析Ⅰ.理论方法

受动物遗传育种中用来估计动态性状育种值的随机回归测定日模型思想的启发 ,将关于时间 (测定日期 )的Legendre多项式镶嵌在遗传模型的每个遗传效应中 ,以刻画QTL对动态性状变化过程的作用 ,从而建立起动态性状基因定位的数学模型。利用远交设计群体 ,阐述了动态性状基因定位的似然分析原理 ,推导了定位参数似然估计的EM法两步求解过程。结合动态性状遗传分析的特点和普通数量性状基因定位研究进展 ,还提出了有关动态性状基因定位进一步研究的设想     

Bayesian analysis of genetic architecture of quantitative trait using data of crosses of multiple inbred lines

Using the data of crosses of multiple of inbred lines for mapping QTL can increase QTL detecting power compared with only cross of two inbred lines. Although many fixed-effect model methods have been proposed to analyze such data, they are largely based on one-QTL model or main effect model, and the interaction effects between QTL are always neglected. However, effectively separating the interaction effects from the residual error can increase the statistical power. In this article, we both extended the novel Bayesian model selection method and Bayesian shrinkage estimation approaches to multiple inbred line crosses. With two extensions, interacting QTL are effectively detected with high solution; in addition, the posterior variances for both main effects and interaction effects are also subjected to full Bayesian estimate, which is more optimal than two step approach involved in maximum-likelihood. A series of simulation experiments have been conducted to demonstrate the performance of the methods. The computer program written in FORTRAN language is freely available on request.     

Bayesian robust analysis for genetic architecture of quantitative traits

MOTIVATION: In most quantitative trait locus (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and long-tailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genome-wide interacting QTLs in line crosses. RESULTS: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared with traditional methods assuming normal-distributed traits, but had a substantially increased power for non-normal phenotypes. When this strategy was applied to a group of traits associated with physical/chemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption.     

远交群体动态性状基因定位的似然分析Ⅱ.模拟研究

以远交设计群体为例,在推导出动态性状基因定位的似然法分析过程的基础上,选择3阶Legendre多项式为子模型,采用Monte-Carlo方法模拟研究了不同个体数、测定日频数、标记密度和QTL遗传贡献率对两种分析方法检测QTL效率的影响。每个因素都取高、中和低3个水平,利用正交设计安排模拟因素试验组合。模拟试验结果表明：高QTL遗传贡献率要比低QTL遗传贡献率的QTL在检测时需要较少个体数和测定日抽样;但不论QTL遗传贡献率多大,300以上的群体大小和5％以上的测定日频数都可以保证足够高的检测效率。个体数和测定日频数对动态性状QTL的分析和检测具有几乎相同的作用,而且相同样本含量条件下两者呈现互补的关系。就某个动态点的QTL检测而言,模拟试验也同时证明：提出的这种以整个动态过程为定位目标的动态性状基因定位方法明显优于传统的逐个动态点的定位分析方法。     

Bayesian methods for estimating GEBVs of threshold traits

Estimation of genomic breeding values is the key step in genomic selection (GS). Many methods have been proposed for continuous traits, but methods for threshold traits are still scarce. Here we introduced threshold model to the framework of GS, and specifically, we extended the three Bayesian methods BayesA, BayesB and BayesCπ on the basis of threshold model for estimating genomic breeding values of threshold traits, and the extended methods are correspondingly termed BayesTA, BayesTB and BayesTCπ. Computing procedures of the three BayesT methods using Markov Chain Monte Carlo algorithm were derived. A simulation study was performed to investigate the benefit of the presented methods in accuracy with the genomic estimated breeding values (GEBVs) for threshold traits. Factors affecting the performance of the three BayesT methods were addressed. As expected, the three BayesT methods generally performed better than the corresponding normal Bayesian methods, in particular when the number of phenotypic categories was small. In the standard scenario (number of categories=2, incidence=30%, number of quantitative trait loci=50, h²=0.3), the accuracies were improved by 30.4%, 2.4%, and 5.7% points, respectively. In most scenarios, BayesTB and BayesTCπ generated similar accuracies and both performed better than BayesTA. In conclusion, our work proved that threshold model fits well for predicting GEBVs of threshold traits, and BayesTCπ is supposed to be the method of choice for GS of threshold traits.     

The genetic architecture of behavioral traits in a spider

The existence of consistent individual differences in behavior has been shown in a number of species, and several studies have found observable sex differences in these behaviors, yet their evolutionary implications remain unclear. Understanding the evolutionary dynamics of behavioral traits requires knowledge of their genetic architectures and whether this architecture differs between the sexes. We conducted a quantitative genetic study in a sexually size‐dimorphic spider, Larinioides sclopetarius, which exhibits sex differences in adult lifestyles. We observed pedigreed spiders for aggression, activity, exploration, and boldness and used animal models to disentangle genetic and environmental influences on these behaviors. We detected trends toward (i) higher additive genetic variances in aggression, activity, and exploration in males than females, and (ii) difference in variances due to common environment/maternal effects, permanent environment and residual variance in aggression and activity with the first two variances being higher in males for both behaviors. We found no sex differences in the amount of genetic and environmental variance in boldness. The mean heritability estimates of aggression, activity, exploration, and boldness range from 0.039 to 0.222 with no sizeable differences between females and males. We note that the credible intervals of the estimates are large, implying a high degree of uncertainty, which disallow a robust conclusion of sex differences in the quantitative genetic estimates. However, the observed estimates suggest that sex differences in the quantitative genetic architecture of the behaviors cannot be ruled out. Notably, the present study suggests that genetic underpinnings of behaviors may differ between sexes and it thus underscores the importance of taking sex differences into account in quantitative genetic studies.     

Strategies for genetic mapping of categorical traits

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F₂ or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families. This revised version was published online in July 2006 with corrections to the Cover Date.     

QTL mapping in outbred half-sib families using Bayesian model selection

In this article, we propose a model selection method, the Bayesian composite model space approach, to map quantitative trait loci (QTL) in a half-sib population for continuous and binary traits. In our method, the identity-by-descent-based variance component model is used. To demonstrate the performance of this model, the method was applied to map QTL underlying production traits on BTA6 in a Chinese half-sib dairy cattle population. A total of four QTLs were detected, whereas only one QTL was identified using the traditional least square (LS) method. We also conducted two simulation experiments to validate the efficiency of our method. The results suggest that the proposed method based on a multiple-QTL model is efficient in mapping multiple QTL for an outbred half-sib population and is more powerful than the LS method based on a single-QTL model.     

A intervarietal genetic map and QTL analysis for yield traits in wheat

A new genetic linkage map was constructed based on recombinant inbred lines (RILs) derived from the cross between the Chinese winter wheat (Triticum aestivum L.) varieties, Chuang 35050 and Shannong 483 (ChSh). The map included 381 loci on all the wheat chromosomes, which were composed of 167 SSR, 94 EST-SSR, 76 ISSR, 26 SRAP, 15 TRAP, and 3 Glu loci. This map covered 3636.7 cM with 1327.7 cM (36.5%), 1485.5 cM (40.9%), and 823.5 cM (22.6%) for A, B, and D genome, respectively, and contained 13 linkage gaps. Using the RILs and the map, we detected 46 putative QTLs on 12 chromosomes for grain yield (GY) per m², thousand-kernel weight (TKW), spike number (SN) per m², kernel number per spike (KNS), sterile spikelet number per spike (SSS), fertile spikelet number per spike (FSS), and total spikelet number per spike (TSS) in four environments. Each QTL explained 4.42–70.25% phenotypic variation. Four QTL cluster regions were detected on chromosomes 1D, 2A, 6B, and 7D. The most important QTL cluster was located on chromosome 7D near the markers of Xwmc31, Xgdm67, and Xgwm428, in which 8 QTLs for TKW, SN, SSS and FSS were observed with very high contributions (27.53–67.63%).     

A method for marker-assisted selection based on QTLs with epistatic effects

A method for marker-assisted selection (MAS) based on quantitative trait loci (QTLs) with epistatic effects is proposed. The efficiency of such method is investigated by simulations under a wide range of situations. In the presence of epistasis, MAS generally yields longer persistence response than that based exclusively on additive or additive and dominance. Neglecting epistasis could result in considerable loss in response, and more pronounced at later generations. In addition to population size and trait heritability, genetic variance configurations play an important role in determining both the short- and long-term efficiencies of MAS. MAS using breeding values not only achieves higher response, but also tends to have smaller standard error than other methods in most cases. Errors in QTL detection cause distinct reductions in responses to MAS in most cases. It is thus concluded that verifications of putative QTL and its magnitude of effect and accurate map chromosome location are imperative to realize the potentials of MAS.     

The genetic architecture of a female sexual ornament

Understanding the evolution of sexual ornaments, and particularly that of female sexual ornaments, is an enduring challenge in evolutionary biology. Key to this challenge are establishing the relationship between ornament expression and female reproductive investment, and determining the genetic basis underpinning such relationship. Advances in genomics provide unprecedented opportunities to study the genetic architecture of sexual ornaments in model species. Here, we present a quantitative trait locus (QTL) analysis of a female sexual ornament, the comb of the fowl, Gallus gallus, using a large-scale intercross between red junglefowl and a domestic line, selected for egg production. First, we demonstrate that female somatic investment in comb reflects female reproductive investment. Despite a trade-off between reproductive and skeletal investment mediated by the mobilization of skeletal minerals for egg production, females with proportionally large combs also had relatively high skeletal investment. Second, we identify a major QTL for bisexual expression of comb mass and several QTL specific to female comb mass. Importantly, QTL for comb mass were nonrandomly clustered with QTL for female reproductive and skeletal investment on chromosomes one and three. Together, these results shed light onto the physiological and genetic architecture of a female ornament.     

Replicated analysis of the genetic architecture of quantitative traits in two wild great tit populations

Currently, there is much debate on the genetic architecture of quantitative traits in wild populations. Is trait variation influenced by many genes of small effect or by a few genes of major effect? Where is additive genetic variation located in the genome? Do the same loci cause similar phenotypic variation in different populations? Great tits (Parus major) have been studied extensively in long‐term studies across Europe and consequently are considered an ecological ‘model organism’. Recently, genomic resources have been developed for the great tit, including a custom SNP chip and genetic linkage map. In this study, we used a suite of approaches to investigate the genetic architecture of eight quantitative traits in two long‐term study populations of great tits—one in the Netherlands and the other in the United Kingdom. Overall, we found little evidence for the presence of genes of large effects in either population. Instead, traits appeared to be influenced by many genes of small effect, with conservative estimates of the number of contributing loci ranging from 31 to 310. Despite concordance between population‐specific heritabilities, we found no evidence for the presence of loci having similar effects in both populations. While population‐specific genetic architectures are possible, an undetected shared architecture cannot be rejected because of limited power to map loci of small and moderate effects. This study is one of few examples of genetic architecture analysis in replicated wild populations and highlights some of the challenges and limitations researchers will face when attempting similar molecular quantitative genetic studies in free‐living populations.     

A note on QTL detecting for censored traits

Most existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and that it is fully observed. However, some phenotypes have skewed distributions and may be censored. This note proposes a simple and efficient approach to QTL detecting for censored traits with the Cox PH model without estimating the baseline hazard function which is "nuisance".     

Quantitative genetic analysis of seed vigour and pre-emergence seedling growth traits in Brassica oleracea

The ability of seeds to germinate and establish seedlings in a predictable manner under a range of conditions has a direct contribution to the economic success of commercial crops, and should therefore be considered in crop improvement. We measured traits associated with seed vigour and pre-emergence seedling growth in a segregating population of 105 doubled haploid Brassica oleracea lines. The germination traits measured were: mean germination times for unstressed germination; germination under water stress or germination after a heat treatment; and conductivity of seed leachate. The seedling growth traits measured were: seed weight; seedling growth rate; and seedling size at the end of the exponential growth phase. There were some correlations, notably among germination traits, and between seed weight and pre-emergence seedling growth. Heritability of the various traits was typically in the 10–15% range, with heritability of conductivity and mean germination time under water stress 25 and 24% respectively. Collectively the results indicate that germination and pre-emergence seedling growth are under separate genetic control. Quantitative trait loci analyses were carried out on all measurements and revealed significant loci on linkage groups O1, O3, O6, O7 and O9. We suggest that genes at these loci are important in determining predictable seed germination and seedling establishment in practice.     

Bayesian shrinkage analysis of quantitative trait Loci for dynamic traits

Many quantitative traits are measured repeatedly during the life of an organism. Such traits are called dynamic traits. The pattern of the changes of a dynamic trait is called the growth trajectory. Studying the growth trajectory may enhance our understanding of the genetic architecture of the growth trajectory. Recently, we developed an interval-mapping procedure to map QTL for dynamic traits under the maximum-likelihood framework. We fit the growth trajectory by Legendre polynomials. The method intended to map one QTL at a time and the entire QTL analysis involved scanning the entire genome by fitting multiple single-QTL models. In this study, we propose a Bayesian shrinkage analysis for estimating and mapping multiple QTL in a single model. The method is a combination between the shrinkage mapping for individual quantitative traits and the Legendre polynomial analysis for dynamic traits. The multiple-QTL model is implemented in two ways: (1) a fixed-interval approach where a QTL is placed in each marker interval and (2) a moving-interval approach where the position of a QTL can be searched in a range that covers many marker intervals. Simulation study shows that the Bayesian shrinkage method generates much better signals for QTL than the interval-mapping approach. We propose several alternative methods to present the results of the Bayesian shrinkage analysis. In particular, we found that the Wald test-statistic profile can serve as a mechanism to test the significance of a putative QTL.     

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.     

Evolution of genetic architecture under directional selection

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.     

The genetic architecture of photosynthesis and plant growth‐related traits in tomato

To identify genomic regions involved in the regulation of fundamental physiological processes such as photosynthesis and respiration, a population of Solanum pennellii introgression lines was analyzed. We determined phenotypes for physiological, metabolic, and growth related traits, including gas exchange and chlorophyll fluorescence parameters. Data analysis allowed the identification of 208 physiological and metabolic quantitative trait loci with 33 of these being associated to smaller intervals of the genomic regions, termed BINs. Eight BINs were identified that were associated with higher assimilation rates than the recurrent parent M82. Two and 10 genomic regions were related to shoot and root dry matter accumulation, respectively. Nine genomic regions were associated with starch levels, whereas 12 BINs were associated with the levels of other metabolites. Additionally, a comprehensive and detailed annotation of the genomic regions spanning these quantitative trait loci allowed us to identify 87 candidate genes that putatively control the investigated traits. We confirmed 8 of these at the level of variance in gene expression. Taken together, our results allowed the identification of candidate genes that most likely regulate photosynthesis, primary metabolism, and plant growth and as such provide new avenues for crop improvement.     

A bivariate quantitative genetic model for a threshold trait and a survival trait

Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.