Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design

Bias correction for estimated QTL effects using the penalized maximum likelihood method

A penalized maximum likelihood method has been proposed as an important approach to the detection of epistatic quantitative trait loci (QTL). However, this approach is not optimal in two special situations: (1) closely linked QTL with effects in opposite directions and (2) small-effect QTL, because the method produces downwardly biased estimates of QTL effects. The present study aims to correct the bias by using correction coefficients and shifting from the use of a uniform prior on the variance parameter of a QTL effect to that of a scaled inverse chi-square prior. The results of Monte Carlo simulation experiments show that the improved method increases the power from 25 to 88% in the detection of two closely linked QTL of equal size in opposite directions and from 60 to 80% in the identification of QTL with small effects (0.5% of the total phenotypic variance). We used the improved method to detect QTL responsible for the barley kernel weight trait using 145 doubled haploid lines developed in the North American Barley Genome Mapping Project. Application of the proposed method to other shrinkage estimation of QTL effects is discussed.

F₂ designs for QTL analysis

This chapter covers the procedure of mapping quantitative trait loci (QTLs) in an F(2) breeding design. I describe genetic design, general methods and software, and several commonly used approaches. The genetic design section includes F(2) population construction. Widely used methods and software are introduced in the section of general methods and software. Finally, composite interval mapping, penalized maximum likelihood, and empirical Bayes are described in detail. Some issues related to the F(2) design are discussed.

Epistatic association mapping in homozygous crop cultivars

The genetic dissection of complex traits plays a crucial role in crop breeding. However, genetic analysis and crop breeding have heretofore been performed separately. In this study, we designed a new approach that integrates epistatic association analysis in crop cultivars with breeding by design. First, we proposed an epistatic association mapping (EAM) approach in homozygous crop cultivars. The phenotypic values of complex traits, along with molecular marker information, were used to perform EAM. In our EAM, all the main-effect quantitative trait loci (QTLs), environmental effects, QTL-by-environment interactions and QTL-by-QTL interactions were included in a full model and estimated by empirical Bayes approach. A series of Monte Carlo simulations was performed to confirm the reliability of the new method. Next, the information from all detected QTLs was used to mine novel alleles for each locus and to design elite cross combination. Finally, the new approach was adopted to dissect the genetic basis of seed length in 215 soybean cultivars obtained, by stratified random sampling, from 6 geographic ecotypes in China. As a result, 19 main-effect QTLs and 3 epistatic QTLs were identified, more than 10 novel alleles were mined and 3 elite parental combinations, such as Daqingdou and Zhengzhou790034, were predicted.

Mapping of epistatic quantitative trait loci in four-way crosses

Four-way crosses (4WC) involving four different inbred lines often appear in plant and animal commercial breeding programs. Direct mapping of quantitative trait loci (QTL) in these commercial populations is both economical and practical. However, the existing statistical methods for mapping QTL in a 4WC population are built on the single-QTL genetic model. This simple genetic model fails to take into account QTL interactions, which play an important role in the genetic architecture of complex traits. In this paper, therefore, we attempted to develop a statistical method to detect epistatic QTL in 4WC population. Conditional probabilities of QTL genotypes, computed by the multi-point single locus method, were used to sample the genotypes of all putative QTL in the entire genome. The sampled genotypes were used to construct the design matrix for QTL effects. All QTL effects, including main and epistatic effects, were simultaneously estimated by the penalized maximum likelihood method. The proposed method was confirmed by a series of Monte Carlo simulation studies and real data analysis of cotton. The new method will provide novel tools for the genetic dissection of complex traits, construction of QTL networks, and analysis of heterosis.

Multiple loci in silico mapping in inbred lines

The in silico mapping (ISM) technique and its extension represent major advances for novel gene discovery in germplasm resources of inbred lines. However, the techniques suffer from a relatively high false-positive rate (FPR) and they do not consider the effect of linkage disequilibrium (LD) markers around the identified quantitative trait locus (QTL). In addition, it has not yet been established whether it is optimal to use absolute trait differences as the response variable. To address these problems, this article presents the multiple loci ISM (MLISM) approach, which uses all markers on the entire genome, along with a penalized maximum likelihood. The method proposed here was verified by a series of simulation experiments with a maize pedigree population of inbred lines of known ancestry. Results from the simulated studies show that the best response variable is the trait product. The MLISM FPR is substantially decreased and the proportion of the number of false QTL to the number of LD markers around the identified QTL is adequately reduced. The MLISM method, with the trait product as the response variable, is an improvement on the existing methods for novel QTL mapping in germplasm resources of inbred lines.

Understanding quantitative genetics in the systems biology era

Biology is now entering the new era of systems biology and exerting a growing influence on the future development of various disciplines within life sciences. In early classical and molecular periods of Biology, the theoretical frames of classical and molecular quantitative genetics have been systematically established, respectively. With the new advent of systems biology, there is occurring a paradigm shift in the field of quantitative genetics. Where and how the quantitative genetics would develop after having undergone its classical and molecular periods? This is a difficult question to answer exactly. In this perspective article, the major effort was made to discuss the possible development of quantitative genetics in the systems biology era, and for which there is a high potentiality to develop towards "systems quantitative genetics". In our opinion, the systems quantitative genetics can be defined as a new discipline to address the generalized genetic laws of bioalleles controlling the heritable phenotypes of complex traits following a new dynamic network model. Other issues from quantitative genetic perspective relating to the genetical genomics, the updates of network model, and the future research prospects were also discussed.

Multiple quantitative trait loci Haseman-Elston regression using all markers on the entire genome

The Haseman-Elston (HE) regression, developed in the 1970s, remains in common use to detect genetic linkage between a quantitative trait and a genetic marker. Although the technique has been improved in a number of ways, it predicts a high rate of false positive quantitative trait locus (QTL) because it is based on a single-QTL model. We have extended the origin HE regression to multi-QTL HE (MQHE) regression, so that all markers across the entire genome can be exploited simultaneously. The parameters have been estimated by the penalized maximum likelihood method, and several response variables for phenotypic difference have been compared in order to optimize the procedure. The method has been tested by simulation in a pedigree population of maize inbred lines of known ancestry. These simulations show that the trait product is the optimal response variable for phenotypic difference. The false positive rate produced by the MQHE regression is substantially lower than that generated by either variance component analysis or the origin HE regression. The MQHE regression, with the trait product as the response variable, represents a significant improvement on existing methods for QTL mapping in a set of inbred lines (or cultivars) of known ancestry.

Methodologies for segregation analysis and QTL mapping in plants

Most characters of biological interest and economic importance are quantitative traits. To uncover the genetic architecture of quantitative traits, two approaches have become popular in China. One is the establishment of an analytical model for mixed major-gene plus polygenes inheritance and the other the discovery of quantitative trait locus (QTL). Here we review our progress employing these two approaches. First, we proposed joint segregation analysis of multiple generations for mixed major-gene plus polygenes inheritance. Second, we extended the multilocus method of Lander and Green (1987), Jiang and Zeng (1997) to a more generalized approach. Our methodology handles distorted, dominant and missing markers, including the effect of linked segregation distortion loci on the estimation of map distance. Finally, we developed several QTL mapping methods. In the Bayesian shrinkage estimation (BSE) method, we suggested a method to test the significance of QTL effects and studied the effect of the prior distribution of the variance of QTL effect on QTL mapping. To reduce running time, a penalized maximum likelihood method was adopted. To mine novel genes in crop inbred lines generated in the course of normal crop breeding work, three methods were introduced. If a well-documented genealogical history of the lines is available, two-stage variance component analysis and multi-QTL Haseman-Elston regression were suggested; if unavailable, multiple loci in silico mapping was proposed.