Zhao-Bang Zeng

Estimating the genetic architecture of quantitative traits.

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study.

General formulas for obtaining the MLEs and the asymptotic variance-covariance matrix in mapping quantitative trait loci when using the EM algorithm.

We present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance-covariance matrix of the positions and effects of quantitative trait loci (QTLs) in a finite normal mixture model when the EM algorithm is used for mapping QTLs. The general formulas are based on two matrices D and Q, where D is the genetic design matrix, characterizing the genetic effects of the QTLs, and Q is the conditional probability matrix of QTL genotypes given flanking marker genotypes, containing the information on QTL positions. With the general formulas, it is relatively easy to extend QTL mapping analysis to using multiple marker intervals simultaneously for mapping multiple QTLs, for analyzing QTL epistasis, and for estimating the heritability of quantitative traits. Simulations were performed to evaluate the performance of the estimates of the asymptotic variances of QTL positions and effects.

LONG-TERM CORRELATED RESPONSE, INTERPOPULATION COVARIATION, AND INTERSPECIFIC ALLOMETRY

A model of long‐term correlated evolution of multiple quantitative characters is analyzed, which partitions selection into two components: one stabilizing and the other directional. The model assumes that the stabilizing component is less variable than the directional component among populations. The major result is that, within a population, the responses of characters to selection in the short term differ qualitatively from those in the long term. In the short term, the responses depend on genetic correlations between characters, but in the long term they are only determined by the fitness functions of stabilizing and directional selection, independent of genetic and phenotypic correlations. Treating the stabilizing component as a constant and assuming the directional component to vary among populations, I present formulas for the interpopulation covariation and interspecific allometry, which are functions of the intensity matrix of stabilizing selection. Particular attention is paid to the relationship between intra‐ and interpopulation correlations.

QUANTITATIVE GENETIC ANALYSIS OF DIVERGENCE IN MALE SECONDARY SEXUAL TRAITS BETWEEN DROSOPHILA SIMULANS AND DROSOPHILA MAURITIANA

The sibling species Drosophila simulans and D. mauritiana differ significantly in a number of male secondary sexual traits, providing an ideal system for genetic analysis of interspecific morphological divergence. In the experiment reported here, F1 hybrids from a cross of two inbred lines were backcrossed in both directions and about 200 flies from each backcross were scored for several traits (bristle numbers and cuticle areas), as well as 18 markers distributed throughout the genome. Each trait was analyzed by composite interval mapping to identify quantitative trait loci (QTL) and estimate their effects. For each trait, from one to eight loci were detected, with more divergent traits showing evidence for greater numbers of QTL. Estimates of additive effects varied widely, with a range of 0.4 to 4.1 environmental standard deviation units and an average of 2.2 units. There was substantial evidence for nonadditive effects, since the magnitude of estimates often differed significantly between the two backcrosses. The sign of the estimated effect differed among QTL for bristle traits, but not for cuticle area traits, suggesting that these two types of trait may have undergone different types of selection. Finally, several similarities were found between different traits in the estimated positions of QTL, suggesting that pleiotropy and/or linkage of QTL may have been important in the evolution of these traits.

Challenges for effective marker-assisted selection in plants.

The basic principle of Marker-Assisted Selection (MAS) is to exploit Linkage Disequilibrium (LD) between markers and QTLs. With strong enough LD, MAS should in theory be easier, faster, cheaper, or more efficient than classical (phenotypic) selection. I briefly review the major MAS methods, describing some ‘success stories’ where MAS was applied successfully in the context of plant breeding, and detailing other cases where efficiency was not as high as expected. I discuss the possible causes explaining the difference between theoretical expectations and practical observations. Finally, I review the principal challenges and issues that must be tackled to make marker-assisted selection in plants more effective in the future, namely: managing and controlling QTL stability to apply MAS to complex traits, and integrating MAS in traditional breeding practices to make it more economically attractive and applicable in developing countries.

Quantitative Trait Loci Mapping and The Genetic Basis of Heterosis in Maize and Rice

Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive × additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software.

The Role of Epistasis in the Manifestation of Heterosis: A Systems-Oriented Approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive × additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive × additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.

An integrated genetic map of Populus deltoides based on amplified fragment length polymorphisms

Abstract Amplified fragment length polymorphism (AFLP) is an efficient molecular technique for generating a large number of DNA-based genetic markers in Populus. We have constructed an integrated genetic map for a Populus backcross population derived from two selected P. deltoides clones using AFLP markers. A traditional strategy for genetic mapping in outcrossing species, such as forest trees, is based on two-way pseudo-testcross configurations of the markers (testcross markers) heterozygous in one parent and null in the other. By using the markers segregating in both parents (intercross markers) as bridges, the two parent-specific genetic maps can be aligned. In this study, we detected a number of non-parental heteroduplex markers resulting from the PCR amplification of two DNA segments that have a high degree of homology to one another but differ in their nucleotide sequences. These heteroduplex markers detected have served as bridges to generate an integrated map which includes 19 major linkage groups equal to the Populus haploid chromosome number and 24 minor groups. The 19 major linkage groups cover a total of 2,927 cM, with an average spacing between two markers of 23. 3 cM. The map developed in this study provides a first step in producing a highly saturated linkage map of the Populus deltoides genome.

A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines.

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.