Mapping quantitative trait loci in tetraploid populations

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound 'gametic effect', which consists of the composite 'genic effect' of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.     

Detection of quantitative trait loci in outbred populations with incomplete marker data.

Augmentation of marker genotypes for ungenotyped individuals is implemented in a Bayesian approach via the use of Markov chain Monte Carlo techniques. Marker data on relatives and phenotypes are combined to compute conditional posterior probabilities for marker genotypes of ungenotyped individuals. The presented procedure allows the analysis of complex pedigrees with ungenotyped individuals to detect segregating quantitative trait loci (QTL). Allelic effects at the QTL were assumed to follow a normal distribution with a covariance matrix based on known QTL position and identity by descent probabilities derived from flanking markers. The Bayesian approach estimates variance due to the single QTL, together with polygenic and residual variance. The method was empirically tested through analyzing simulated data from a complex granddaughter design. Ungenotyped dams were related to one or more sons or grandsires in the design. Heterozygosity of the marker loci and size of QTL were varied. Simulation results indicated a significant increase in power when ungenotyped dams were included in the analysis.     

High-confidence discovery of genetic network regulators in expression quantitative trait loci data

Expression QTL (eQTL) studies involve the collection of microarray gene expression data and genetic marker data from segregating individuals in a population to search for genetic determinants of differential gene expression. Previous studies have found large numbers of trans-regulated genes (regulated by unlinked genetic loci) that link to a single locus or eQTL "hotspot," and it would be desirable to find the mechanism of coregulation for these gene groups. However, many difficulties exist with current network reconstruction algorithms such as low power and high computational cost. A common observation for biological networks is that they have a scale-free or power-law architecture. In such an architecture, highly influential nodes exist that have many connections to other nodes. If we assume that this type of architecture applies to genetic networks, then we can simplify the problem of genetic network reconstruction by focusing on discovery of the key regulatory genes at the top of the network. We introduce the concept of "shielding" in which a specific gene expression variable (the shielder) renders a set of other gene expression variables (the shielded genes) independent of the eQTL. We iteratively build networks from the eQTL to the shielder down using tests of conditional independence. We have proposed a novel test for controlling the shielder false-positive rate at a predetermined level by requiring a threshold number of shielded genes per shielder. Using simulation, we have demonstrated that we can control the shielder false-positive rate as well as obtain high shielder and edge specificity. In addition, we have shown our method to be robust to violation of the latent variable assumption, an important feature in the practical application of our method. We have applied our method to a yeast expression QTL data set in which microarray and marker data were collected from the progeny of a backcross of two species of Saccharomyces cerevisiae (Brem et al. 2002). Seven genetic networks have been discovered, and bioinformatic analysis of the discovered regulators and corresponding regulated genes has generated plausible hypotheses for mechanisms of regulation that can be tested in future experiments.     

Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.     

Modeling epistasis of quantitative trait loci using Cockerham's model

We use the orthogonal contrast scales proposed by Cockerham to construct a genetic model, called Cockerham's model, for studying epistasis between genes. The properties of Cockerham's model in modeling and mapping epistatic genes under linkage equilibrium and disequilibrium are investigated and discussed. Because of its orthogonal property, Cockerham's model has several advantages in partitioning genetic variance into components, interpreting and estimating gene effects, and application to quantitative trait loci (QTL) mapping when compared to other models, and thus it can facilitate the study of epistasis between genes and be readily used in QTL mapping. The issues of QTL mapping with epistasis are also addressed. Real and simulated examples are used to illustrate Cockerham's model, compare different models, and map for epistatic QTL. Finally, we extend Cockerham's model to multiple loci and discuss its applications to QTL mapping.     

Joint mapping of quantitative trait loci using F2 populations

In this paper, the theory of joint mapping of quantitative trait loci is extended to F₂ populations. Two independent regression equations, related to the additive and dominance effects respectively, are derived. Therefore, there are three alternative strategies for mapping QTLs, called additive-based mapping (ABM), dominance-based mapping (DBM) and additive-dominance-based mapping (ADBM). Simulation results have shown that ADBM is the most appropriate in most situations.     

Methods for multiple-marker mapping of quantitative trait loci in half-sib populations

In this paper we consider the detection of individual loci controlling quantitative traits of interest (quantitative trait loci or QTLs) in the large half-sib family structure found in some species. Two simple approaches using multiple markers are proposed, one using least squares and the other maximum likelihood. These methods are intended to provide a relatively fast screening of the entire genome to pinpoint regions of interest for further investigation. They are compared with a more traditional single-marker least-squares approach. The use of multiple markers is shown to increase power and has the advantage of providing an estimate for the location of the QTL. The maximum-likelihood and the least-squares approaches using multiple markers give similar power and estimates for the QTL location, although the likelihood approach also provides estimates of the QTL effect and sire heterozygote frequency. A number of assumptions have been made in order to make the likelihood calculations feasible, however, and computationally it is still more demanding than the least-squares approach. The least-squares approach using multiple markers provides a fast method that can easily be extended to include additional effects.     

Assessing the significance of quantitative trait loci in replicable mapping populations

Replicable populations, such as panels of recombinant inbred or doubled haploid lines, are convenient resources for the mapping of QTL. To increase mapping power, replications are often collected within each RI line and a common way to analyze such data is to include in the QTL model only a single measurement from each line that represents the average among the replicates (a line means model). An obvious, but seldom explored, alternative, is to include every replicate in the model (a full data model). Here, we use simulations to compare these two approaches. Further, we propose an extension of the standard permutation procedure that is required to correctly control the type I error in mapping populations with nested structure.     

Heritability and tissue specificity of expression quantitative trait loci

Variation in gene expression is heritable and has been mapped to the genome in humans and model organisms as expression quantitative trait loci (eQTLs). We applied integrated genome-wide expression profiling and linkage analysis to the regulation of gene expression in fat, kidney, adrenal, and heart tissues using the BXH/HXB panel of rat recombinant inbred strains. Here, we report the influence of heritability and allelic effect of the quantitative trait locus on detection of cis- and trans-acting eQTLs and discuss how these factors operate in a tissue-specific context. We identified several hundred major eQTLs in each tissue and found that cis-acting eQTLs are highly heritable and easier to detect than trans-eQTLs. The proportion of heritable expression traits was similar in all tissues; however, heritability alone was not a reliable predictor of whether an eQTL will be detected. We empirically show how the use of heritability as a filter reduces the ability to discover trans-eQTLs, particularly for eQTLs with small effects. Only 3% of cis- and trans-eQTLs exhibited large allelic effects, explaining more than 40% of the phenotypic variance, suggestive of a highly polygenic control of gene expression. Power calculations indicated that, across tissues, minor differences in genetic effects are expected to have a significant impact on detection of trans-eQTLs. Trans-eQTLs generally show smaller effects than cis-eQTLs and have a higher false discovery rate, particularly in more heterogeneous tissues, suggesting that small biological variability, likely relating to tissue composition, may influence detection of trans-eQTLs in this system. We delineate the effects of genetic architecture on variation in gene expression and show the sensitivity of this experimental design to tissue sampling variability in large-scale eQTL studies.     

Determining causality and consequence of expression quantitative trait loci

Expression quantitative trait loci (eQTLs) are currently the most abundant and systematically-surveyed class of functional consequence for genetic variation. Recent genetic studies of gene expression have identified thousands of eQTLs in diverse tissue types for the majority of human genes. Application of this large eQTL catalog provides an important resource for understanding the molecular basis of common genetic diseases. However, only now has both the availability of individuals with full genomes and corresponding advances in functional genomics provided the opportunity to dissect eQTLs to identify causal regulatory variants. Resolving the properties of such causal regulatory variants is improving understanding of the molecular mechanisms that influence traits and guiding the development of new genome-scale approaches to variant interpretation. In this review, we provide an overview of current computational and experimental methods for identifying causal regulatory variants and predicting their phenotypic consequences.     

Identification of quantitative trait loci for production traits in commercial pig populations

The aim of this study was to investigate methods for detecting QTL in outbred commercial pig populations. Several QTL for back fat and growth rate, previously detected in experimental resource populations, were examined for segregation in 10 different populations. Two hundred trait-by-population-by-chromosome tests were performed, resulting in 20 tests being significant at the 5% level. In addition, 53 QTL tests for 11 meat quality traits were declared significant, using a subset of the populations. These results show that a considerable amount of phenotypic variance observed in these populations can be explained by major alleles segregating at several of the loci described. Thus, despite a relatively strong selection pressure for growth and back fat traits in these populations, these alleles have not yet reached fixation. The approaches used here demonstrate that it is possible to verify segregation of QTL in commercial populations by limited genotyping of a selection of informative animals. Such verified QTL may be directly exploited in marker-assisted selection (MAS) programs in commercial populations and their molecular basis may be revealed by positional candidate cloning.     

Semiparametric methods for mapping quantitative trait loci with censored data

Statistical methods for the detection of genes influencing quantitative traits with the aid of genetic markers are well developed for normally distributed, fully observed phenotypes. Many experiments are concerned with failure-time phenotypes, which have skewed distributions and which are usually subject to censoring because of random loss to follow-up, failures from competing causes, or limited duration of the experiment. In this article, we develop semiparametric statistical methods for mapping quantitative trait loci (QTLs) based on censored failure-time phenotypes. We formulate the effects of the QTL genotype on the failure time through the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model and derive efficient likelihood-based inference procedures. In addition, we show how to assess statistical significance when searching several regions or the entire genome for QTLs. Extensive simulation studies demonstrate that the proposed methods perform well in practical situations. Applications to two animal studies are provided.     

Mapping quantitative trait loci in selected breeding populations: A segregation distortion approach

Quantitative trait locus (QTL) mapping is often conducted in line-crossing experiments where a sample of individuals is randomly selected from a pool of all potential progeny. QTLs detected from such an experiment are important for us to understand the genetic mechanisms governing a complex trait, but may not be directly relevant to plant breeding if they are not detected from the breeding population where selection is targeting for. QTLs segregating in one population may not necessarily segregate in another population. To facilitate marker-assisted selection, QTLs must be detected from the very population which the selection is targeting. However, selected breeding populations often have depleted genetic variation with small population sizes, resulting in low power in detecting useful QTLs. On the other hand, if selection is effective, loci controlling the selected trait will deviate from the expected Mendelian segregation ratio. In this study, we proposed to detect QTLs in selected breeding populations via the detection of marker segregation distortion in either a single population or multiple populations using the same selection scheme. Simulation studies showed that QTL can be detected in strong selected populations with selected population sizes as small as 25 plants. We applied the new method to detect QTLs in two breeding populations of rice selected for high grain yield. Seven QTLs were identified, four of which have been validated in advanced generations in a follow-up study. Cloned genes in the vicinity of the four QTLs were also reported in the literatures. This mapping-by-selection approach provides a new avenue for breeders to improve breeding progress. The new method can be applied to breeding programs not only in rice but also in other agricultural species including crops, trees and animals.     

Multipoint genetic mapping of quantitative trait loci with dominant markers in outbred populations

We present a multipoint algorithm for mapping quantitative trait loci (QTLs) using dominant markers. The algorithm is designed for outbred populations and is particularly suited for large families. The algorithm works with either codominant or dominant markers, either of which may be interspersed within the same linkage map. Concurrently, the algorithm also partitions dominance variance at the QTL. Computer simulations show that with large families, QTL mapping with dominant markers can be almost as powerful as with bi-allelic, codominant markers. Yet despite this, other situations show a large standard deviation in the estimate of the QTL position, thus making QTL mapping with dominant markers in outbred populations a useful detection tool, albeit limited in its resolution. This revised version was published online in July 2006 with corrections to the Cover Date.