Mapping quantitative trait loci in oligogenic models

We discuss strategies for mapping quantitative trait loci with emphasis on certain issues of study design that have recently received attention: e.g. genotyping only selected pedigrees and the comparative value of large pedigrees versus sib pairs. We use a standard variance components model and a parametrization of the genetic effects in which the 'segregation' parameters are locally orthogonal to the 'linkage' parameters. This permits simple explicit expressions for the expectation of the score statistic, which we use to compare the power of different strategies. We also discuss robustness of the score statistic.     

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.     

Mapping quantitative trait loci with censored observations

The existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and is fully observed. These assumptions may not be satisfied when the phenotype pertains to the survival time or failure time, which has a skewed distribution and is usually subject to censoring due to random loss of follow-up or limited duration of the experiment. In this article, we propose an interval-mapping approach for censored failure time phenotypes. We formulate the effects of QTL on the failure time through parametric proportional hazards models and develop efficient likelihood-based inference procedures. In addition, we show how to assess genome-wide statistical significance. The performance of the proposed methods is evaluated through extensive simulation studies. An application to a mouse cross is provided.     

Mapping quantitative trait loci using binned genotypes

Precise mapping of quantitative trait loci(QTLs)is critical for assessing genetic effects and identifying candidate genes for quantitative traits.Interval and composite interval mappings have been the methods of choice for several decades,which have provided tools for identifying genomic regions harboring causal genes for quantitative traits.Historically,the concept was developed on the basis of sparse marker maps where genotypes of loci within intervals could not be observed.Currently,genomes of many organisms have been saturated with markers due to the new sequencing technologies.Genotyping by sequencing usually generates hundreds of thousands of single nucleotide polymorphisms(SNPs),which often include the causal polymorphisms.The concept of interval no longer exists,prompting the necessity of a norm change in QTL mapping technology to make use of the high-volume genomic data.Here we developed a statistical method and a software package to map QTLs by binning markers into haplotype blocks,called bins.The new method detects associations of bins with quantitative traits.It borrows the mixed model methodology with a polygenic control from genome-wide association studies(GWAS)and can handle all kinds of experimental populations under the linear mixed model(LMM)framework.We tested the method using both simulated data and data from populations of rice.The results showed that this method has higher power than the current methods.An R package named binQTL is available from GitHub.     

Mapping quantitative trait loci with epistatic effects

Epistatic variance can be an important source of variation for complex traits. However, detecting epistatic effects is difficult primarily due to insufficient sample sizes and lack of robust statistical methods. In this paper, we develop a Bayesian method to map multiple quantitative trait loci (QTLs) with epistatic effects. The method can map QTLs in complicated mating designs derived from the cross of two inbred lines. In addition to mapping QTLs for quantitative traits, the proposed method can even map genes underlying binary traits such as disease susceptibility using the threshold model. The parameters of interest are various QTL effects, including additive, dominance and epistatic effects of QTLs, the locations of identified QTLs and even the number of QTLs. When the number of QTLs is treated as an unknown parameter, the dimension of the model becomes a variable. This requires the reversible jump Markov chain Monte Carlo algorithm. The utility of the proposed method is demonstrated through analysis of simulation data.     

Mapping of quantitative trait loci on porcine chromosome 4

A F₂ population derived from a cross between European Large White and Chinese Meishan pigs was established in order to study the genetic basis of breed differences for growth and fat traits. Chromosome 4 was chosen for initial study as previous work had revealed quantitative trait loci (QTLs) on this chromosome affected growth and fat traits in a Wild Boar × Large White cross. Individuals in the F₂ population were typed for nine markers spanning a region of approximately 124 c m . We found evidence for QTLs affecting growth between weaning and the end of test (additive effect: 43·4 g/day) and fat depth measured in the mid-back position (additive effect: 1·82 mm). There was no evidence of interactions between the QTLs and sex, grandparents or F₁ sires, suggesting that the detected QTLs were fixed for alternative alleles in the Meishan and Large White breeds. Comparison of locations suggests that these QTLs could be the same as those found in the Wild Boar × Large White cross.     

Mapping quantitative trait loci for bovine ovulation rate

An elite, three-generation family from the USDA Meat Animal Research Center twinning population was examined for evidence of ovulation rate quantitative trait loci (QTL). This work was both a continuation of previously reported results suggesting evidence for ovulation rate QTL on bovine Chromosome (Chr) 7 and an extension of a genome-wide search for QTL. Additional markers were typed on Chr 7 to facilitate interval mapping and testing of the hypothesis of one versus two QTL on that chromosome. In addition, 14 other informative markers were added to a selective genotyping genome screening of this family, and markers exhibiting nominal significance were used to identify chromosomal regions that were then subjected to more exhaustive analysis. For Chr 7, a total of 12 markers were typed over a region spanning the proximal two-thirds of the chromosome. Results from interval mapping analyses indicated evidence suggestive of the presence of QTL (nominal P < 0.00077) within this region. Subsequent analysis with a model postulating two QTL provided evidence (P < 0.05) for two rather than one QTL on this chromosome. Preliminary analysis with additional markers indicated nominal significance (P < 0.05) for regions of Chrs 5, 10, and 19. Each of these regions was then typed with additional markers for the entire three-generation pedigree. Significant evidence (P < 0.000026) of ovulation rate QTL was found for Chrs 5 and 19, while support on Chr 10 failed to exceed a suggestive linkage threshold (P > 0.00077). Received: 14 May 1999 / Accepted: 14 October 1999     

Mapping quantitative trait loci mediating sensitivity to etomidate

Long- and Short-Sleep (LS and SS) mice were selectively bred for differences in ethanol-induced loss of the righting reflex (LORR) and have been found to differ in LORR induced by various anesthetic agents. We used a two-stage mapping strategy to identify quantitative trait loci (QTLs) affecting duration of LORR caused by the general anesthetic etomidate and brain levels of etomidate (BEL) following regain of the righting reflex. Analysis of recombinant-inbred strains derived from a cross between LS and SS mice (LSXSS) yielded a heritability estimate of 0.23 for etomidate-induced LORR and identified one marker that showed suggestive linkage for a QTL, on mouse Chromosome (chr) 12. Mapping in an F(2) population derived from a cross between inbred LS and SS (ILS and ISS) revealed a significant QTL for etomidate-induced LORR on Chr 12, and two significant QTLs mediating BEL on Chrs 6 and 12. Several QTLs showing suggestive linkage for etomidate-induced LORR and BEL were also identified in the F(2) population. Brain levels of etomidate in the RI and F(2) mice suggested that differences in LORR were due to differential central nervous system sensitivity, rather than differential etomidate metabolism. Interestingly, the region on Chr 7 has also been identified as a region influencing ethanol-induced LORR, suggesting the possibility of a common genetic mechanism mediating etomidate and ethanol sensitivity. These QTL regions need to be further narrowed before the testing of candidate genes is feasible.     

Mapping quantitative trait loci in noninbred mosquito crosses

The identification of genes that affect quantitative traits has been of great interest to geneticists for many decades, and many statistical methods have been developed to map quantitative trait loci (QTL). Most QTL mapping studies in experimental organisms use purely inbred lines, where the two homologous chromosomes in each individual are identical. As a result, many existing QTL mapping methods developed for experimental organisms are applicable only to genetic crosses between inbred lines. However, it may be difficult to obtain inbred lines for certain organisms, e.g., mosquitoes. Although statistical methods for QTL mapping in outbred populations, e.g., humans, can be applied for such crosses, these methods may not fully take advantage of the uniqueness of these crosses. For example, we can generally assume that the two grandparental lines are homozygous at the QTL of interest, but such information is not be utilized through methods developed for outbred populations. In addition, mating types and phases can be relatively easy to establish through the analysis of adjacent markers due to the large number of offspring that can be collected, substantially simplifying the computational need. In this article, motivated by a mosquito intercross experiment involving two selected lines that are not genetically homozygous across the genome, we develop statistical methods for QTL mapping for genetic crosses involving noninbred lines. In our procedure, we first infer parental mating types and use likelihood-based methods to infer phases in each parent on the basis of genotypes of offspring and one parent. A hidden Markov model is then employed to estimate the number of high-risk alleles at marker positions and putative QTL positions between markers in each offspring, and QTL mapping is finally conducted through the inferred QTL configuration across all offspring in all crosses. The performance of the proposed methods is assessed through simulation studies, and the usefulness of this method is demonstrated through its application to a mosquito data set.     

Mapping quantitative trait loci underlying triploid endosperm traits

Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue in cereals. Endosperm tissue determines the grain quality of cereals. Improving grain quality is one of the important breeding objectives in cereals. However, current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. In this paper, we derive for the first time the conditional probabilities of F(3) endosperm QTL genotypes given different flanking marker genotypes in F(2) plants. Using these probabilities, we develop a multiple linear regression method implemented via the iteratively reweighted least-squares (IRWLS) algorithm and a maximum likelihood method (ML) implemented via the expectation-maximization (EM) algorithm to map QTL underlying endosperm traits. We use the mean value of endosperm traits of F(3) seeds as the dependent variable and the expectations of genotypic indicators for additive and dominance effect of a putative QTL flanked by a pair of markers as independent variables for IRWLS mapping. However, if an endosperm trait is measured quantitatively using a single endosperm sample, the ML mapping method can be used to separate the two dominance effects. Efficiency of the methods is verified through extensive Monte Carlo simulation studies. Results of simulation show that the proposed methods provide accurate estimates of both the QTL effects and locations with very high statistical power. With these methods, we are now ready to map endosperm traits, as we can for regular quantitative trait under diploid control.     

Mapping of quantitative trait loci affecting behaviour in swine

Behavioural indices in vertebrates are under genetic control at least to some extent. In spite of significant behavioural problems in farm animals, information on the genetic background of behaviour is sparse. The aim of this study was to map QTL for behavioural indices in swine under healthy conditions and after infection with Sarcocystis miescheriana , as behaviour can be significantly influenced by disease . This well-described parasite model subsequently leads to acute (day 14 p.i.), subclinical (day 28 p.i.) and chronic disease (day 42 p.i.), allowing the study and comparison of the behaviour of pigs under four different states of health or disease. The study was based on a well-described Pietrain/Meishan F₂ family that has recently allowed the detection of QTL for disease resistance. We have mapped six genome-wide significant and 24 chromosome-wide significant QTL for six behavioural indices in swine. Six of these QTL (i.e. 20% of total QTL) showed effects on behavioural traits of the healthy pigs (day 0). Some of them (QTL on SSC11 and 18) lost influence on behavioural activities during disease, while the effects of others (QTL on SSC5, SSC8) partly remained during the whole experiment, although with different effects on the distinct behavioural indices. The disease model has been of high relevance to detect effects of gene loci on behavioural indices. Considering the importance of segregating alleles and environmental conditions that allow the identification of the phenotype, we conclude that there are indeed QTL with interesting effects on behavioural indices in swine.     

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.     

Mapping quantitative trait loci regulating chicken body composition traits

Genome scans were conducted on an F₂ resource population derived from intercross of the White Plymouth Rock with the Silkies Fowl to detect QTL affecting chicken body composition traits. The population was genotyped with 129 microsatellite markers and phenotyped for 12 body composition traits on 238 F₂ individuals from 15 full-sib families. In total, 21 genome-wide QTL were found to be responsible for 11 traits, including two newly studied traits of proventriculus weight and shank girth. Three QTL were genome-wide significant: at 499 c m on GGA1 (explained 3.6% of phenotypic variance, P  < 0.01) and 51 c m on GGA5 (explained 3.3% of phenotypic variance, P  < 0.05) for the shank & claw weight and 502 c m on GGA1 (explained 1.4% of phenotypic variance, P  < 0.05) for wing weight. The QTL on GGA1 seemed to have pleiotropic effects, also affecting gizzard weight at 490 c m , shank girth at 489 c m and intestine length at 481 c m . It is suggested that further efforts be made to understand the possible pleiotropic effects of the QTL on GGA1 and that on GGA5 for two shank-related traits.     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Mapping temporally varying quantitative trait loci in time-to-failure experiments

Existing methods for mapping quantitative trait loci (QTL) in time-to-failure experiments assume that the QTL effect is constant over the course of the study. This assumption may be violated when the gene(s) underlying the QTL are up- or downregulated on a biologically meaningful timescale. In such situations, models that assume a constant effect can fail to detect QTL in a whole-genome scan. To investigate this possibility, we utilize an extension of the Cox model (EC model) within an interval-mapping framework. In its simplest form, this model assumes that the QTL effect changes at some time point t0 and follows a linear function before and after this change point. The approximate time point at which this change occurs is estimated. Using simulated and real data, we compare the mapping performance of the EC model to the Cox proportional hazards (CPH) model, which explicitly assumes a constant effect. The results show that the EC model detects time-dependent QTL, which the CPH model fails to detect. At the same time, the EC model recovers all of the QTL the CPH model detects. We conclude that potentially important QTL may be missed if their time-dependent effects are not accounted for.     

Mapping epistatic quantitative trait loci with one-dimensional genome searches

The discovery of epistatically interacting QTL is hampered by the intractability and low power to detect QTL in multidimensional genome searches. We describe a new method that maps epistatic QTL by identifying loci of high QTL by genetic background interaction. This approach allows detection of QTL involved not only in pairwise but also higher-order interaction, and does so with one-dimensional genome searches. The approach requires large populations derived from multiple related inbred-line crosses as is more typically available for plants. Using maximum likelihood, the method contrasts models in which QTL allelic values are either nested within, or fixed over, populations. We apply the method to simulated doubled-haploid populations derived from a diallel among three inbred parents and illustrate the power of the method to detect QTL of different effect size and different levels of QTL by genetic background interaction. Further, we show how the method can be used in conjunction with standard two-locus QTL detection models that use two-dimensional genome searches and find that the method may double the power to detect first-order epistasis.     

Mapping quantitative trait loci for cytokines in the pig

Increased disease resistance through improved general immune capacity would be beneficial for the welfare and productivity of farm animals. Cytokines are essential diagnostic parameters in veterinary practice. To identify quantitative trait loci (QTL) for cytokine levels in serum in the pig, Interferon‐gamma (IFN‐γ) and Interleukin 10 (IL‐10) levels and the ratio of IFN‐γ to IL‐10 were measured in a composite pig population, before and after challenge with modified live CSF (classical swine fever) vaccine. Through interval mapping using the variance component approach and the permutation test, 11 QTL (five for IFN‐γ, two for IL‐10 and four for the ratio of IFN‐γ to IL‐10) with significance levels of P < 0.10 were identified, of which five were significant at the P < 0.05 level. The most significant QTL (P < 0.01) was found on chromosome 16, with effect on the ratio of IFN‐γ to IL‐10. Within these QTL regions, a number of known genes were revealed and their potential relationships to the studied traits were discussed. Some of these genes may serve as candidate genes for these traits in swine.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

Mapping quantitative trait loci for traits defined as ratios

Many traits are defined as ratios of two quantitative traits. Methods of QTL mapping for regular quantitative traits are not optimal when applied to ratios due to lack of normality for traits defined as ratios. We develop a new method of QTL mapping for traits defined as ratios. The new method uses a special linear combination of the two component traits, and thus takes advantage of the normal property of the new variable. Simulation study shows that the new method can substantially increase the statistical power of QTL detection relative to the method which treats ratios as regular quantitative traits. The new method also outperforms the method that uses Box-Cox transformed ratio as the phenotype. A real example of QTL mapping for relative growth rate in soybean demonstrates that the new method can detect more QTL than existing methods of QTL mapping for traits defined as ratios.