Quantitative Trait Loci Genotypes Research Articles

Limitations of a two-step moment method for mapping linked multiple QTL

As an alternative to multiple-interval mapping a two-step moment method was recently proposed to map linked multiple quantitative trait loci (QTLs). The advantage of this moment method was supposed to be its simplicity and computational efficiency, especially in detecting closely linked QTLs within a marker bracket, but also in mapping QTLs in different marker intervals. Using simulations it is shown that the two-step moment method may give poor results compared with multiple-interval mapping, irrespective of whether the QTLs are in the same or in different marker intervals, especially if linked QTLs are in repulsion. The criteria of comparison are number of identified QTLs, likelihood ratio test statistics, means and empirical standard errors of the QTL position and QTL effects estimates, and the accuracy of the residual variance estimates. Further, the joint conditional probabilities of QTL genotypes for two putative QTLs within a marker interval were derived and compared with the unmodified approach ignoring the non-independence of the conditional probabilities.

An algorithm for molecular dissection of tumor progression

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.

IGF2 antisense transcript expression in porcine postnatal muscle is affected by a quantitative trait nucleotide in intron 3

A paternally expressed quantitative trait locus (QTL) for muscle mass was mapped to the insulin-like growth factor II ( IGF2) locus at the distal end of pig chromosome 2p. It was recently demonstrated that a G to A transition at position intron 3–nt 3072 is the quantitative trait nucleotide (QTN) underlying this QTL. In this study we report for the first time the existence of imprinted porcine IGF2 antisense transcripts ( IGF2-AS) and demonstrate that their expression in postnatal muscle is also affected by the QTN. A coregulated expression of IGF2 and IGF2-AS RNAs in muscle and liver with decreasing transcription from fetal to adult age was demonstrated. Further, the significant difference found in expression of IGF2-AS in postnatal muscle between individuals with different QTL genotypes and the lack of significant differences in fetal muscle and liver reflect completely what has been found for IGF2 sense transcripts.

A statistical model for functional mapping of quantitative trait loci regulating drug response.

Differential drug response, that is, pharmacodynamics, is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, that is, quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing pharmacodynamic processes. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high-resolution mapping of QTL by making use of recombination events created at a historic time. We implement a closed-form solution for the Expectation-Maximization algorithm to estimate the population genetic parameters of QTL and the simplex algorithm to estimate the curve parameters describing the pharmacodynamic changes of different QTL genotypes in response to drug dose or concentrations. Extensive simulations are performed to investigate the statistical properties of our model. The implications of our model in pharmacogenetic and pharmacogenomic research are discussed.

Detection of multiple QTL with epistatic effects under a mixed inheritance model in an outbred population

A quantitative trait depends on multiple quantitative trait loci (QTL) and on the interaction between two or more QTL, named epistasis. Several methods to detect multiple QTL in various types of design have been proposed, but most of these are based on the assumption that each QTL works independently and epistasis has not been explored sufficiently. The objective of the study was to propose an integrated method to detect multiple QTL with epistases using Bayesian inference via a Markov chain Monte Carlo (MCMC) algorithm. Since the mixed inheritance model is assumed and the deterministic algorithm to calculate the probabilities of QTL genotypes is incorporated in the method, this can be applied to an outbred population such as livestock. Additionally, we treated a pair of QTL as one variable in the Reversible jump Markov chain Monte Carlo (RJMCMC) algorithm so that two QTL were able to be simultaneously added into or deleted from a model. As a result, both of the QTL can be detected, not only in cases where either of the two QTL has main effects and they have epistatic effects between each other, but also in cases where neither of the two QTL has main effects but they have epistatic effects. The method will help ascertain the complicated structure of quantitative traits.

Using Environmental Covariates to Explain Genotype × Environment and QTL × Environment Interactions for Agronomic Traits on Chromosome 3A of Wheat

Genotype × environment interactions (GEI) and quantitative trait loci × environment interactions (QEI) are known to influence the expression of agronomic performance traits in wheat. The aim of this study was to provide biological and environmental explanations for large GEI and QEI known to affect the expression of genes on chromosome 3A of wheat (Triticum aestivum L.). Agronomic performance and molecular marker data available for a population of chromosome 3A recombinant inbred chromosome lines (RICLs‐3A) in seven environments was used along with environmental covariate data to construct individual factorial regressions to explain GEI and QEI. Precipitation and temperature before anthesis had the greatest influence on agronomic performance traits for the RICLs‐3A, and explained a sizeable portion of the total GEI for those traits. Individual molecular marker × environmental covariate interactions explained a large portion of the total marker × environment interactions for several agronomic traits. Seventy‐six percent of the QEI for a major grain yield quantitative trait locus (QTL) was explained by the effect of temperature during preanthesis growth on dissimilar QTL genotype differentials across testing environments. Environmental covariates provided a strong basis for explaining QEI using marker × environmental covariate interactions.

Mapping multiple quantitative trait Loci for ordinal traits.

Many complex traits in humans and other organisms show ordinal phenotypic variation but do not follow a simple Mendelian pattern of inheritance. These ordinal traits are presumably determined by many factors, including genetic and environmental components. Several statistical approaches to mapping quantitative trait loci (QTL) for such traits have been developed based on a single-QTL model. However, statistical methods for mapping multiple QTL are not well studied as continuous traits. In this paper, we propose a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to map multiple QTL for ordinal traits in experimental crosses. We model the ordinal traits under the multiple threshold model, which assumes a latent continuous variable underlying the ordinal phenotypes. The ordinal phenotype and the latent continuous variable are linked through some fixed but unknown thresholds. We adopt a standardized threshold model, which has several attractive features. An efficient sampling scheme is developed to jointly generate the threshold values and the values of latent variable. With the simulated latent variable, the posterior distributions of other unknowns, for example, the number, locations, genetic effects, and genotypes of QTL, can be computed using existing algorithms for normally distributed traits. To this end, we provide a unified approach to mapping multiple QTL for continuous, binary, and ordinal traits. Utility and flexibility of the method are demonstrated using simulated data.

Detection of multiple QTL with epistatic effects under a mixed inheritance model in an outbred population.

A quantitative trait depends on multiple quantitative trait loci (QTL) and on the interaction between two or more QTL, named epistasis. Several methods to detect multiple QTL in various types of design have been proposed, but most of these are based on the assumption that each QTL works independently and epistasis has not been explored sufficiently. The objective of the study was to propose an integrated method to detect multiple QTL with epistases using Bayesian inference via a Markov chain Monte Carlo (MCMC) algorithm. Since the mixed inheritance model is assumed and the deterministic algorithm to calculate the probabilities of QTL genotypes is incorporated in the method, this can be applied to an outbred population such as livestock. Additionally, we treated a pair of QTL as one variable in the Reversible jump Markov chain Monte Carlo (RJMCMC) algorithm so that two QTL were able to be simultaneously added into or deleted from a model. As a result, both of the QTL can be detected, not only in cases where either of the two QTL has main effects and they have epistatic effects between each other, but also in cases where neither of the two QTL has main effects but they have epistatic effects. The method will help ascertain the complicated structure of quantitative traits.

Prospects for Positional Cloning of QTL in General Pedigrees using the Bovine Whole Genome Sequence

It has proven to be extremely difficult to identify the causal mutations underlying livestock quantitative trait loci (QTLs) and this has severely handicapped the application of marker-assisted selection (MAS) in commercial livestock species. The availability of a whole genome sequence will assist in the identification of candidate genes within a critical region harboring a QTL and also in the design of PCR primers to screen for diversity within coding and non-coding regulatory regions of targeted candidate genes. However it will not overcome the key problem for quantitative trait nucleotide (QTN) identification; viz., the recognition of the important regulatory regions and the identification of causal mutations within these regions. The central tenet of this paper is that new approaches are required for the successful implementation of MAS within commercial livestock populations. We propose that a useful paradigm will be to conduct whole genome scans for QTL within the populations in which MAS is to be employed allowing the application of MAS using linked-markers within these populations. This approach also has utility for QTN identification since the genome scan will identify unrelated or distantly related animals possessing alternative QTL genotypes which can be sequenced. This approach should provide an increased power for QTN identification over designed experimental crosses which often employ a small number of parents and that result in a limited number of haplotypes within the QTL critical region, often confounding many mutations with the causal QTN. In this paper, we describe our approach to QTL mapping, MAS and QTN identification using the U.S. Angus population as target population.

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.

Estimation of quantitative trait locus allele frequency via a modified granddaughter design.

A method is described on the basis of a modification of the granddaughter design to obtain estimates of quantitative trait loci (QTL) allele frequencies in dairy cattle populations and to determine QTL genotypes for both homozygous and heterozygous grandsires. The method is based on determining the QTL allele passed from grandsires to their maternal granddaughters using haplotypes consisting of several closely linked genetic markers. This method was applied to simulated data of 10 grandsire families, each with 500 granddaughters, and a QTL with a substitution effect of 0.4 phenotypic standard deviations and to actual data for a previously analyzed QTL in the center of chromosome 6, with substitution effect of 1 phenotypic standard deviation on protein percentage. In the simulated data the standard error for the estimated QTL substitution effect with four closely linked multiallelic markers was only 7% greater than the expected standard error with completely correct identification of QTL allele origin. The method estimated the population QTL allelic frequency as 0.64 +/- 0.07, compared to the simulated value of 0.7. In the actual data, the frequency of the allele that increases protein percentage was estimated as 0.63 +/- 0.06. In both data sets the hypothesis of equal allelic frequencies was rejected at P < 0.05.

On the Differences Between Maximum Likelihood and Regression Interval Mapping in the Analysis of Quantitative Trait Loci

The differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.

An improved procedure of mapping a quantitative trait locus via the EM algorithm using posterior probabilities

Mapping a locus controlling a quantitative genetic trait (e.g. blood pressure) to a specific genomic region is of considerable contemporary interest. Data on the quantitative trait under consideration and several codominant genetic markers with known genomic locations are collected from members of families and statistically analysed to estimate the recombination fraction, θ, between the putative quantitative trait locus and a genetic marker. One of the major complications in estimating θ for a quantitative trait in humans is the lack of haplotype information on members of families. We have devised a computationally simple two-stage method of estimation of θ in the absence of haplotypic information using the expectation-maximization (EM) algorithm. In the first stage, parameters of the quantitative trait locus (QTL) are estimated on the basis of data of a sample of unrelated individuals and a Bayes’s rule is used to classify each parent into a QTL genotypic class. In the second stage, we have proposed an EM algorithm for obtaining the maximum-likelihood estimate of θ based on data of informative families (which are identified upon inferring parental QTL genotypes performed in the first stage). The purpose of this paper is to investigate whether, instead of using genotypically ‘classified’ data of parents, the use of posterior probabilities of QT genotypes of parents at the second stage yields better estimators. We show, using simulated data, that the proposed procedure using posterior probabilities is statistically more efficient than our earlier classification procedure, although it is computationally heavier.

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.

More about quantitative trait locus mapping with diallel designs.

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.

Localization of a quantitative trait locus via a Bayesian approach.

A Bayesian approach to the direct mapping of a quantitative trait locus (QTL), fully utilizing information from multiple linked gene markers, is presented in this paper. The joint posterior distribution (a mixture distribution modeling the linkage between a biallelic QTL and N gene markers) is computationally challenging and invites exploration via Markov chain Monte Carlo methods. The parameter's complete marginal posterior densities are obtained, allowing a diverse range of inferences. Parameters estimated include the QTL genotype probabilities for the sires and the offspring, the allele frequencies for the QTL, and the position and additive and dominance effects of the QTL. The methodology is applied through simulation to a half-sib design to form an outbred pedigree structure where there is an entire class of missing information. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.

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 with dominant markers in four-way crosses

A common problem in mapping quantitative trait loci (QTLs) is that marker data are often incomplete. This includes missing data, dominant markers, and partially informative markers, arising in outbred populations. Here we briefly present an iteratively re-weighted least square method (IRWLS) to incorporate dominant and missing markers for mapping QTLs in four-way crosses under a heterogeneous variance model. The algorithm uses information from all markers in a linkage group to infer the QTL genotype. Monte Carlo simulations indicate that with half dominant markers, QTL detection is almost as efficient as with all co-dominant markers. However, the precision of the estimated QTL parameters generally decreases as more markers become missing or dominant. Notable differences are observed on the standard deviation of the estimated QTL position for varying levels of marker information content. The method is relatively simple so that more complex models including multiple QTLs or fixed effects can be fitted. Finally, the method can be readily extended to QTL mapping in full-sib families.

Linkage disequilibrium in two‐stage marker‐assisted selection

Linkage disequilibrium in two‐stage marker‐assisted selection

A strategy for QTL detection in half-sib populations

AbstractA statistical analysis strategy for the detection of quantitative trait loci (QTLs) in half-sib populations is outlined. The initial exploratory analysis is a multiple regression of the trait score on a subset of markers to allow a rapid identification of possible chromosomal regions of interest. This is followed by multiple marker interval mapping with regression methods within and across families fitting one or two QTLs. Empirical thresholds are determined by experiment-wise permutation tests for different significance levels and empirical confidence intervals for the QTLs' positions are obtained by bootstrapping methods. For traits with evidence for a significant single-QTL effect, an approximate maximum likelihood analysis is performed to obtain estimates of QTL effect and the probability of the QTL genotype for each parent of a group of half-sibs. The strategy is demonstrated in an analysis of previously published data on chromosome 6 and five production traits from a granddaughter design in dairy cattle. The results confirm and extend evidence for QTLs affecting protein percentage. Informativeness of markers limited the possibility of mapping more than one QTL on the same linkage group.