Selective genotyping for determination of linkage between a marker locus and a quantitative trait locus

Summary Selective genotyping is the term used when the determination of linkage between marker loci and quantitative trait loci (QTL) affecting some particular trait is carried out by genotyping only individuals from the high and low phenotypic tails of the entire sample population. Selective genotyping can markedly decrease the number of individuals genotyped for a given power at the expense of an increase in the number of individuals phenotyped. The optimum proportion of individuals genotyped from the point of view of minimizing costs for a given experimental power depends strongly on the cost of completely genotyping an individual for all of the markers included in the experiment (including the costs of obtaining a DNA sample) relative to the cost of rearing and trait evaluation of an individual. However, in single trait studies, it will almost never be useful to genotype more than the upper and lower 25% of a population. It is shown that the observed difference in quantitative trait values associated with alternative marker genotypes in the selected population can be much greater than the actual gene effect at the quantitative trait locus when the entire population is considered. An expression and a figure is provided for converting observed differences under selective genotyping to actual gene effects.     

A correlation method for detecting and estimating linkage between a marker locus and a quantitative trait locus using inbred lines

The advent of molecular genetic markers has stimulated interest in detecting linkage between a marker locus and a quantitative trait locus (QTL) because the marker locus, even without direct effect on the quantitative trait, could be useful in increasing the response to selection. A correlation method for detecting and estimating linkage between a marker locus and a QTL is described using selfing and sib-mating populations. Computer simulations were performed to estimate the power of the method, the sample size (N) needed to detect linkage, and the recombination value (r). The power of this method was a function of the expected recombination value E(r), the standardized difference (d) between the QTL genotypic means, and N. The power was highest at complete linkage, decreased with an increase in E(r), and then increased at E(r)=0.5. A larger d and N led to a higher power. The sample size needed to detect linkage was dependent upon E(r) and d. The sample size had a minimum value at E(r)=0, increased with an increase in E(r) and a decrease in d. In general, the r was overestimated. With an increase in d, the r was closer to its expectation. Detection of linkage by the proposed method under incomplete linkage was more efficient than estimation of recombination values. The correlation method and the method of comparison of marker-genotype means have a similar power when there is linkage, but the former has a slightly higher power than the latter when there is no linkage.     

Estimation of recombination parameters between a quantitative trait locus (QTL) and two marker gene loci

Summary A new method is described to obtain maximum likelihood estimates of recombination frequencies between quantitative trait loci (QTL) and marker gene loci; it is based on Fisher's method of scoring and numerical differentiation. The method is applied to data from chromosome-doubled monoploid lines of barley originating from the F₁ generation of a cross between two well-adapted barley varieties. The lines segregated for marker gene loci ddt (DDT resistance) and s (short rachilla hairs) on chromosome 7. The quantitative trait of single-kernel weight was found statistically significantly associated with locus s, but not with locus ddt. The association is ascribed to a QTL designated Kw1. It could not be ascribed to pleiotropism at locus s since the recombination frequency between s and Kw1 (0.26±0.09) differed significantly from zero. The recombination frequencies between Kw1 and ddt and between ddt and s were 0.42±0.07 and 0.31±0.03, respectively, suggesting the locus order ddt, s, Kw1. The segregation ratio for alleles in locus Kw1 was estimated to be 4357, which is not significantly different from a 11 ratio. Means and standard deviations of single-kernel weight for lines with either of the two Kw1 alleles were estimated; the Kw1 locus accounted for 25% of the variance of the single kernel weight.     

Linkage between quantitative trait loci and marker loci: resolution power of three statistical approaches in single marker analysis

This paper presents a comparison of three methods of parameter estimation in analysis of linkage between a quantitative trait locus (QTL) and a marker locus: maximum likelihood, mean square for trait cumulative distribution function, and method of moments, employing simulated backcross data. The sensitivity of estimates to violation of assumptions of normality and equal variances were also studied. Some measures of discrepancy between the trait distributions in the QTL groups are considered to evaluate the potential dependence of the resolution capacity of the QTL substitution effect with respect to trait mean value and variance.     

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.     

Estimating linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.     

Linkage between quantitative and marker loci. V. Joint analysis of various marker and quantitative traits

New versions are suggested to analyse marker and quantitative characters combinations. Possible modes of application of the algorithms developed for recombination analysis are discussed, including: 1) the estimation of crossing-over frequency between markers with incomplete penetrance, 2) the quantitative character variability account to analyse genetic interference, 3) search for genetic factors affecting a set of quantitative characters, 4) the evaluation of differences between male and female meiosis at the crossingover level etc.     

Linkage between loci of quantitative traits and marker loci: multi-trait analysis with a single marker

An efficient approach to increase the resolution power of linkage analysis between a quantitative trait locus (QTL) and a marker is described in this paper. It is based on a counting of the correlations between the QTs of interest. Such correlations may be caused by the segregation of other genes, environmental effects and physiological limitations. Let a QT locus A/a affect two correlated traits, x and y. Then, within the framework of mixture models, the accuracy of the parameter estimates may be seriously increased, if bivariate densities f _aa(x, y), f _Aa(x, y) and f _AA(x, y) rather than the marginals are considered as the basis for mixture decomposition. The efficiency of the proposed method was demonstrated employing Monte-Carlo simulations. Several types of progeny were considered, including backcross, F₂ and recombinant inbred lines. It was shown that provided the correlation between the traits involved was high enough, a good resolution to the problem is possible even if the QTL groups are strongly overlapping for their marginal densities.     

Complex genetic interactions in a quantitative trait locus

Whether in natural populations or between two unrelated members of a species, most phenotypic variation is quantitative. To analyze such quantitative traits, one must first map the underlying quantitative trait loci. Next, and far more difficult, one must identify the quantitative trait genes (QTGs), characterize QTG interactions, and identify the phenotypically relevant polymorphisms to determine how QTGs contribute to phenotype. In this work, we analyzed three Saccharomyces cerevisiae high-temperature growth (Htg) QTGs (MKT1, END3, and RHO2). We observed a high level of genetic interactions among QTGs and strain background. Interestingly, while the MKT1 and END3 coding polymorphisms contribute to phenotype, it is the RHO2 3′UTR polymorphisms that are phenotypically relevant. Reciprocal hemizygosity analysis of the Htg QTGs in hybrids between S288c and ten unrelated S. cerevisiae strains reveals that the contributions of the Htg QTGs are not conserved in nine other hybrids, which has implications for QTG identification by marker-trait association. Our findings demonstrate the variety and complexity of QTG contributions to phenotype, the impact of genetic background, and the value of quantitative genetic studies in S. cerevisiae.     

Linkage disequilibrium on the bovine X chromosome: characterization and use in quantitative trait locus mapping

We herein demonstrate that in the Holstein-Friesian dairy cattle population, microsatellites are as polymorphic on the X chromosome as on the autosomes but that the level of linkage disequilibrium between these markers is higher on the X chromosome than on the autosomes. The latter observation is not compatible with the small male-to-female ratio that prevails in this population and results in a higher gonosomal than autosomal effective population size. It suggests that the X chromosome undergoes distinct selective or mutational forces. We describe and characterize a novel Markovian approach to exploit this linkage disequilibrium to compute the probability that two chromosomes are identical-by-descent conditional on flanking marker data. We use the ensuing probabilities in a restricted maximum-likelihood approach to search for quantitative trait loci (QTL) affecting 48 traits of importance to the dairy industry and provide evidence for the presence of QTL affecting 5 of these traits on the bovine X chromosome.     

Models and tests of linkage and association studies of quantitative trait locus for multi-allele marker Loci

In this paper, we explore models and tests for association and linkage studies of a quantitative trait locus (QTL) linked to a multi-allele marker locus. Based on the difference between an offspring's conditional trait means of receiving and not receiving an allele from a parent at marker locus, we propose three statistics T(m), T(m,row) and T(m,col) to test association or linkage disequilibrium between the marker locus and the QTL. These tests are composite tests, and use the offspring marginal sample means including offspring data of both homozygous and heterozygous parents. For the linkage study, we calculate the offspring's conditional trait mean given the allele transmission status of a heterozygous parent at the marker locus. Based on the difference between the conditional means of a transmitted and a nontransmitted allele from a heterozygous parent, we propose statistics T(parsi), T(satur), T(gen) and T(m,het) to perform composite tests of linkage between the marker locus and the quantitative trait locus in the presence of association. These tests only use the offspring data that are related to the heterozygous parents at the marker locus. T(parsi) is a parsimonious or allele-wise statistic, T(satur) and T(gen )are satured or genotype-wise statistics, and T(m,het) compares the row and column sample means for offspring data of heterozygous parents. After comparing the powers and the sample sizes, we conclude that T(parsi) has higher power than those of the bi-allele tests, T(satur), T(gen), and T(m,het). If there is tight linkage between the marker and the trait locus, T(parsi) is powerful in detecting linkage between the marker and the trait locus in the presence of association. By investigating the goodness-of-fit of T(parsi), we find that T(satur) does not gain much power compared to that of T(parsi). Moreover, T(parsi) takes into account the pattern of the data that is consistent with linkage and linkage disequilibrium. As the number of alleles at the marker locus increases, T(parsi) is very conservative, and can be useful even for sparse data. To illustrate the usefulness and the power of the methods proposed in this paper, we analyze the chromosome 6 data of the Oxford asthma data, Genetic Analysis Workshop 12.     

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.     

A review of family-based tests for linkage disequilibrium between a quantitative trait and a genetic marker

Quantitative trait transmission/disequilibrium tests (quantitative TDTs) are commonly used in family-based genetic association studies of quantitative traits. Despite the availability of various quantitative TDTs, some users are not aware of the properties of these tests and the relationships between them. This review aims at outlining the broad features of the various quantitative TDT procedures carried out in the frequently used QTDT and FBAT packages. Specifically, we discuss the “Rabinowitz” and the “Monks-Kaplan” procedures, as well as the various “Abecasis” and “Allison” regression-based procedures. We focus on the models assumed in these tests and the relationships between them. Moreover, we discuss what hypotheses are tested by the various quantitative TDTs, what testing procedures are best suited to various forms of data, and whether the regression-based tests overcome population stratification problems. Finally, we comment on power considerations in the choice of the test to be used. We hope this brief review will shed light on the similarities and differences of the various quantitative TDTs.     

Sequential sampling in determining linkage between marker loci and quantitative trait loci

Summary As compared to classical, fixed sample size techniques, simulation studies showed that a proposed sequential sampling procedure can provide a substantial decrease (up to 50%, in some cases) in the mean sample size required for the detection of linkage between marker loci and quantitative trait loci. Sequential sampling with truncation set at the required sample size for the non-sequential test, produced a modest further decrease in mean sample size, accompanied by a modest increase in error probabilities. Sequential sampling with observations taken in groups produced a noticeable increase in mean sample size, with a considerable decrease in error probabilities, as compared to straightforward sequential sampling. It is concluded that sequential sampling has a particularly useful application to experiments aimed at investigating the genetics of differences between lines or strains that differ in some single outstanding trait.     

Mapping of a quantitative trait locus for morphine withdrawal severity

Chronic morphine exposure results in physical dependence, manifested by physical symptoms during naloxone-precipitated withdrawal. Jumping frequency is widely considered the most sensitive and reliable index of withdrawal intensity in mice. Inbred mouse strains surveyed for naloxone-precipitated withdrawal display large and significant strain differences in jumping frequency, including an approximately tenfold difference between C57BL/6 and 129P3 mice. In the present study, (B6 × 129)F₂ hybrid mice were given daily morphine injections for four days using an escalating dosing schedule, and naloxone-precipitated withdrawal on day 5 was measured. A full-genome scan for linkage to phenotypic data was performed using polymorphic microsatellite markers. Significant linkage was observed between withdrawal jumping frequencies and a 28 cM-wide region of Chromosome 1 (32–60 cM; peak at 51 cM), accounting for 20% of the overall phenotypic variance. Two other suggestive QTLs were found, on Chromosomes 5 and 10, and an additive model fitting all three loci accounted for 43% of the total variance. F₂ mice were also assessed for changes in morphine analgesic potency using the tail-withdrawal test in dose–response studies on days 1 and 4. No linkage was observed between Chromosomes 1, 5, and 10 and morphine analgesic tolerance, suggestive of genetic dissociation of naloxone-precipitated withdrawal from morphine and chronic morphine intake per se. The significant quantitative trait locus for naloxone-precipitated withdrawal severity in morphine-dependent mice, which we name Depmq1, may prove to be of considerable heuristic value once the underlying gene or genes are identified.     

The effect of epistasis between linked genes on quantitative trait locus analysis

The effect of epistasis between linked genes on quantitative trait locus (QTL) analysis was studied as a function of their contribution to the phenotypic variance and their genetic distance by simulation of F2 (at least 200 individuals) and recombinant inbred line (RIL) populations. Data sets were replicated 100 times. For F2 populations, the presence of epistasis improves the detection of QTLs having effects in opposite directions. Epistasis between linked QTLs (26.5 cM) was poorly detected even when its contribution was relatively high compared to the main effects, and was null for heritabilities lower than 0.10. The detection of false-positive main effects is strongly affected by the distance between epistatic QTLs. The closer they are (≤11.5 cM), the higher the probability of detecting false-positive main-effect QTLs and the lower the probability of detecting epistatic effects. In this case, the presence of main-effect QTLs is due to the deviation of the heterozygote from the homozygotes at each linked interacting QTL and is algebraically explained by the joint effect of the linkage and the additive-by-additive interaction, resulting in a heterosis at a single genomic region in the absence of simulated dominant genetic effects. The number of false-positive main effects only reached nominal levels at about 100 cM. For RIL populations, the number of false positives or the detection of existing epistasis does not depend on the distance, and the power to detect epistatic QTLs is much higher even with small sample sizes and low contributions to the trait. RIL populations are highly recommended to detect epistatic QTLs and to better infer the genetic architecture of a quantitative trait.