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Efficient score statistics for mapping quantitative trait loci with extended pedigrees.

The method of variance components is the method of choice for mapping quantitative trait loci (QTLs) with general pedigrees. Being a likelihood-based method, this method can be computation intensive even for nuclear families, and has excessive false positive rates under some situations. Here two efficient score statistics to detect QTLs are derived, one assumes that the candidate locus has no dominance effect, and the other one does not make such an assumption. These two score statistics are asymptotically equivalent to the method of variance components but they are easier to compute and more robust than the likelihood ratio statistic. The derivation of these score statistics is facilitated by separating the segregation parameters, the parameters that describe the distribution of the phenotypic value in the population, from the linkage parameters, the parameters that measure the effect of the candidate locus on the phenotypic value. Such a separation of the model parameters greatly reduces the number of parameters to be dealt with in the analysis of linkage. The asymptotic distributions of both score statistics are derived. Simulation studies indicate that, compared to the method of variance components, both score statistics have comparable or higher power, and their false-positive rates are closer to their respective nominal significance levels.

Chromosome Mapping↗

Quantitative trait loci mapped to single-nucleotide resolution in yeast.

Identifying the genetic variation underlying quantitative trait loci remains problematic. Consequently, our molecular understanding of genetically complex, quantitative traits is limited. To address this issue directly, we mapped three quantitative trait loci that control yeast sporulation efficiency to single-nucleotide resolution in a noncoding regulatory region (RME1) and to two missense mutations (TAO3 and MKT1). For each quantitative trait locus, the responsible polymorphism is rare among a diverse set of 13 yeast strains, suggestive of genetic heterogeneity in the control of yeast sporulation. Additionally, under optimal conditions, we reconstituted approximately 92% of the sporulation efficiency difference between the two genetically distinct parents by engineering three nucleotide changes in the appropriate yeast genome. Our results provide the highest resolution to date of the molecular basis of a quantitative trait, showing that the interaction of a few genetic variants can have a profound phenotypic effect.

Adaptor Proteins, Signal Transducing↗

Efficiency robust tests for mapping quantitative trait loci using extremely discordant sib pairs.

In 1972, Haseman and Elston proposed a pioneering regression method for mapping quantitative trait loci using randomly selected sib pairs. Recently, the statistical power of their method was shown to be increased when extremely discordant sib pairs are ascertained. While the precise genetic model may not be known, prior information that constrains IBD probabilities is often available. We investigate properties of tests that are robust against model uncertainty and show that the power gain from further constraining IBD probabilities is marginal. The additional linkage information contained in the trait values can be incorporated by combining the Haseman-Elston regression method and a robust allele sharing test.

Chromosome Mapping↗

Mapping quantitative trait loci in humans: achievements and limitations.

Recent advances in statistical methods and genomic technologies have ushered in a new era in mapping clinically important quantitative traits. However, many refinements and novel statistical approaches are required to enable greater successes in this mapping. The possible impact of recent findings pertaining to the structure of the human genome on efforts to map quantitative traits is yet unclear.

Genome, Human↗

Using the expectation or the distribution of the identity by descent for mapping quantitative trait loci under the random model.

We examine the ability of four implementations of the random model to map quantitative trait loci (QTLs). The implementations use either the expectation or the distribution of the identity-by-descent value at a putative QTL and either a 2 x 1 vector of sib-pair traits or their scalar difference. When the traits of both sibs are used, there is little difference between the expectation and distribution methods, while the expectation method suffers in both precision and power when the difference between traits is used. This is consistent with the prediction that the difference between the expectation and distribution methods is inversely proportional to the amount of information available for mapping. We find, though, that the amount of information must be very low for this difference to be noticeable. This is exemplified when both marker loci are fixed. In this case, while the expectation method is powerless to detect the QTL, the distribution method can still detect the presence (but not the position) of the QTL 59% of the time (when using trait values) or 14% of the time (when using trait differences). We also note a confounding between estimates of the QTL, polygenic, and error variance. The degree of confounding is small when the vector of trait values is used but can be substantial when the expectation method and trait differences are used. We discuss this in light of the general ability of the random model to partition these components.

Chromosome Mapping↗

High-resolution quantitative trait locus mapping reveals sign epistasis controlling ovariole number between two Drosophila species.

Identifying the genes underlying genetically complex traits is of fundamental importance for medicine, agriculture, and evolutionary biology. However, the level of resolution offered by traditional quantitative trait locus (QTL) mapping is usually coarse. We analyze here a trait closely related to fitness, ovariole number. Our initial interspecific mapping between Drosophila sechellia (8 ovarioles/ovary) and D. simulans (15 ovarioles/ovary) identified a major QTL on chromosome 3 and a minor QTL on chromosome 2. To refine the position of the major QTL, we selected 1038 additional recombinants in the region of interest using flanking morphological markers (selective phenotyping). This effort generated approximately one recombination event per gene and increased the mapping resolution by approximately seven times. Our study thus shows that using visible markers to select for recombinants can efficiently increase the resolution of QTL mapping. We resolved the major QTL into two epistatic QTL, QTL3a and QTL3b. QTL3a shows sign epistasis: it has opposite effects in two different genetic backgrounds, the presence vs. the absence of the QTL3b D. sechellia allele. This property of QTL3a allows us to reconstruct the probable order of fixation of the QTL alleles during evolution.

Animals↗

Selection bias in quantitative trait loci mapping.

A simulation study was performed to see whether selection affected quantitative trait loci (QTL) mapping. Populations under random selection, under selection among full-sib families, and under selection within a full-sib family were simulated each with heritability of 0.3, 0.5, and 0.7. They were analyzed with the marker spacing of 10 cM and 20 cM. The accuracy for QTL detection decreased for the populations under selection within full-sib family. Estimates of QTL effects and positions differed (P < .05) from their input values. The problems could be ignored when mapping a QTL for the populations under selection among full-sib families. A large heritability helped reduction of such problems. When the animals were selected within a full-sib family, the QTL was detected for the populations with heritability of 0.5 or larger using the marker spacing of 10 cM, and with heritability of 0.7 using the marker spacing of 20 cM. This study implied that when selection was introduced, the accuracy for QTL detection decreased and the estimates of QTL effects were biased. A caution was warranted on the decision of data (including selected animals to be genotyped) for QTL mapping.

Animals↗

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.

Algorithms↗

Quantitative trait locus mapping in natural populations: progress, caveats and future directions.

Over the last 15 years quantitative trait locus (QTL) mapping has become a popular method for understanding the genetic basis of continuous variation in a variety of systems. For example, the technique is now an integral tool in medical genetics, livestock production, plant breeding and population genetics of model organisms. Ten years ago, it was suggested that the method could be used to understand continuous variation in natural populations. In this review I: (i) clarify what is meant by natural population in the QTL context, (ii) discuss whether evolutionary biologists have successfully mapped QTL in natural populations, (iii) highlight some of the questions that have been addressed by QTL mapping in natural populations, (iv) describe how QTL mapping can be conducted in unmanipulated natural populations, (v) highlight some of the limitations of QTL mapping and (vi) try to predict some future directions for QTL mapping in natural populations.

Biological Evolution↗

Mapping quantitative traits with random and with ascertained sibships.

Use of a robust score statistic based on a variance components model to map quantitative trait loci in randomly sampled pedigrees is reviewed. Sibships ascertained through a single proband are discussed. Under a standard assumption of multivariate normality, two suggested methods of ascertainment correction are shown to be asymptotically equivalent when the number of sibships is large.

Chromosome Mapping↗

Quantitative trait loci mapping for cholesterol gallstones in AKR/J and C57L/J strains of mice.

Quantitative trait locus (QTL) mapping was used to locate genes that determine the difference in cholesterol gallstone disease between the gallstone-susceptible strain C57L/J and the gallstone-resistant strain AKR/J. Gallstone weight was determined in 231 male (AKR x C57L) F(1) x AKR backcross mice fed a lithogenic diet containing 1% cholesterol, 0.5% cholic acid, and 15% butterfat for 8 wk. Mice having no stones and mice having the largest stones were genotyped at approximately 20-cM intervals to find the loci determining cholesterol gallstone formation. The major locus, Lith1, mapped near D2Mit56 and was confirmed by constructing a congenic strain, AK. L-Lith1(s). Another locus, Lith2, mapped near D19Mit58 and was also confirmed by constructing a congenic strain AK.L-Lith2(s). Other suggestive, but not statistically significant, loci mapped to chromosomes 6, 7, 8, 10, and X. The identification of these Lith genes will elucidate the pathophysiology of cholesterol gallstone formation.

Animals↗

Mapping quantitative trait loci with extreme discordant sib pairs: sampling considerations.

Elsewhere we have proposed the use of extreme discordant sib pairs (EDSPs) for mapping quantitative trait loci in humans. Here we present sample sizes necessary to achieve a given level of power with this study design, as well as the number of sibs that need to be screened to obtain the required sample. Further, we present simple formulas for adjusting sample sizes to account for variable significance levels and power, as well as the density and informativeness of linkage markers in a multipoint sib-pair analysis. We conclude that with EDSPs, the most powerful study design, the smallest genetic effect detectable with a realistic sample size is approximately 10% of the variance of the trait.

Analysis of Variance↗

Evaluation of a restricted likelihood ratio test for mapping quantitative trait loci with extreme discordant sib pairs.

Risch and Zhang recently proposed to use extreme discordant sib pairs for mapping quantitative trait loci. Here, it is shown that the set of genetically possible distributions of the number of marker alleles in such sib-pairs is described by two inequalities. Thus, a likelihood ratio test analogous to Holmans's possible triangle test for affected sib pairs can be defined. The performance of this test is compared to the mean test considered by Risch and Zhang. For most of the genetic models considered, the mean test is slightly more powerful than the restricted likelihood ratio test. However, for models with a rare recessive gene (or equivalently a common dominant gene), the restricted likelihood ratio test is much more powerful.

Alleles↗

Mapping quantitative trait loci controlling milk production in dairy cattle by exploiting progeny testing.

We have exploited "progeny testing" to map quantitative trait loci (QTL) underlying the genetic variation of milk production in a selected dairy cattle population. A total of 1,518 sires, with progeny tests based on the milking performances of > 150,000 daughters jointly, was genotyped for 159 autosomal microsatellites bracketing 1645 centimorgan or approximately two thirds of the bovine genome. Using a maximum likelihood multilocus linkage analysis accounting for variance heterogeneity of the phenotypes, we identified five chromosomes giving very strong evidence (LOD score > or = 3) for the presence of a QTL controlling milk production: chromosomes 1, 6, 9, 10 and 20. These findings demonstrate that loci with considerable effects on milk production are still segregating in highly selected populations and pave the way toward marker-assisted selection in dairy cattle breeding.

Animals↗

Integrating sibship data for mapping quantitative trait loci.

Sibship methods have been shown to be more powerful than traditional sib-pair methods in mapping quantative trait loci. We propose a statistical procedure which integrates data on sibships into a so-called 'contrast function', a natural extension of the classical squared sib-pair trait difference proposed by Haseman & Elston (1972). We also develop a combined mean and contrast function which provides more information on linkage compared to the contrast function. Our method is extended to multiple, epistatically interacting trait loci. Monte-Carlo simulations are included to compare the efficiencies of the proposed procedures with some currently used methods. An application of our proposed method is presented using data on alcohol dependence.

Alcoholism↗

Theoretical basis for separation of multiple linked gene effects in mapping quantitative trait loci.

It is now possible to use complete genetic linkage maps to locate major quantitative trait loci (QTLs) on chromosome regions. The current methods of QTL mapping (e.g., interval mapping, which uses a pair or two pairs of flanking markers at a time for mapping) can be subject to the effects of other linked QTLs on a chromosome because the genetic background is not controlled. As a result, mapping of QTLs can be biased, and the resolution of mapping is not very high. Ideally when we test a marker interval for a QTL, we would like our test statistic to be independent of the effects of possible QTLs at other regions of the chromosome so that the effects of QTLs can be separated. This test statistic can be constructed by using a pair of markers to locate the testing position and at the same time using other markers to control the genetic background through a multiple regression analysis. Theory is developed in this paper to explore the idea of a conditional test via multiple regression analysis. Various properties of multiple regression analysis in relation to QTL mapping are examined. Theoretical analysis indicates that it is advantageous to construct such a testing procedure for mapping QTLs and that such a test can potentially increase the precision of QTL mapping substantially.

Chromosome Mapping↗

Quantitative trait locus mapping of airway responsiveness to chromosomes 6 and 7 in inbred mice.

Quantitative trait locus (QTL) mapping was used to identify chromosomal regions contributing to airway hyperresponsiveness in mice. Airway responsiveness to methacholine was measured in A/J and C3H/HeJ parental strains as well as in progeny derived from crosses between these strains. QTL mapping of backcross [(A/J x C3H/HeJ) x C3H/HeJ] progeny (n = 137-227 informative mice for markers tested) revealed two significant linkages to loci on chromosomes 6 and 7. The QTL on chromosome 6 confirms the previous report by others of a linkage in this region in the same genetic backgrounds; the second QTL, on chromosome 7, represents a novel locus. In addition, we obtained suggestive evidence for linkage (logarithm of odds ratio = 1.7) on chromosome 17, which lies in the same region previously identified in a cross between A/J and C57BL/6J mice. Airway responsiveness in a cross between A/J and C3H/HeJ mice is under the control of at least two major genetic loci, with evidence for a third locus that has been previously implicated in an A/J and C57BL/6J cross; this indicates that multiple genetic factors control the expression of this phenotype.

Animals↗

Molecular dissection of complex traits in autopolyploids: mapping QTLs affecting sugar yield and related traits in sugarcane.

Mapping quantitative trait loci (QTLs) for sugar yield and related traits will provide essential information for sugarcane improvement through marker-assisted selection. Two sugarcane segregating populations derived from interspecific crosses between Saccharum offinarum and Saccharum spontaneum with 264 and 239 individuals, respectively, were evaluated in three replications each for field performance from 1994 to 1996 at Weslaco, Texas. These two populations were analyzed for a total of 735 DNA marker loci to seek QTLs for sugar yield, pol, stalk weight, stalk number, fiber content and ash content. Among the 102 significant associations found between these six traits and DNA markers, 61 could be located on sugarcane linkage maps, while the other 41 were associated with unlinked DNA markers. Fifty of the 61 mapped QTLs were clustered in 12 genomic regions of seven sugarcane homologous groups. Many cases in which QTLs from different genotypes mapped to corresponding locations suggested that at least some of the QTLs on the same cluster might be different allelic forms of the same genes. With a few exceptions that explained part of the transgressive segregation observed for particular traits, the allele effects of most QTLs were consistent with the parental phenotype from which the allele was derived. Plants with a high sugar yield possessed a large number of positive QTLs for sugar yield components and a minimal number of negative QTLs. This indicates the potential effectiveness of marker-assisted selection for sugar yield in sugarcane.

Journal Article↗