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Practical application of residuals from survival models in quantitative trait linkage analysis.

A number of familial diseases have an age-of-onset component, which can be considered as a censored quantitative trait. However, few software resources are available for the use of time-to-event endpoints in linkage analysis. The purpose of this analysis was to examine the use of martingale residuals from Cox survival models as quantitative traits for familial diseases with variable age at onset. We used these residuals as quantitative traits in variance components linkage scans for the 50 replicates of the general population simulated data for chromosomes 6 and 7. The region on chromosome 6 containing markers D06G034 and D06G035 demonstrated evidence for linkage, consistent with the underlying genetic model. This analysis demonstrates the applicability of using martingale residuals as a quantitative trait in linkage analyses of diseases that depend on age of onset.

Adult↗

Detection of closely linked multiple quantitative trait loci using a genetic algorithm.

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the "genotype" with alterations called "recombination" and "mutation." The "genotype" of our GA is the number and location of QTL. The "fitness" is a function based on the likelihood plus Akaike's information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.

Algorithms↗

Identifying pedigrees segregating at a major locus for a quantitative trait: an efficient strategy for linkage analysis.

Having found evidence for segregation at a major locus for a quantitative trait, a logical next step is to identify those pedigrees in which major-locus segregation is occurring. If the quantitative trait is a risk factor for an associated disease, identifying such segregating pedigrees can be important in classifying families by etiology, in risk assessment, and in suggesting treatment modalities. Identifying segregating pedigrees can also be helpful in selecting pedigrees to include in a subsequent linkage study to map the major locus. Here, we describe a strategy to identify pedigrees segregating at a major locus for a quantitative trait. We apply this pedigree selection strategy to simulated data generated under a major-locus or mixed model with a rare dominant allele and sampled according to one of several fixed-structure or sequential sampling designs. We demonstrate that for the situations considered, the pedigree selection strategy is sensitive and specific and that a linkage study based only on the pedigrees classified as segregating extracts essentially all the linkage information in the entire sample of pedigrees. Our results suggest that for large-scale linkage studies involving many genetic markers, the savings from this strategy can be substantial and that, compared with fixed-structure sampling, sequential sampling of pedigrees can greatly improve the efficiency for linkage analysis of a quantitative trait.

Genetic Linkage↗

Transmission/disequilibrium tests for quantitative traits.

The transmission/disequilibrium test (TDT) is a powerful method of locating disease genes. The TDT was originally proposed for use in studies of qualitative traits in families with both parents available. Recently, the TDT has been extended to studies of qualitative traits in sibships without parents available and in families with one parent available. It has also been extended for use in studies of quantitative traits in families with both parents available and in sibships with multiple offspring. In this paper, we first propose a new class of TDT-type tests for linkage in the presence of linkage disequilibrium for use in studies of families with both parents available. The TDT of Spielman et al. (1993) for qualitative traits and the TDT of Rabinowitz (1997) for quantitative traits are special cases of the new tests. Second, we propose a new class of TDT-type tests for linkage for use in studies of families with one parent available. Third, we study the validity and the power of the tests using simulations. Finally, we propose a method of combining data from different types of families. The combined test is valuable and allows researchers full use of the available data in detecting linkage between a marker locus and an unobservable quantitative trait locus. An important feature of the tests proposed in this paper is that no assumptions on the distribution of the quantitative traits are needed.

Computer Simulation↗

Quantitative trait loci that determine plasma lipids and obesity in C57BL/6J and 129S1/SvImJ inbred mice.

The plasma lipid concentrations and obesity of C57BL/6J (B6) and 129S1/SvImJ (129) inbred mouse strains fed a high-fat diet containing 15% dairy fat, 1% cholesterol, and 0.5% cholic acid differ markedly. To identify the loci controlling these traits, we conducted a quantitative trait loci (QTL) analysis of 294 (B6 x 129) F(2) females fed a high-fat diet for 14 weeks. Non-HDL cholesterol concentrations were affected by five significant loci: Nhdlq1 [chromosome 8, peak centimorgan (cM) 38, logarithm of odds [LOD] 4.4); Nhdlq4 (chromosome 10, cM 70, LOD 4.0); Nhdlq5 (chromosome 6, cM 0) interacting with Nhdlq4; Nhdlq6 (chromosome 7, cM 10) interacting with Nhdlq1; and Nhdlq7 (chromosome 15, cM 0) interacting with Nhdlq4. Triglyceride (TG) concentrations were affected by three significant loci: Tgq1 (chromosome 18, cM 42, LOD 3.2) and Tgq2 (chromosome 9, cM 66) interacting with Tgq3 (chromosome 4, cM 58). Obesity measured by percentage of body fat mass and body mass index was affected by two significant loci: Obq16 (chromosome 8, cM 48, LOD 10.0) interacting with Obq18 (chromosome 9, cM 65). Knowing the genes for these QTL will enhance our understanding of obesity and lipid metabolism.

Animals↗

Mapping quantitative trait loci that influence femoral cross-sectional area in mice.

Size and shape are critical determinants of the mechanical properties of skeletal elements and can be anticipated to be highly heritable. Moreover, the genes responsible may be independent of those that regulate bone mineral density (BMD). To begin to identify the heritable determinants of skeletal geometry, we have examined femoral cross-sectional area (FCSA) in male and female mice from two inbred strains of mice with divergent FCSA (C57BL/6 [B6] and DBA/2 [D2]), a large genetically heterogeneous population (n = 964) of B6D2F2 mice and 18 BXD recombinant inbred (RI) strains derived from their F2 cross. Femora were harvested from 16-week-old mice and FCSA (bone and marrow space enclosed within the periosteum) was measured at the midshaft by digital image analysis. In all mouse populations examined, FCSA was positively correlated with body weight and weight-corrected FCSA (WC-FCSA) values were normally distributed in the BXD-RI and F2 populations, suggesting polygenic control of this trait. Genome-wide quantitative trait locus (QTL) analysis of the B6D2F2 population revealed regions on four different chromosomes that were very strongly linked to WC-FCSA (chromosomes 6, 8, 10, and X) in both genders. Evidence of gender-specific genetic influences on femoral geometry was also identified at three other chromosomal sites (chromosomes 2, 7, and 12). Supporting evidence for the WC-FCSA QTLs on chromosomes 2, 7, 8, 10, and 12 also was present in the RI strains. Interestingly, none of these WC-FCSA QTLs were identified in our previous QTL analysis of whole body BMD in the same B6D2F2 population. Thus, the genetic determinants of bone size appear to be largely, if not entirely, distinct from those that regulate BMD attainment. The identification of the genes responsible for geometric differences in bone development should reveal fundamentally important processes in the control of skeletal integrity.

Animals↗

Genetic variation at marker loci and in quantitative traits in natural populations of Arabidopsis thaliana.

Genetic variation was studied in quantitative traits and molecular markers in six natural Scandinavian populations of Arabidopsis thaliana. Only two of the populations had several molecular marker haplotypes and significant between-family variance components in quantitative traits. There was no genetic variation in the other four populations. The differentiation between the populations was high in both molecular markers and quantitative traits, with FST estimates of above 0.60 in almost all traits. The patterns of variation of the neutral markers and morphological and phenological traits were consistent in all the analyses, as opposed to what has been found in predominantly outcrossing species. The general picture of the level and distribution of genetic variance agrees with the information from other predominantly inbreeding species.

Arabidopsis↗

The impact of marker allele frequency misspecification in variance components quantitative trait locus analysis using sibship data.

In cases where sibship data are collected for a quantitative trait locus (QTL) linkage study without access to parental genotypes, the proportion of genes shared identical by descent must be estimated using the marker allele frequencies. No systematic study has been conducted to date to evaluate the effect of misspecification of these frequencies on a test of quantitative trait linkage. Analysis of both simulated and actual data on quantitative traits was carried out under various sets of allele frequency estimates. While correctly specifying the allele frequency distribution led to a slightly more powerful test and higher lod scores, the differences were small and would not likely alter the conclusion of a study. These results suggest that, at least for QTL analysis, there is a great deal of tolerance for misspecifying marker allele frequencies with little, if any, appreciable effect on the linkage test. However, the observed variations may be sufficiently large to alter the priority on might give to a positive finding for follow up.

Alcoholism↗

The value of relatives with phenotypes but missing genotypes in association studies for quantitative traits.

The additional statistical power of association studies for quantitative traits was derived when ungenotyped relatives with phenotypes are included in the analysis. It was shown that the extra power is a simple function of the coefficient of additive genetic relationship and the phenotypic correlation coefficient between the genotyped and ungenotyped relatives. For close relatives, such as pairs of fullsibs and identical twin pairs, gains in power in the range of 10 to 30% are achieved if only one of the pair is genotyped. The theoretical results were verified by simulations. It was shown that ignoring the error in estimating the genotype of the ungenotyped relative has little impact on the estimates and on statistical power, consistent with results from quantitative trait loci (QTL) linkage studies. For genome-wide association studies in which not all relatives with phenotypes can be genotyped, our study provides a prediction of the additional power of an analysis that includes phenotypes on ungenotyped individuals, and can be used in experimental design. We show that a two-step procedure, in which missing genotypes are imputed and subsequently an association analysis is performed, is efficient and powerful.

Genetic Predisposition to Disease↗

hairy: A quantitative trait locus for drosophila sensory bristle number.

Advances in medicine, agriculture, and an understanding of evolution depend on resolving the genetic architecture of quantitative traits, which is challenging since variation for complex traits is caused by multiple interacting quantitative trait loci (QTL) with small and conditional effects. Here, we show that the key developmental gene, hairy (h), is a QTL for Drosophila sternopleural bristle number, a model quantitative trait. Near-isoallelic lines (NIL) for the h gene region exhibited significant variation in bristle number and failed to complement a hairy mutation. Sequencing 10 h alleles from a single population revealed 330 polymorphic sites in approximately 10 kb. Genotypes for 25 of these and 14 additional sites in the flanking regions were determined for the 57 NIL and associated with variation in bristle number in four genetic backgrounds. A highly significant association was found for a complicated insertion/deletion polymorphism upstream of the transcription start site. This polymorphism, present in 17.5% of the h alleles, was associated with an increase of 0.5 bristle and accounted for 31% of the genetic variance in bristle number in the NIL.

Animals↗

Genetic mapping of quantitative trait loci for traits with ordinal distributions.

Statistical methods for mapping quantitative trait loci relative to genetic markers are now well established for continuous traits with normal distributions. However, many traits of economic importance are recorded on a discrete, ordinal scale. Here we describe a model developed for the analysis of ordinal traits, such as degree of difficulty in calving or categories of plant disease resistance. The model estimates the distance from the quantitative trait locus to neighbouring genetic markers, and also genetic parameters, either as gene effects on an underlying continuous scale or as probabilities of the observed categories. The model is tested on simulated data and is compared with an analysis based on mixtures of normal distributions. The ordinal model is found to estimate the parameters more accurately, especially when the number of categories is small or when only one linked marker is available.

Animal Husbandry↗

[Identification of mixed major genes and polygenes inheritance model of quantitative traits by using DH or RIL population].

The accuracy of the mixed inheritance analysis of quantitative traits with larger experimental error could be improved while using DH or RIL population. The segregation analysis method of identifying mixed major genes and polygenes inheritance model, including linkage inheritance model, of quantitative traits by using DH or RIL population was developed in this paper. The method may be applied to identify the mixed major gene and polygenes inheritance model of quantitative traits, estimate genetic effects and variances of major genes and polygenes, and the recombination value while there is linkage between two major genes. Finally, an example was used to illuminate the above procedure.

Genetic Linkage↗

Poor performance of bootstrap confidence intervals for the location of a quantitative trait locus.

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTL) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTL are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the nonparametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals behave poorly and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum-likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately.

Bayes Theorem↗

Quantitative trait loci for growth traits in C57BL/6J x DBA/2J mice.

Quantitative trait loci (QTLs) for body weight and tail length are mapped in an F2 population of 927 C57BL/6J x DBA/2J mice. We test the concordance between the locations of the mapped QTLs with those detected by changes of marker frequency under artificial selection in a previous experiment with the same base population. The directions of effects of the QTLs are generally in agreement, and in many cases significant QTLs are found in similar map positions, but there are also discrepancies between the two experiments. There are indications of age-specific QTL effects on growth. For body weight traits, the genetic variation in the F2 appears to result from many loci with relatively small effects. For tail length at 10 weeks, however, a single QTL on Chromosome (Chr) 1 with a peak LOD score of approximately 33 contributes most of the genetic variation detected, changes the trait value by about 6%, and explains about 20% of the phenotypic variance of the trait.

Animals↗

Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers.

A method is presented to estimate the biometric parameters of a quantitative trait locus linked to a genetic marker when both loci are segregating in the F-2 generation of a cross between two inbred lines. The method, which assumes underlying normal distributions, is a combination of maximum likelihood and moments methods and uses the statistics of the genetic marker genotype samples for the quantitative trait to estimate the recombination frequency between the two loci and the means and variances of the genotypes of the quantitative trait locus. With this method, the genetic parameters of a locus affecting plant height linked to an electrophoretic marker for esterase were accurately estimated from a sample of 1596 F-2 progeny of a cross between two species of Lycopersicon (tomato). Linkage distance between the two loci was 38 map units and the effect of the quantitative trait locus was 1.6 phenotypic standard deviation units. Accurate estimates of the genetic parameters and linkage distance for populations of 2000 individuals simulated with a segregating codominant locus with an effect of 1.63 standard deviations linked to a genetic marker with .2 recombination were also derived by this method. The method is not effective in distinguishing between complete and partial linkage in samples of only 500 individuals or for quantitative loci with effects less than a phenotypic standard deviation. The method is more effective for codominant than for dominant loci.

Algorithms↗

A primary screen of the bovine genome for quantitative trait loci affecting carcass and growth traits.

A primary genomic screen for quantitative trait loci (QTL) affecting carcass and growth traits was performed by genotyping 238 microsatellite markers on 185 out of 300 total progeny from a Bos indicus x Bos taurus sire mated to Bos taurus cows. The following traits were analyzed for QTL effects: birth weight (BWT), weaning weight (WW), yearling weight (YW), hot carcass weight (HCW), dressing percentage (DP), fat thickness (FT), marbling score (MAR), longissimus muscle area (LMA), rib bone (RibB), rib fat (RibF), and rib muscle (RibM), and the predicted whole carcass traits, retail product yield (RPYD), fat trim yield (FATYD), bone yield (BOYD), retail product weight (RPWT), fat weight (FATWT), and bone weight (BOWT). Data were analyzed by generating an F-statistic profile computed at 1-cM intervals for each chromosome by the regression of phenotype on the conditional probability of receiving the Brahman allele from the sire. There was compelling evidence for a QTL allele of Brahman origin affecting an increase in RibB and a decrease in DP on chromosome 5 (BTA5). Putative QTL at or just below the threshold for genome-wide significance were as follows: an increase in RPYD and component traits on BTA2 and BTA13, an increase in LMA on BTA14, and an increase in BWT on BTA1. Results provided represent a portion of our efforts to identify and characterize QTL affecting carcass and growth traits.

Animals↗

Haplotype-based quantitative trait mapping using a clustering algorithm.

BACKGROUND: With the availability of large-scale, high-density single-nucleotide polymorphism (SNP) markers, substantial effort has been made in identifying disease-causing genes using linkage disequilibrium (LD) mapping by haplotype analysis of unrelated individuals. In addition to complex diseases, many continuously distributed quantitative traits are of primary clinical and health significance. However the development of association mapping methods using unrelated individuals for quantitative traits has received relatively less attention. RESULTS: We recently developed an association mapping method for complex diseases by mining the sharing of haplotype segments (i.e., phased genotype pairs) in affected individuals that are rarely present in normal individuals. In this paper, we extend our previous work to address the problem of quantitative trait mapping from unrelated individuals. The method is non-parametric in nature, and statistical significance can be obtained by a permutation test. It can also be incorporated into the one-way ANCOVA (analysis of covariance) framework so that other factors and covariates can be easily incorporated. The effectiveness of the approach is demonstrated by extensive experimental studies using both simulated and real data sets. The results show that our haplotype-based approach is more robust than two statistical methods based on single markers: a single SNP association test (SSA) and the Mann-Whitney U-test (MWU). The algorithm has been incorporated into our existing software package called HapMiner, which is available from our website at http://www.eecs.case.edu/~jxl175/HapMiner.html. CONCLUSION: For QTL (quantitative trait loci) fine mapping, to identify QTNs (quantitative trait nucleotides) with realistic effects (the contribution of each QTN less than 10% of total variance of the trait), large samples sizes (>or= 500) are needed for all the methods. The overall performance of HapMiner is better than that of the other two methods. Its effectiveness further depends on other factors such as recombination rates and the density of typed SNPs. Haplotype-based methods might provide higher power than methods based on a single SNP when using tag SNPs selected from a small number of samples or some other sources (such as HapMap data). Rank-based statistics usually have much lower power, as shown in our study.

Algorithms↗

Effects of Phenotyping Environment on Identification of Quantitative Trait Loci for Rice Root Morphology under Anaerobic Conditions.

In the rainfed lowlands, rice (Oryza sativa L.) develops roots under anaerobic soil conditions with ponded water, prior to exposure to aerobic soil conditions and water stress. Constitutive root system development in anaerobic soil conditions has been reported to have a positive effect on subsequent expression of adaptive root traits and water extraction during water stress. We examined effects of phenotyping environment on identification of quantitative trait loci (QTLs) for constitutive root morphology traits using 220 doubled-haploid lines (DHLs) from the cross of 'CT9993-5-10-1-M' (CT9993; japonica, upland adapted) x 'IR62266-42-6-2' (IR62266; indica, lowland adapted) in four greenhouse experiments. Broad sense heritability (h(2)) was 75, 60, and 64% on average for shoot biomass, deep root morphology, and root thickness traits, respectively. Quantitative trait loci analysis identified 18 genomic regions associated with deep root morphology traits, but only three were identified consistently across experiments. Three out of a total of eight QTLs for root thickness traits were found in more than one experiment. The maximum genetic effects caused by a single QTL were increments of 0.05 g of deep root mass below a 30-cm soil depth, 0.9% of deep root ratio, 1.6 cm of rooting depth, and 0.09 cm of root thickness, with phenotypic variation explained by a single QTL ranging from 6.8 to 51.8%. The results demonstrate the importance of phenotyping environment and suggest prospects for selection of QTLs for deep root morphology, root thickness, and vigorous seedling growth under anaerobic conditions to improve the constitutive root system of rainfed lowland rice. There was some consistency in QTL regions identified, despite the presence of QTL x environment interactions.

Journal Article↗