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Quantitative trait linkage analysis using Gaussian copulas.

Mapping and identifying variants that influence quantitative traits is an important problem for genetic studies. Traditional QTL mapping relies on a variance-components (VC) approach with the key assumption that the trait values in a family follow a multivariate normal distribution. Violation of this assumption can lead to inflated type I error, reduced power, and biased parameter estimates. To accommodate nonnormally distributed data, we developed and implemented a modified VC method, which we call the "copula VC method," that directly models the nonnormal distribution using Gaussian copulas. The copula VC method allows the analysis of continuous, discrete, and censored trait data, and the standard VC method is a special case when the data are distributed as multivariate normal. Through the use of link functions, the copula VC method can easily incorporate covariates. We use computer simulations to show that the proposed method yields unbiased parameter estimates, correct type I error rates, and improved power for testing linkage with a variety of nonnormal traits as compared with the standard VC and the regression-based methods.

Analysis of Variance↗

Replication of small effect quantitative trait loci for behavioral traits facilitated by estimation of effect size from independent cohorts.

Quantitative trait locus (QTL) mapping is often done in a single segregating population, such as a backcross or an intercross. Both QTL location and effect size are then estimated from the same dataset. This approach results in an over-estimate of effect size for two reasons: (1) LOD scores, which are maximized over numerous point-wise tests, are correlated with estimated effect size and (2) small effect QTLs are often undetected in underpowered experiments, yielding inflated effect sizes for detected QTLs (the Beavis effect). When it is impractical to maintain or generate large population sizes, an alternative is to use two populations, one for initial detection and localization and a second for a locus-matched estimate of effect size, not conditioned on significance. Recombinant inbred (RI) panels are eminently suitable for this approach, as each strain genotype can be sampled repeatedly. We present mapping results from the LXS RI panel for two behavioral phenotypes relating to ethanol response: low-dose ethanol activation and loss of righting following high-dose injection. Both the phenotypes were measured in two or three independent cohorts, which were then used to re-estimate effect size. Many small-effect QTLs replicated using this approach, but in all cases, effect size, in the replicate cohorts, was reduced from the initial estimate, often substantially. Such a reduction will have important consequences for power analyses in which sample sizes are determined for subsequent confirmation studies.

Alcoholism↗

Review of quantitative trait loci identified in the chicken.

Methods for mapping QTL are actively used in the chicken to identify chromosomal regions contributing to variation in traits related to growth, disease resistance, egg production, behavior, and metabolic parameters. However, higher-resolution mapping and better knowledge of the genetic architecture underlying QTL are needed for successful application of this information into breeding programs. Therefore, this paper summarizes and integrates original, primary QTL studies in the chicken to identify basic information on the genetic architecture of quantitative traits in chickens. The results of this review show several instances of consensus of QTL locations for similar traits from independent studies. Furthermore, the consensus of QTL location for different traits and evidence for QTL with parent-of-origin effect, transgressive alleles, epistatic QTL, and QTL x sex interaction in chicken are presented and discussed. This information can be helpful in identifying genes or mutations underlying the QTL and in the application of genomic information in marker-assisted breeding programs.

Animals↗

Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion.

We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-delta criterion, with the parameter delta increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.

Alleles↗

Quantitative trait loci and interaction effects responsible for variation in female postmating mortality in Drosophila simulans and D. sechellia introgression lines.

Mating appears to inflict a cost to Drosophila females, resulting in a reduction of their lifespan shortly after mating. Males from different chromosome extracted lines differ significantly in their detrimental effects on postmating female survival, and seminal fluid proteins produced in the male accessory glands are at least partially responsible for the effect. This suggests that there is a genetic basis underlying the male inflicted effect on female's postmating mortality. However, the genes responsible for this effect remain elusive. Using males from introgression lines between D. simulans and D. sechellia genomes and a quantitative trait locus (QTL) mapping approach, we identified chromosomal regions that affect postmating mortality of females. We found a second chromosome QTL with an effect on average female lifespan after mating and a third chromosome QTL with an effect on postmating female mortality rate. Under the general observation of a faster divergence of sex-related genes among closely related species, it is predicted that genes for reproductive traits other than hybrid sterility will show evidence of epistatic effects when brought into a heterospecific background. We detected a significant epistatic genetic effect on postmating female mortality rate that supports this prediction.

Animals↗

An AFLP-based linkage map of Japanese red pine (Pinus densiflora) using haploid DNA samples of megagametophytes from a single maternal tree.

We have constructed an AFLP-based linkage map of Japanese red pine (Pinus densiflora Siebold et Zucc.) using haploid DNA samples of 96 megagametophytes from a single maternal tree, selection clone Kyungbuk 4. Twenty-eight primer pairs generated a total of 5,780 AFLP fragments. Five hundreds and thirteen fragments were verified as genetic markers with two alleles by their Mendelian segregation. At the linkage criteria LOD 4.0 and maximum recombination fraction 0.25(theta), a total of 152 markers constituted 25 framework maps for 19 major linkage groups. The maps spanned a total length of 2,341 cM with an average framework marker spacing of 18.4 cM. The estimated genome size was 2,662 cM. With an assumption of equal marker density, 82.2% of the estimated genome would be within 10 cM of one of the 230 linked markers, and 68.1% would be within 10 cM of one of the 152 framework markers. We evaluated map completeness in terms of LOD value, marker density, genome length, and map coverage. The resulting map will provide crucial information for future genomic studies of the Japanese red pine, in particular for QTL mapping of economically important breeding target traits.

Base Sequence↗

Integration of the rat recombination and EST maps in the rat genomic sequence and comparative mapping analysis with the mouse genome.

Inbred strains of the laboratory rat are widely used for identifying genetic regions involved in the control of complex quantitative phenotypes of biomedical importance. The draft genomic sequence of the rat now provides essential information for annotating rat quantitative trait locus (QTL) maps. Following the survey of unique rat microsatellite (11,585 including 1648 new markers) and EST (10,067) markers currently available, we have incorporated a selection of 7952 rat EST sequences in an improved version of the integrated linkage-radiation hybrid map of the rat containing 2058 microsatellite markers which provided over 10,000 potential anchor points between rat QTL and the genomic sequence of the rat. A total of 996 genetic positions were resolved (avg. spacing 1.77 cM) in a single large intercross and anchored in the rat genomic sequence (avg. spacing 1.62 Mb). Comparative genome maps between rat and mouse were constructed by successful computational alignment of 6108 mapped rat ESTs in the mouse genome. The integration of rat linkage maps in the draft genomic sequence of the rat and that of other species represents an essential step for translating rat QTL intervals into human chromosomal targets.

Animals↗

Efficient algorithms for quantitative trait loci mapping problems.

Rapid advances in molecular genetics push the need for efficient data analysis. Advanced algorithms are necessary for extracting all possible information from large experimental data sets. We present a general linear algebra framework for quantitative trait loci (QTL) mapping, using both linear regression and maximum likelihood estimation. The formulation simplifies future comparisons between and theoretical analyses of the methods. We show how the common structure of QTL analysis models can be used to improve the kernel algorithms, drastically reducing the computational effort while retaining the original analysis results. We have evaluated our new algorithms on data sets originating from two large F(2) populations of domestic animals. Using an updating approach, we show that 1-3 orders of magnitude reduction in computational demand can be achieved for matrix factorizations. For interval-mapping/composite-interval-mapping settings using a maximum likelihood model, we also show how to use the original EM algorithm instead of the ECM approximation, significantly improving the convergence and further reducing the computational time. The algorithmic improvements makes it feasible to perform analyses which have previously been deemed impractical or even impossible. For example, using the new algorithms, it is reasonable to perform permutation testing using exhaustive search on populations of 200 individuals using an epistatic two-QTL model.

Algorithms↗

Strategy for mapping quantitative trait loci (QTL) by using human metapopulations.

AIM: To present a novel strategy for mapping quantitative trait loci (QTL), using human metapopulations. The strategy is based on the expectation that in geographic clusters of small and distinct human isolates, a combination of founder effect and genetic drift can dramatically increase population frequency of rare QTL variants with large effect. In such cases, the distribution of QT measurements in an (affected) isolate is expected to deviate from that observed in neighboring isolates. METHODS: We tested this hypothesis in 9 villages from a larger Croatian isolate resource, where 7 Mendelian disorders have been previously reported. The values of 10 physiological and biochemical QTs were measured in a random sample of 1001 individuals (100 inhabitants of each of 9 villages and 101 immigrant controls). RESULTS: Significant over- or under- representation of individuals from specific villages in extreme ends of standardized QT measurement distribution was found 10 times more frequently than expected by chance. The large majority of such clusters of individuals with extreme QT values (34/36, 94.4%) originated from the 6 villages with the most pronounced geographic isolation and endogamy. CONCLUSION: Early epidemiological assessment supports the feasibility of the proposed strategy. Clusters of individuals with extreme QT values responsible for over-representation of single villages can usually be linked to a larger pedigree and may be useful for further QTL mapping, using linkage analysis.

Body Height↗

Construction of an integrated map of rose with AFLP, SSR, PK, RGA, RFLP, SCAR and morphological markers.

A high-density genetic map with a number of anchor markers has been created to be used as a tool to dissect genetic variation in rose. Linkage maps for the diploid 94/1 population consisting of 88 individuals were constructed using a total of 520 molecular markers including AFLP, SSR, PK, RGA, RFLP, SCAR and morphological markers. Seven linkage groups, putatively corresponding to the seven haploid rose chromosomes, were identified for each parent, spanning 487 cM and 490 cM, respectively. The average length of 70 cM may cover more than 90% of the rose genome. An integrated map was constructed by incorporating the homologous parental linkage groups, resulting in seven linkage groups with a total length of 545 cM. The present linkage map is currently the most advanced map in rose with regard to marker density, genome coverage and with robust markers, giving good perspectives for QTL mapping and marker-assisted breeding in rose. The SSR markers, together with RFLP markers, provide good anchor points for future map alignment studies in rose and related species. Codominantly scored AFLP markers were helpful in the integration of the parental maps.

Chromosome Mapping↗

Identification of QTLs influencing wood property traits in loblolly pine ( Pinus taeda L.). II. Chemical wood properties.

Chemical wood property traits were analyzed for the presence of quantitative trait loci (QTLs) in a three-generation outbred pedigree of loblolly pine ( Pinus taeda L.). These traits were assayed using pyrolysis molecular beam mass spectrometry and include mass spectrum peak intensities associated with carbohydrates, alpha-cellulose and hemicellulose sugars, and lignin. Models for projection to latent structures (PLS) were used to also estimate the chemical composition of cell walls (i.e., alpha-cellulose, galactan and lignin) from mass spectrum data using multivariate regression. Both earlywood and latewood fractions from the fifth annual ring were analyzed for each trait. An interval mapping approach designed for an outbred pedigree was used to estimate the number of QTLs, the magnitude of QTL effects, and their genomic position. Eight unique QTLs influencing cell wall chemistry were detected from multiple peak intensities and/or PLS estimates using the one- and two-QTL models. Significant differences in chemical contents were observed among the populations from North Carolina vs Oklahoma, and results from QTLxenvironment analyses suggest that QTLs interact with environmental location. QTLs should be verified in larger experiments and in different genetic and environmental backgrounds. QTL mapping will help towards eventually identifying genes having a major effect on chemical wood properties.

Journal Article↗

Investigating the probability of sign inconsistency in the regression coefficients of markers flanking quantitative trait loci.

Estimates of the locations and effects of quantitative trait loci (QTL) can be obtained by regressing phenotype on marker genotype. Under certain basic conditions, the signs of regression coefficients flanking QTL must be the same. There is no guarantee, however, that the signs of the regression coefficient estimates will be the same. We use sign inconsistency to describe the situation in which there is disagreement between the signs of the estimated regression coefficients flanking QTL. The presence of sign inconsistency can undermine the effectiveness of QTL mapping strategies that presume intervals whose markers have regression coefficient estimates of differing sign to be devoid of QTL. This article investigates the likelihood of sign inconsistency under various conditions. We derive an analytic expression for the approximate probability of sign inconsistency in the single-QTL case. We also examine sign inconsistency probabilities when multiple QTL are present through simulation. We have discovered that the probability of sign inconsistency can be unacceptably high, even when the conditions for QTL detection are otherwise quite favorable.

Computer Simulation↗

Mapping of genomic regions (quantitative trait loci) controlling production and quality in industrial cultures of the edible basidiomycete Pleurotus ostreatus.

Industrial production of the edible basidiomycete Pleurotus ostreatus (oyster mushroom) is based on a solid fermentation process in which a limited number of selected strains are used. Optimization of industrial mushroom production depends on improving the culture process and breeding new strains with higher yields and productivities. Traditionally, fungal breeding has been carried out by an empirical trial and error process. In this study, we used a different approach by mapping quantitative trait loci (QTLs) controlling culture production and quality within the framework of the genetic linkage map of P. ostreatus. Ten production traits and four quality traits were studied and mapped. The production QTLs identified explain nearly one-half of the production variation. More interestingly, a single QTL mapping to the highly polymorphic chromosome VII appears to be involved in control of all the productivity traits studied. Quality QTLs appear to be scattered across the genome and to have less effect on the variation of the corresponding traits. Moreover, some of the new hybrid strains constructed in the course of our experiments had production or quality values higher than those of the parents or other commercial strains. This approach opens the possibility of marker-assisted selection and breeding of new industrial strains of this fungus.

Chromosome Mapping↗

Survival analysis of life span quantitative trait loci in Drosophila melanogaster.

We used quantitative trait loci (QTL) mapping to evaluate the age specificity of naturally segregating alleles affecting life span. Estimates of age-specific mortality rates were obtained from observing 51,778 mated males and females from a panel of 144 recombinant inbred lines (RILs). Twenty-five QTL were found, having 80 significant effects on life span and weekly mortality rates. Generation of RILs from heterozygous parents enabled us to contrast effects of QTL alleles with the means of RIL populations. Most of the low-frequency alleles increased mortality, especially at younger ages. Two QTL had negatively correlated effects on mortality at different ages, while the remainder were positively correlated. Chromosomal positions of QTL were roughly concordant with estimates from other mapping populations. Our findings are broadly consistent with a mix of transient deleterious mutations and a few polymorphisms maintained by balancing selection, which together contribute to standing genetic variation in life span.

Alleles↗

Search for pleiotropic QTL on chromosome BTA6 affecting yield traits of milk production.

The primary aim of this study was to investigate whether previous findings of similar quantitative trait loci (QTL) positions for correlated yield traits are due to a pleiotropic QTL. We applied a multitrait variance component based QTL mapping method to a dataset involving five granddaughter families from the German Holstein dairy cattle population. The marker map contained 16 microsatellite markers, distributed across chromosome BTA6. A chromosomewise significance threshold was used, because BTA6 is known to harbor QTL for several milk traits. To evaluate the results from the multivariate, across-family analysis, we also conducted single-family analyses using the least squares method of QTL estimation. The results provided two significant QTL findings at 49 and 64 cM for milk yield in different families and putative QTL at 68 cM for fat yield and at 71 cM for protein yield in another family. The results for fat and protein yield were confirmed by a univariate, across-family variance components analysis. The multivariate analysis of three bivariate trait combinations resulted in a significant pleiotropic QTL finding at 68 cM for fat yield and protein yield, bracketed by markers TGLA37 and FBN13. The estimates of variance contribution due to this QTL were 23% and 25%, respectively.

Analysis of Variance↗

Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework.

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.

Bayes Theorem↗

High resolution of quantitative traits into multiple loci via interval mapping.

A very general method is described for multiple linear regression of a quantitative phenotype on genotype [putative quantitative trait loci (QTLs) and markers] in segregating generations obtained from line crosses. The method exploits two features, (a) the use of additional parental and F1 data, which fixes the joint QTL effects and the environmental error, and (b) the use of markers as cofactors, which reduces the genetic background noise. As a result, a significant increase of QTL detection power is achieved in comparison with conventional QTL mapping. The core of the method is the completion of any missing genotypic (QTL and marker) observations, which is embedded in a general and simple expectation maximization (EM) algorithm to obtain maximum likelihood estimates of the model parameters. The method is described in detail for the analysis of an F2 generation. Because of the generality of the approach, it is easily applicable to other generations, such as backcross progenies and recombinant inbred lines. An example is presented in which multiple QTLs for plant height in tomato are mapped in an F2 progeny, using additional data from the parents and their F1 progeny.

Chromosome Mapping↗

A mechanistic model for genetic machinery of ontogenetic growth.

Two different genetic mechanisms can be proposed to explain variation in growth trajectories. The allelic sensitivity hypothesis states that growth trajectory is controlled by the time-dependent expression of alleles at the deterministic quantitative trait loci (dQTL) formed during embryogenesis. The gene regulation hypothesis states that the differentiation in growth process is due to the opportunistic quantitative trait loci (oQTL) through their mediation with new developmental signals. These two hypotheses of genetic control have been elucidated in the literature. Here, we propose a new statistical model for discerning these two mechanisms in the context of growth trajectories by integrating growth laws within a QTL-mapping framework. This model is developed within the maximum-likelihood context, implemented with a grid approach for estimating the genomic positions of the deterministic and opportunistic QTL and the simplex algorithm for estimating the growth curve parameters of the genotypes at these QTL and the parameters modeling the residual (co)variance matrix. Our model allows for extensive hypothesis tests for the genetic control of growth processes and developmental events by these two types of QTL. The application of this new model to an F(2) progeny in mice leads to the detection of deterministic and opportunistic QTL on chromosome 1 for mouse body mass growth. The estimates of QTL positions and effects from our model are broadly in agreement with those by traditional interval-mapping approaches. The implications of this model for biological and biomedical research are discussed.

Algorithms↗