A multi-marker model for detecting chromosomal segments displaying QTL activity

Fine mapping by composite genome-wide association analysis

Genome-wide association (GWA) studies play a key role in current genetics research, unravelling genomic regions linked to phenotypic traits of interest in multiple species. Nevertheless, the extent of linkage disequilibrium (LD) may provide confounding results when significant genetic markers span along several contiguous cM. In this study, we have adapted the composite interval mapping approach to the GWA framework (composite GWA), in order to evaluate the impact of including competing (possibly linked) genetic markers when testing for the additive allelic effect inherent to a given genetic marker. We tested model performance on simulated data sets under different scenarios (i.e., qualitative trait loci effects, LD between genetic markers and width of the genomic region involved in the analysis). Our results showed that the genomic region had a small impact on the number of competing single nucleotide polymorphisms (SNPs) as well as on the precision of the composite GWA analysis. A similar conclusion was derived from the preferable range of LD between the tested SNP and competing SNPs, although moderate-to-high LD seemed to attenuate the loss of statistical power. The composite GWA improved specificity and reduced the number of significant genetic markers. The composite GWA model contributes a novel point of view for GWA analyses where testing circumscribed to the genomic region flanking each SNP (delimited by the nearest competing SNPs) and conditioning on linked markers increases the precision to locate causal mutations, but possibly at the expense of power.

Block network mapping approach to quantitative trait locus analysis

Background

Advances in experimental biology have enabled the collection of enormous troves of data on genomic variation in living organisms. The interpretation of this data to extract actionable information is one of the keys to developing novel therapeutic strategies to treat complex diseases. Network organization of biological data overcomes measurement noise in several biological contexts. Does a network approach, combining information about the linear organization of genomic markers with correlative information on these markers in a Bayesian formulation, lead to an analytic method with higher power for detecting quantitative trait loci?

Results

Block Network Mapping, combining Similarity Network Fusion (Wang et al., NM 11:333–337, 2014) with a Bayesian locus likelihood evaluation, leads to large improvements in area under the receiver operating characteristic and power over interval mapping with expectation maximization. The method has a monotonically decreasing false discovery rate as a function of effect size, unlike interval mapping.

Conclusions

Block Network Mapping provides an alternative data-driven approach to mapping quantitative trait loci that leverages correlations in the sampled genotypes. The evaluation methodology can be combined with existing approaches such as Interval Mapping. Python scripts are available at http://lbm.niddk.nih.gov/vipulp/. Genotype data is available at http://churchill-lab.jax.org/website/GattiDOQTL.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1351-8) contains supplementary material, which is available to authorized users.

A novel generalized ridge regression method for quantitative genetics

As the molecular marker density grows, there is a strong need in both genome-wide association studies and genomic selection to fit models with a large number of parameters. Here we present a computationally efficient generalized ridge regression (RR) algorithm for situations in which the number of parameters largely exceeds the number of observations. The computationally demanding parts of the method depend mainly on the number of observations and not the number of parameters. The algorithm was implemented in the R package bigRR based on the previously developed package hglm. Using such an approach, a heteroscedastic effects model (HEM) was also developed, implemented, and tested. The efficiency for different data sizes were evaluated via simulation. The method was tested for a bacteria-hypersensitive trait in a publicly available Arabidopsis data set including 84 inbred lines and 216,130 SNPs. The computation of all the SNP effects required <10 sec using a single 2.7-GHz core. The advantage in run time makes permutation test feasible for such a whole-genome model, so that a genome-wide significance threshold can be obtained. HEM was found to be more robust than ordinary RR (a.k.a. SNP-best linear unbiased prediction) in terms of QTL mapping, because SNP-specific shrinkage was applied instead of a common shrinkage. The proposed algorithm was also assessed for genomic evaluation and was shown to give better predictions than ordinary RR.

Genetic and nongenetic bases for the L-shaped distribution of quantitative trait loci effects

The L-shaped distribution of estimated QTL effects (R(2)) has long been reported. We recently showed that a metabolic mechanism could account for this phenomenon. But other nonexclusive genetic or nongenetic causes may contribute to generate such a distribution. Using analysis and simulations of an additive genetic model, we show that linkage disequilibrium between QTL, low heritability, and small population size may also be involved, regardless of the gene effect distribution. In addition, a comparison of the additive and metabolic genetic models revealed that estimates of the QTL effects for traits proportional to metabolic flux are far less robust than for additive traits. However, in both models the highest R(2)'s repeatedly correspond to the same set of QTL.

Quantitative trait loci mapping in F(2) crosses between outbred lines

We develop a mixed-model approach for QTL analysis in crosses between outbred lines that allows for QTL segregation within lines as well as for differences in mean QTL effects between lines. We also propose a method called "segment mapping" that is based in partitioning the genome in a series of segments. The expected change in mean according to percentage of breed origin, together with the genetic variance associated with each segment, is estimated using maximum likelihood. The method also allows the estimation of differences in additive variances between the parental lines. Completely fixed random and mixed models together with segment mapping are compared via simulation. The segment mapping and mixed-model behaviors are similar to those of classical methods, either the fixed or random models, under simple genetic models (a single QTL with alternative alleles fixed in each line), whereas they provide less biased estimates and have higher power than fixed or random models in more complex situations, i.e., when the QTL are segregating within the parental lines. The segment mapping approach is particularly useful to determining which chromosome regions are likely to contain QTL when these are linked.

A nonparametric bootstrap method for testing close linkage vs. pleiotropy of coincident quantitative trait loci

A novel method using the nonparametric bootstrap is proposed for testing whether a quantitative trait locus (QTL) at one chromosomal position could explain effects on two separate traits. If the single-QTL hypothesis is accepted, pleiotropy could explain the effect on two traits. If it is rejected, then the effects on two traits are due to linked QTLs. The method can be used in conjunction with several QTL mapping methods as long as they provide a straightforward estimate of the number of QTLs detectable from the data set. A selection step was introduced in the bootstrap procedure to reduce the conservativeness of the test of close linkage vs. pleiotropy, so that the erroneous rejection of the null hypothesis of pleiotropy only happens at a frequency equal to the nominal type I error risk specified by the user. The approach was assessed using computer simulations and proved to be relatively unbiased and robust over the range of genetic situations tested. An example of its application on a real data set from a saline stress experiment performed on a recombinant population of wheat (Triticum aestivum L. ) doubled haploid lines is also provided.

Empirical nonparametric bootstrap strategies in quantitative trait loci mapping: conditioning on the genetic model

Several nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

Estimation of the contribution of quantitative trait loci (QTL) to the variance of a quantitative trait by means of genetic markers

The estimation of the contribution of an individual quantitative trait locus (QTL) to the variance of a quantitative trait is considered in the framework of an analysis of variance (ANOVA). ANOVA mean squares expectations which are appropriate to the specific case of QTL mapping experiments are derived. These expectations allow the specificities associated with the limited number of genotypes at a given locus to be taken into account. Discrepancies with classical expectations are particularly important for two-class experiments (backcross, recombinant inbred lines, doubled haploid populations) and F2 populations. The result allows us firstly to reconsider the power of experiments (i.e. the probability of detecting a QTL with a given contribution to the variance of the trait). It illustrates that the use of classical formulae for mean squares expectations leads to a strong underestimation of the power of the experiments. Secondly, from the observed mean squares it is possible to estimate directly the variance associated with a locus and the fraction of the total variance associated to this locus (r l (2) ). When compared to other methods, the values estimated using this method are unbiased. Considering unbiased estimators increases in importance when (1) the experimental size is limited; (2) the number of genotypes at the locus of interest is large; and (3) the fraction of the variation associated with this locus is small. Finally, specific mean squares expectations allows us to propose a simple analytical method by which to estimate the confidence interval of r l (2) . This point is particularly important since results indicate that 95% confidence intervals for r l (2) can be rather wide:2-23% for a 10% estimate and 8-34% for a 20% estimate if 100 individuals are considered.

Quantitative genetic dissection of complex traits in a QTL-mapping pedigree

This paper summarizes and modifies quantitative genetic analyses on a pedigree used to map genetic factors (i.e., QTLs) underlying a complex trait. The total genetic variance can be exactly estimated based on the F2 family derived from two homozygous parents for alternative alleles at all QTLs of interest. The parents, F1 hybrids, and two backcrosses are combined to each parent, and the total number of QTLs and the number of dominant QTLs are estimated under the assumptions of gene association with the two parents, equal gene effect, no linkage, and no epistasis among QTLs. Further relaxation for each of the assumptions are made in detail. The biometric estimator for the QTL number and action mode averaged over the entire genome could provide some basic and complementary information to QTL mapping designed to detect the effect and location of specific genetic factors.

Molecular dissection of quantitative traits: progress and prospects

QTL mapping is an increasingly useful approach to the study and manipulation of complex traits important in agriculture, evolution, and medicine. The molecular dissection of quantitative phenotypes, supplementing the principles of classical quantitative genetics, is accelerating progress in the manipulation of plant and animal genomes. A growing appreciation of the similarities among different organisms and the usefulness of comparative genetic information is making genome analysis more efficient, and providing new opportunities for using model systems to overcome the limitations of less-favorable systems. The expanding repertoire of techniques and information available for studying heredity is removing obstacles to the cloning of QTLs. Although QTL mapping alone is limited to a resolution of 0.1%-1.0% of a genome, use of QTL mapping in conjunction with a search for mapped candidate genes, with emerging technologies for isolation of genes expressed under conditions likely to account for the quantitative phenotype, and with ever more efficient megabase DNA manipulation and characterization bodes well for the prospect of isolating the genetic determinants of QTLs in the foreseeable future. In the words of Thoday (1961), "An extensive attack on quantitative genetics made from this point of view as well as the biometric approach should be a great help in answering questions concerning the nature of polygenes...."

A nonparametric approach for mapping quantitative trait loci

Genetic mapping of quantitative trait loci (QTLs) is performed typically by using a parametric approach, based on the assumption that the phenotype follows a normal distribution. Many traits of interest, however, are not normally distributed. In this paper, we present a nonparametric approach to QTL mapping applicable to any phenotypic distribution. The method is based on a statistic ZW, which generalizes the nonparametric Wilcoxon rank-sum test to the situation of whole-genome search by interval mapping. We determine the appropriate significance level for the statistic ZW, by showing that its asymptotic null distribution follows an Ornstein-Uhlenbeck process. These results provide a robust, distribution-free method for mapping QTLs.