Multiple interval mapping for quantitative trait loci.

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Significance thresholds for quantitative trait locus mapping under selective genotyping

In the case of selective genotyping, the usual permutation test to establish statistical significance for quantitative trait locus (QTL) mapping can give inappropriate significance thresholds, especially when the phenotype distribution is skewed. A stratified permutation test should be used, with phenotypes shuffled separately within the genotyped and ungenotyped individuals.     

Multiple-interval mapping for quantitative trait loci controlling endosperm traits

Endosperm traits are trisomic inheritant and are of great economic importance because they are usually directly related to grain quality. Mapping for quantitative trait loci (QTL) underlying endosperm traits can provide an efficient way to genetically improve grain quality. As the traditional QTL mapping methods (diploid methods) are usually designed for traits under diploid control, they are not the ideal approaches to map endosperm traits because they ignore the triploid nature of endosperm. In this article, a statistical method considering the triploid nature of endosperm (triploid method) is developed on the basis of multiple-interval mapping (MIM) to map for the underlying QTL. The proposed triploid MIM method is derived to broadly use the marker information either from only the maternal plants or from both the maternal plants and their embryos in the backcross and F2 populations for mapping endosperm traits. Due to the use of multiple intervals simultaneously to take multiple QTL into account, the triploid MIM method can provide better detection power and estimation precision, and as shown in this article it is capable of analyzing and searching for epistatic QTL directly as compared to the traditional diploid methods and current triploid methods using only one (or two) interval(s). Several important issues in endosperm trait mapping, such as the relation and differences between the diploid and triploid methods, variance components of genetic variation, and the problems if effects are present and ignored, are also addressed. Simulations are performed to further explore these issues, to investigate the relative efficiency of different experimental designs, and to evaluate the performance of the proposed and current methods in mapping endosperm traits. The MIM-based triploid method can provide a powerful tool to estimate the genetic architecture of endosperm traits and to assist the marker-assisted selection for the improvement of grain quality in crop science. The triploid MIM FORTRAN program for mapping endosperm traits is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Mapping quantitative trait loci using the experimental designs of recombinant inbred populations

In the data collection of the QTL experiments using recombinant inbred (RI) populations, when individuals are genotyped for markers in a population, the trait values (phenotypes) can be obtained from the genotyped individuals (from the same population) or from some progeny of the genotyped individuals (from the different populations). Let Fu be the genotyped population and Fv (v>or=u) be the phenotyped population. The experimental designs that both marker genotypes and phenotypes are recorded on the same populations can be denoted as (Fu/Fv, u=v) designs and that genotypes and phenotypes are obtained from the different populations can be denoted as (Fu/Fv, v>u) designs. Although most of the QTL mapping experiments have been conducted on the backcross and F2(F2/F2) designs, the other (Fu/Fv, v>or=u) designs are also very popular. The great benefits of using the other (Fu/Fv, v>or=u) designs in QTL mapping include reducing cost and environmental variance by phenotyping several progeny for the genotyped individuals and taking advantages of the changes in population structures of other RI populations. Current QTL mapping methods including those for the (Fu/Fv, u=v) designs, mostly for the backcross or F2/F2 design, and for the F2/F3 design based on a one-QTL model are inadequate for the investigation of the mapping properties in the (Fu/Fv, uor=u) designs. In addition, the QTL mapping properties of the proposed and approximate methods in different designs are discussed. Simulations were performed to evaluate the performance of the proposed and approximate methods. The proposed method is proven to be able to correct the problems of the approximate and current methods for improving the resolution of genetic architecture of quantitative traits and can serve as an effective tool to explore the QTL mapping study in the system of RI populations.     

A Novel Method for Identification and Quantification of Consistently Differentially Methylated Regions

Advances in biotechnology have resulted in large-scale studies of DNA methylation. A differentially methylated region (DMR) is a genomic region with multiple adjacent CpG sites that exhibit different methylation statuses among multiple samples. Many so-called “supervised” methods have been established to identify DMRs between two or more comparison groups. Methods for the identification of DMRs without reference to phenotypic information are, however, less well studied. An alternative “unsupervised” approach was proposed, in which DMRs in studied samples were identified with consideration of nature dependence structure of methylation measurements between neighboring probes from tiling arrays. Through simulation study, we investigated effects of dependencies between neighboring probes on determining DMRs where a lot of spurious signals would be produced if the methylation data were analyzed independently of the probe. In contrast, our newly proposed method could successfully correct for this effect with a well-controlled false positive rate and a comparable sensitivity. By applying to two real datasets, we demonstrated that our method could provide a global picture of methylation variation in studied samples. R source codes to implement the proposed method were freely available at http://www.csjfann.ibms.sinica.edu.tw/eag/programlist/ICDMR/ICDMR.html.     

Effectiveness of selective genotyping for detection of quantitative trait loci: an analysis of grain and malt quality traits in three barley populations.

Marker genotype data and grain and malt quality phenotype data from three barley (Hordeum vulgare L.) mapping populations were used to investigate the feasibility of selective genotyping for detection of quantitative trait loci (QTLs). With selective genotyping, only individuals with high and low phenotypic values for the trait of interest are genotyped. Here, genotyping of 10 to 70% of each population (i.e., 5 to 35% in each tail of the phenotypic distribution) was considered. Genomic positions detected by selective genotyping were compared to QTL position estimates from interval mapping analysis using marker genotype data from the entire population. Selective genotyping reliably detected almost all of the mapped QTLs, often with only 10% of the population genotyped. Selective genotyping also detected spurious QTLs in regions of the genome where no significant QTL had been mapped. Even with additional genotyping to verify putative QTLs, the total genotyping effort for detection of QTLs for a single trait by selective genotyping was usually less than 30% of that required for conventional interval mapping. Simultaneous investigation of two or more traits by selective genotyping would require additional genotyping effort, but could still be worthwhile.     

Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation

Background

In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation.

Methods

For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers.

Results

The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers.

Conclusions

The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritability.     

Comparison of methods for analysis of selective genotyping survival data

Survival traits and selective genotyping datasets are typically not normally distributed, thus common models used to identify QTL may not be statistically appropriate for their analysis. The objective of the present study was to compare models for identification of QTL associated with survival traits, in particular when combined with selective genotyping. Data were simulated to model the survival distribution of a population of chickens challenged with Marek disease virus. Cox proportional hazards (CPH), linear regression (LR), and Weibull models were compared for their appropriateness to analyze the data, ability to identify associations of marker alleles with survival, and estimation of effects when all individuals were genotyped (full genotyping) and when selective genotyping was used. Little difference in power was found between the CPH and the LR model for low censoring cases for both full and selective genotyping. The simulated data were not transformed to follow a Weibull distribution and, as a result, the Weibull model generally resulted in less power than the other two models and overestimated effects. Effect estimates from LR and CPH were unbiased when all individuals were genotyped, but overestimated when selective genotyping was used. Thus, LR is preferred for analyzing survival data when the amount of censoring is low because of ease of implementation and interpretation. Including phenotypic data of non-genotyped individuals in selective genotyping analysis increased power, but resulted in LR having an inflated false positive rate, and therefore the CPH model is preferred for this scenario, although transformation of the data may also make the Weibull model appropriate for this case. The results from the research presented herein are directly applicable to interval mapping analyses.     

Power calculations for selective genotyping in QTL mapping in backcross mice

Selective genotyping concerns the genotyping of a portion of individuals chosen on the basis of their phenotypic values. Often individuals are selected for genotyping from the high and low extremes of the phenotypic distribution. This procedure yields savings in cost and time by decreasing the total number of individuals genotyped. Previous work by Darvasi et al. (1993) has shown that the power to detect a QTL by genotyping 40-50 % of a population is roughly equivalent to genotyping the entire sample. However, these power studies have not accounted for different strategies of analysing the data when phenotypes of individuals in the middle are excluded, nor have they investigated the genome-wide type I error rate under these different strategies or different selection percentages. Further, these simulation studies have not considered markers over the entire genome. In this paper, we present simulation studies of power for the maximum likelihood approach to QTL mapping by Lander & Botstein (1989) in the context of selective genotyping. We calculate the power of selectively genotyping the individuals from the middle of the phenotypic distribution when performing QTL mapping over the whole mouse genome.     

Simultaneous estimation of multiple quantitative trait loci and growth curve parameters through hierarchical Bayesian modeling

A novel hierarchical quantitative trait locus (QTL) mapping method using a polynomial growth function and a multiple-QTL model (with no dependence in time) in a multitrait framework is presented. The method considers a population-based sample where individuals have been phenotyped (over time) with respect to some dynamic trait and genotyped at a given set of loci. A specific feature of the proposed approach is that, instead of an average functional curve, each individual has its own functional curve. Moreover, each QTL can modify the dynamic characteristics of the trait value of an individual through its influence on one or more growth curve parameters. Apparent advantages of the approach include: (1) assumption of time-independent QTL and environmental effects, (2) alleviating the necessity for an autoregressive covariance structure for residuals and (3) the flexibility to use variable selection methods. As a by-product of the method, heritabilities and genetic correlations can also be estimated for individual growth curve parameters, which are considered as latent traits. For selecting trait-associated loci in the model, we use a modified version of the well-known Bayesian adaptive shrinkage technique. We illustrate our approach by analysing a sub sample of 500 individuals from the simulated QTLMAS 2009 data set, as well as simulation replicates and a real Scots pine (Pinus sylvestris) data set, using temporal measurements of height as dynamic trait of interest.     

OSIRISv1.2: A named entity recognition system for sequence variants of genes in biomedical literature

Background

The hierarchical clustering tree (HCT) with a dendrogram [1] and the singular value decomposition (SVD) with a dimension-reduced representative map [2] are popular methods for two-way sorting the gene-by-array matrix map employed in gene expression profiling. While HCT dendrograms tend to optimize local coherent clustering patterns, SVD leading eigenvectors usually identify better global grouping and transitional structures.

Results

This study proposes a flipping mechanism for a conventional agglomerative HCT using a rank-two ellipse (R2E, an improved SVD algorithm for sorting purpose) seriation by Chen [3] as an external reference. While HCTs always produce permutations with good local behaviour, the rank-two ellipse seriation gives the best global grouping patterns and smooth transitional trends. The resulting algorithm automatically integrates the desirable properties of each method so that users have access to a clustering and visualization environment for gene expression profiles that preserves coherent local clusters and identifies global grouping trends.

Conclusion

We demonstrate, through four examples, that the proposed method not only possesses better numerical and statistical properties, it also provides more meaningful biomedical insights than other sorting algorithms. We suggest that sorted proximity matrices for genes and arrays, in addition to the gene-by-array expression matrix, can greatly aid in the search for comprehensive understanding of gene expression structures. Software for the proposed methods can be obtained at http://gap.stat.sinica.edu.tw/Software/GAP.     

QTL mapping in outbred half-sib families using Bayesian model selection

In this article, we propose a model selection method, the Bayesian composite model space approach, to map quantitative trait loci (QTL) in a half-sib population for continuous and binary traits. In our method, the identity-by-descent-based variance component model is used. To demonstrate the performance of this model, the method was applied to map QTL underlying production traits on BTA6 in a Chinese half-sib dairy cattle population. A total of four QTLs were detected, whereas only one QTL was identified using the traditional least square (LS) method. We also conducted two simulation experiments to validate the efficiency of our method. The results suggest that the proposed method based on a multiple-QTL model is efficient in mapping multiple QTL for an outbred half-sib population and is more powerful than the LS method based on a single-QTL model.     

Quantitative trait locus study design from an information perspective

We examine the efficiency of different genotyping and phenotyping strategies in inbred line crosses from an information perspective. This provides a mathematical framework for the statistical aspects of QTL experimental design, while guiding our intuition. Our central result is a simple formula that quantifies the fraction of missing information of any genotyping strategy in a backcross. It includes the special case of selectively genotyping only the phenotypic extreme individuals. The formula is a function of the square of the phenotype and the uncertainty in our knowledge of the genotypes at a locus. This result is used to answer a variety of questions. First, we examine the cost-information trade-off varying the density of markers and the proportion of extreme phenotypic individuals genotyped. Then we evaluate the information content of selective phenotyping designs and the impact of measurement error in phenotyping. A simple formula quantifies the information content of any combined phenotyping and genotyping design. We extend our results to cover multigenotype crosses, such as the F(2) intercross, and multiple QTL models. We find that when the QTL effect is small, any contrast in a multigenotype cross benefits from selective genotyping in the same manner as in a backcross. The benefit remains in the presence of a second unlinked QTL with small effect (explaining <20% of the variance), but diminishes if the second QTL has a large effect. Software for performing power calculations for backcross and F(2) intercross incorporating selective genotyping and marker spacing is available from http://www.biostat.ucsf.edu/sen.     

Identifying RNA-binding residues based on evolutionary conserved structural and energetic features

Increasing numbers of protein structures are solved each year, but many of these structures belong to proteins whose sequences are homologous to sequences in the Protein Data Bank. Nevertheless, the structures of homologous proteins belonging to the same family contain useful information because functionally important residues are expected to preserve physico-chemical, structural and energetic features. This information forms the basis of our method, which detects RNA-binding residues of a given RNA-binding protein as those residues that preserve physico-chemical, structural and energetic features in its homologs. Tests on 81 RNA-bound and 35 RNA-free protein structures showed that our method yields a higher fraction of true RNA-binding residues (higher precision) than two structure-based and two sequence-based machine-learning methods. Because the method requires no training data set and has no parameters, its precision does not degrade when applied to ‘novel’ protein sequences unlike methods that are parameterized for a given training data set. It was used to predict the ‘unknown’ RNA-binding residues in the C-terminal RNA-binding domain of human CPEB3. The two predicted residues, F430 and F474, were experimentally verified to bind RNA, in particular F430, whose mutation to alanine or asparagine nearly abolished RNA binding. The method has been implemented in a webserver called DR_bind1, which is freely available with no login requirement at http://drbind.limlab.ibms.sinica.edu.tw.     

Combining two Meishan F2 crosses improves the detection of QTL on pig chromosomes 2, 4 and 6

Background

In pig, a number of experiments have been set up to identify QTL and a multitude of chromosomal regions harbouring genes influencing traits of interest have been identified. However, the mapping resolution remains limited in most cases and the detected QTL are rather inaccurately located. Mapping accuracy can be improved by increasing the number of phenotyped and genotyped individuals and/or the number of informative markers. An alternative approach to overcome the limited power of individual studies is to combine data from two or more independent designs.

Methods

In the present study we report a combined analysis of two independent design (a French and a Dutch F2 experimental designs), with 2000 F2 individuals. The purpose was to further map QTL for growth and fatness on pig chromosomes 2, 4 and 6. Using QTL-map software, uni- and multiple-QTL detection analyses were applied separately on the two pedigrees and then on the combination of the two pedigrees.

Results

Joint analyses of the combined pedigree provided (1) greater significance of shared QTL, (2) exclusion of false suggestive QTL and (3) greater mapping precision for shared QTL.

Conclusions

Combining two Meishan x European breeds F2 pedigrees improved the mapping of QTL compared to analysing pedigrees separately. Our work was facilitated by the access to raw phenotypic data and DNA of animals from both pedigrees and the combination of the two designs with the addition of new markers allowed us to fine map QTL without phenotyping additional animals.     

Binary Trait Mapping in Experimental Crosses With Selective Genotyping

Selective genotyping is an efficient strategy for mapping quantitative trait loci. For binary traits, where there are only two distinct phenotypic values (e.g., affected/unaffected or present/absent), one may consider selective genotyping of affected individuals, while genotyping none or only some of the unaffecteds. If selective genotyping of this sort is employed, the usual method for binary trait mapping, which considers phenotypes conditional on genotypes, cannot be used. We present an alternative approach, instead considering genotypes conditional on phenotypes, and compare this to the more standard method of analysis, both analytically and by example. For studies of rare binary phenotypes, we recommend performing an initial genome scan with all affected individuals and an equal number of unaffecteds, followed by genotyping the full cross in genomic regions of interest to confirm results from the initial screen.WE consider the problem of mapping genetic loci contributing to a binary trait in an experimental cross with selective genotyping. There are two clear approaches for linkage analysis with a binary trait. Typically, we compare the proportion of affected individuals across genotype groups (Xu and Atchley 1996). Alternatively, we can compare genotype frequencies between affected and unaffected individuals, similar to Henshall and Goddard (1999). Beyond these two basic approaches, binary trait mapping has seen fundamental advances in regression models (McIntyre et al. 2001; Deng et al. 2006), extensions to multiple-QTL mapping (Coffman et al. 2005; Chen and Liu 2009), and the development of Bayesian algorithms (Yi and Xu 2000; Huang et al. 2007). However, the original data structure and approach have remained intact. Existing methods for binary trait mapping largely require the availability of genotype and phenotype data for a representative sample of both affected and unaffected individuals, and we have not yet seen a well-developed framework for binary trait mapping in the presence of selective genotyping.It is not uncommon to see genotype data on affected individuals only, in which case the above methods cannot be used. Instead, we can compare observed genotype frequencies to the expected segregation ratios given the cross type, in a test for segregation distortion (see Faris et al. 1998; Lambrides et al. 2004). For example, the expected segregation proportions for an intercross are 1:2:1. The observed genotypes can then be described by a multinomial model, and statistically significant deviation from the expected segregation ratios among the genotyped affected individuals would suggest genotype–phenotype association. Gene mapping approaches that model genotypes rather than phenotypes have been developed extensively in the analysis of affected human relative pairs (see, for example, Risch 1990; Holmans 1993; Hauser and Boehnke 1998). In the analysis of experimental crosses, however, this type of approach has been developed primarily for the identification of monogenic mutants (Moran et al. 2006).Once all affected individuals are genotyped, an investigator may go on to genotype unaffected individuals. With this genotyping strategy in mind, we present several potential methods of analysis that might be applied in this context. First, we consider a standard analysis of the genotyped individuals, with disease proportions compared across genotype groups (Xu and Atchley 1996). Having omitted ungenotyped individuals, this method of analysis appears invalid because the estimated disease proportions are biased upward, reflecting an overrepresentation of affecteds in the set of genotyped individuals under consideration. As an alternative, we develop a reverse approach with genotype frequencies compared across phenotype groups. Because selective genotyping does provide a representative sample of genotypes for each phenotype group, this reverse approach does not face the bias in parameter estimation seen with the standard approach. We further extend the reverse approach to incorporate a segregation assumption, as is necessary for an affecteds only analysis. Finally, we present a full-likelihood analysis accounting for selective genotyping, similar to that suggested by Lander and Botstein (1989) for quantitative traits. We develop the full-likelihood approach both with and without incorporating an assumption on the genotype segregation proportions.Having put forth each of these methods, we derive analytic relationships among them. These relationships provide important insight regarding application of the presented methods under selective genotyping. Most notably, we find that making a segregation assumption can lead to spurious evidence of a QTL, but is necessary to treat the case of affecteds only genotyping. We demonstrate properties of the methods in an analysis of recovery from infection by Listeria monocytogenes in intercross mice and further compare power of the methods through computer simulations. Finally, we synthesize our analytical and simulation results to offer more general suggestions for the analysis of binary trait data with selective genotyping.     

RADtyping: An Integrated Package for Accurate De Novo Codominant and Dominant RAD Genotyping in Mapping Populations

Genetic linkage maps are indispensable tools in genetic, genomic and breeding studies. As one of genotyping-by-sequencing methods, RAD-Seq (restriction-site associated DNA sequencing) has gained particular popularity for construction of high-density linkage maps. Current RAD analytical tools are being predominantly used for typing codominant markers. However, no genotyping algorithm has been developed for dominant markers (resulting from recognition site disruption). Given their abundance in eukaryotic genomes, utilization of dominant markers would greatly diminish the extensive sequencing effort required for large-scale marker development. In this study, we established, for the first time, a novel statistical framework for de novo dominant genotyping in mapping populations. An integrated package called RADtyping was developed by incorporating both de novo codominant and dominant genotyping algorithms. We demonstrated the superb performance of RADtyping in achieving remarkably high genotyping accuracy based on simulated and real mapping datasets. The RADtyping package is freely available at http://www2.ouc.edu.cn/mollusk/ detailen.asp?id=727.     

An Index of Information Content for Genotype Probabilities Derived from Segregation Analysis

A genotype probability index (GPI) is proposed to indicate the information content of genotype probabilities derived from a segregation analysis. Typically, some individuals are genotyped at a marker locus or a quantitative trait locus, and segregation analysis is used to make genotype inferences about ungenotyped relatives. Genotype probabilities for a two-allele autosomal locus are plotted on a triangular surface. The GPI has a value of zero at the point corresponding to Hardy-Weinberg frequencies, and a value of 100% at the vertices of the triangle. Trigonometric functions are used to help calculate intermediate index values. It is proposed that such an index can be useful to help identify which ungenotyped individuals or loci should be genotyped to maximize the benefit/cost of genotyping operations.