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

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

Identity-by-descent genomic selection using selective and sparse genotyping

Background

Genomic selection methods require dense and widespread genotyping data, posing a particular challenge if both sexes are subject to intense selection (e.g., aquaculture species). This study focuses on alternative low-cost genomic selection methods (IBD-GS) that use selective genotyping with sparse marker panels to estimate identity-by-descent relationships through linkage analysis. Our aim was to evaluate the potential of these methods in selection programs for continuous traits measured on sibs of selection candidates in a typical aquaculture breeding population.

Methods

Phenotypic and genomic data were generated by stochastic simulation, assuming low to moderate heritabilities (0.10 to 0.30) for a Gaussian trait measured on sibs of the selection candidates in a typical aquaculture breeding population that consisted of 100 families (100 training animals and 20 selection candidates per family). Low-density marker genotype data (~ 40 markers per Morgan) were used to trace genomic identity-by-descent relationships. Genotyping was restricted to selection candidates from 30 phenotypically top-ranking families and varying fractions of their phenotypically extreme training sibs. All phenotypes were included in the genetic analyses. Classical pedigree-based and IBD-GS models were compared based on realized genetic gain over one generation of selection.

Results

Genetic gain increased substantially (13 to 32%) with IBD-GS compared to classical selection and was greatest with higher heritability. Most of the extra gain from IBD-GS was obtained already by genotyping the 5% phenotypically most extreme sibs within the pre-selected families. Additional genotyping further increased genetic gains, but these were small when going from genotyping 20% of the extremes to all phenotyped sibs. The success of IBD-GS with sparse and selective genotyping can be explained by the fact that within-family haplotype blocks are accurately traced even with low-marker densities and that most of the within-family variance for normally distributed traits is captured by a small proportion of the phenotypically extreme sibs.

Conclusions

IBD-GS was substantially more effective than classical selection, even when based on very few markers and combined with selective genotyping of small fractions of the population. The study shows that low-cost GS programs can be successful by combining sparse and selective genotyping with pedigree and linkage information.     

Optimal sibship selection for genotyping in quantitative trait locus linkage analysis

In this paper we present a novel method for selecting optimally informative sibships of any size for quantitative trait locus (QTL) linkage analysis. The method allocates a quantitative index of potential informativeness to each sibship on the basis of observed trait scores and an assumed true QTL model. Any sample of phenotypically screened sibships can therefore be easily rank-ordered for selective genotyping. The quantitative index is the sibship's expected contribution to the non-centrality parameter. This expectation represents the weighted sum of chi(2) test statistics that would be obtained given the observed trait values over all possible sibship genotypic configurations; each configuration is weighted by the likelihood of it occurring given the assumed true genetic model. The properties of this procedure are explored in relation to the accuracy of the assumed true genetic model and sibship size. In comparison to previous methods of selecting phenotypically extreme sibships for genotyping, the proposed method is considerably more efficient and is robust with regard to the specification of the genetic model.     

A simple note on how to save money in linkage analysis

Genetic linkage maps are often based on maximum-likelihood estimates of recombination fractions which are converted into map units by mapping functions. This paper presents a cost analysis of linkage analysis for a segregating F₂␣population with codominant or dominant molecular markers and a qualitative monogenic dominant–recessive trait. For illustration, a disease-resistance trait is considered, where the susceptible allele is recessive. Three sub-populations of the F₂ can be used for linkage analysis [susceptible (= recessive) individuals, resistant (= dominant) individuals, complete F₂]. While it is well-known that recessive individuals are more informative than dominant individuals, it is not obvious a priori, which of the three sub-populations should be preferred, when costs of phenotyping and genotyping are taken into consideration. A comparative economic analysis of alternative procedures of linkage detection based on these three sub-populations does exhibit a clear economic superiority of the sub-population of susceptible (= recessive) individuals, when costs of genotyping are high. This cost-effectiveness is due to the higher information content of this sub-population compared to the sub-population of dominant (= resistant) individuals and also compared to the complete F₂. Our final conclusion/recommendation is as follows: If the cost to genotype an individual is sufficiently large compared with the cost to phenotype an individual, then linkage analysis and genetic mapping should be only based on susceptible (= recessive) individuals. Conversely, if the cost of phenotyping exceeds that for genotyping, it may be preferable to genotype all plants. The exact conditions under which a strategy is preferable are described in the paper.     

Economic aspects of implementing genomic evaluations in a pig sire line breeding scheme

Background

Replacing pedigree-based BLUP evaluations by genomic evaluations in pig breeding schemes can result in greater selection accuracy and genetic gains, especially for traits with limited phenotypes. However, this methodological change would generate additional costs. The objective of this study was to determine whether additional expenditures would be more profitably devoted to implementing genomic evaluations or to increasing phenotyping capacity while retaining traditional evaluations.

Methods

Stochastic simulation was used to simulate a population with 1050 breeding females and 50 boars that was selected for 10 years for a breeding goal with two uncorrelated traits with heritabilities of 0.4. The reference breeding scheme was based on phenotyping 13 770 candidates per year for trait 1 and 270 sibs of candidates per year for trait 2, with selection based on pedigree-based BLUP estimated breeding values. Increased expenditures were allocated to either increasing the phenotyping capacity for trait 2 while maintaining traditional evaluations, or to implementing genomic selection. The genomic scheme was based on two training populations: one for trait 2, consisting of phenotyped sibs of the candidates whose number increased from 1000 to 3430 over time, and one for trait 1, consisting of the selection candidates. Several genomic scenarios were tested, where the size of the training population for trait 1, and the number of genotyped candidates pre-selected based on their parental estimated breeding value, varied.

Results

Both approaches resulted in higher genetic trends for the population breeding goal and lower rates of inbreeding compared to the reference scheme. However, even a very marked increase in phenotyping capacity for trait 2 could not match improvements achieved with genomic selection when the number of genotyped candidates was large. Genotyping just a limited number of pre-selected candidates significantly reduced the extra costs, while preserving most of the benefits in terms of genetic trends and inbreeding. Implementing genomic evaluations was the most efficient approach when major expenditure was possible, whereas increasing phenotypes was preferable when limited resources were available.

Conclusions

Economic decisions on implementing genomic evaluations in a pig nucleus population must take account of population characteristics, phenotyping and genotyping costs, and available funds.     

Isolation of a major genetic interaction associated with an extreme phenotype using assorted F2 populations in rice

Detection of quantitative trait loci (QTLs) is dependent on the materials used in the analysis, as different combinations of parental materials may lead to different outcomes in QTLs for the same trait. On the other hand, an extreme phenotype associated with a given trait implies the potential involvement of a particular allele in various allelic interactions. A genetic factor associated with such an extreme phenotype may frequently be identified from various genetic populations consisting of different parental combinations. In this study, we attempted to uncover the genetic factor associated with extremely early heading date in rice, using various F2 populations. Heading date in rice has been characterized by at least 19 QTLs, from which 12 genes have been identified. A58, a rice strain with an extremely early heading date, is adapted to Hokkaido, the northernmost limit of rice cultivation. Six F2 populations derived from crosses of A58 with six other strains displayed a range of heading dates. Genotyping using 19 QTL markers indicated that the A58 allele of the Ghd7 locus was present in most F2 individuals exhibiting extremely early heading dates. This analysis also demonstrated that when the wild-type Ehd1 allele was present, the Ghd7 allele from A58 accelerated floral induction. The results of this study demonstrate that assorted F2 populations are valuable materials for comprehensive genotyping to explore major genetic factors for extreme phenotypes, and that this methodology is broadly applicable to other unknown traits.     

Next-generation phenotyping: requirements and strategies for enhancing our understanding of genotype–phenotype relationships and its relevance to crop improvement

More accurate and precise phenotyping strategies are necessary to empower high-resolution linkage mapping and genome-wide association studies and for training genomic selection models in plant improvement. Within this framework, the objective of modern phenotyping is to increase the accuracy, precision and throughput of phenotypic estimation at all levels of biological organization while reducing costs and minimizing labor through automation, remote sensing, improved data integration and experimental design. Much like the efforts to optimize genotyping during the 1980s and 1990s, designing effective phenotyping initiatives today requires multi-faceted collaborations between biologists, computer scientists, statisticians and engineers. Robust phenotyping systems are needed to characterize the full suite of genetic factors that contribute to quantitative phenotypic variation across cells, organs and tissues, developmental stages, years, environments, species and research programs. Next-generation phenotyping generates significantly more data than previously and requires novel data management, access and storage systems, increased use of ontologies to facilitate data integration, and new statistical tools for enhancing experimental design and extracting biologically meaningful signal from environmental and experimental noise. To ensure relevance, the implementation of efficient and informative phenotyping experiments also requires familiarity with diverse germplasm resources, population structures, and target populations of environments. Today, phenotyping is quickly emerging as the major operational bottleneck limiting the power of genetic analysis and genomic prediction. The challenge for the next generation of quantitative geneticists and plant breeders is not only to understand the genetic basis of complex trait variation, but also to use that knowledge to efficiently synthesize twenty-first century crop varieties.     

Efficiency of selective genotyping for genetic analysis of complex traits and potential applications in crop improvement

Selective genotyping of individuals from the two tails of the phenotypic distribution of a population provides a cost efficient alternative to analysis of the entire population for genetic mapping. Past applications of this approach have been confounded by the small size of entire and tail populations, and insufficient marker density, which result in a high probability of false positives in the detection of quantitative trait loci (QTL). We studied the effect of these factors on the power of QTL detection by simulation of mapping experiments using population sizes of up to 3,000 individuals and tail population sizes of various proportions, and marker densities up to one marker per centiMorgan using complex genetic models including QTL linkage and epistasis. The results indicate that QTL mapping based on selective genotyping is more powerful than simple interval mapping but less powerful than inclusive composite interval mapping. Selective genotyping can be used, along with pooled DNA analysis, to replace genotyping the entire population, for mapping QTL with relatively small effects, as well as linked and interacting QTL. Using diverse germplasm including all available genetics and breeding materials, it is theoretically possible to develop an “all-in-one plate” approach where one 384-well plate could be designed to map almost all agronomic traits of importance in a crop species. Selective genotyping can also be used for genomewide association mapping where it can be integrated with selective phenotyping approaches. We also propose a breeding-to-genetics approach, which starts with identification of extreme phenotypes from segregating populations generated from multiple parental lines and is followed by rapid discovery of individual genes and combinations of gene effects together with simultaneous manipulation in breeding programs.     

一个基于熵的精细定位数量性状位点的指数

针对数量性状位点的精细定位,本文采用群体的极端样本,利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数是标记基因和性状位点间连锁不平衡系数的函数,它不依赖于标记基因的频率。该指数对应我们之前提出的数量性状位点精细定位的哈迪-温伯格不平衡(HWD)指数,但在精细定位数量性状位点时,本文提出的指数的效能要高于哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作精细定位是有效的。     

Identity-by-descent genomic selection using selective and sparse genotyping for binary traits

Background

Genomic selection (GS) allows estimation of the breeding value of individuals, even for non-phenotyped animals. The aim of the study was to examine the potential of identity-by-descent genomic selection (IBD-GS) in genomic selection for a binary, sib-evaluated trait, using different strategies of selective genotyping. This low-cost GS approach is based on linkage analysis of sparse genome-wide marker loci.

Findings

Lowly to highly heritable (h² = 0.15, 0.30 or 0.60) binary traits with varying incidences (10 to 90%) were simulated for an aquaculture-like population. Genotyping was restricted to the 30% best families according to phenotype, using three genotyping strategies for training sibs. IBD-GS increased genetic gain compared to classical pedigree-based selection; the differences were largest at incidences of 10 to 50% of the desired category (i.e. a relative increase in genetic gain greater than 20%). Furthermore, the relative advantage of IBD-GS increased as the heritability of the trait increased. Differences were small between genotyping strategies, and most of the improvement was achieved by restricting genotyping to sibs with the least common binary phenotype. Genetic gains of IBD-GS relative to pedigree-based models were highest at low to moderate (10 to 50%) incidences of the category selected for, but decreased substantially at higher incidences (80 to 90%).

Conclusions

The IBD-GS approach, combined with sparse and selective genotyping, is well suited for genetic evaluation of binary traits. Genetic gain increased considerably compared with classical pedigree-based selection. Most of the improvement was achieved by selective genotyping of the sibs with the least common (minor) binary category phenotype. Furthermore, IBD-GS had greater advantage over classical pedigree-based models at low to moderate incidences of the category selected for.     

A low-marker density implementation of genomic selection in aquaculture using within-family genomic breeding values

Background

Genomic selection can increase genetic gain within aquaculture breeding programs, but the high costs related to high-density genotyping of a large number of individuals would make the breeding program expensive. In this study, a low-cost method using low-density genotyping of pre-selected candidates and their sibs was evaluated by stochastic simulation.

Methods

A breeding scheme with selection for two traits, one measured on candidates and one on sibs was simulated. Genomic breeding values were estimated within families and combined with conventional family breeding values for candidates that were pre-selected based on conventional BLUP breeding values. This strategy was compared with a conventional breeding scheme and a full genomic selection program for which genomic breeding values were estimated across the whole population. The effects of marker density, level of pre-selection and number of sibs tested and genotyped for the sib-trait were studied.

Results

Within-family genomic breeding values increased genetic gain by 15% and reduced rate of inbreeding by 15%. Genetic gain was robust to a reduction in marker density, with only moderate reductions, even for very low densities. Pre-selection of candidates down to approximately 10% of the candidates before genotyping also had minor effects on genetic gain, but depended somewhat on marker density. The number of test-individuals, i.e. individuals tested for the sib-trait, affected genetic gain, but the fraction of the test-individuals genotyped only affected the relative contribution of each trait to genetic gain.

Conclusions

A combination of genomic within-family breeding values, based on low-density genotyping, and conventional BLUP family breeding values was shown to be a possible low marker density implementation of genomic selection for species with large full-sib families for which the costs of genotyping must be kept low without compromising the effect of genomic selection on genetic gain.     

Nonpaternity in Linkage Studies of Extremely Discordant Sib Pairs

An approach commonly used to increase statistical power in linkage studies is the study of extremely discordant sibling pairs. This design is powerful under both additive and dominant-gene models and across a wide range of allele frequencies. A practical problem with the design is that extremely discordant pairs that are ostensibly full sibs may be half sibs. Although estimates vary, the population rates of such nonpaternity may be as high as 5%-10%. The proportion in discordant pairs may be much higher. The present article explores this potential inflation as a function of the resemblance of sib pairs and the criteria for discordance used for selection.     

Optimal designs for linkage disequilibrium mapping and candidate gene association tests in livestock populations

Simulation was used to evaluate the performance of different selective genotyping strategies when using linkage disequilibrium across large half-sib families to position a QTL within a previously defined genomic region. Strategies examined included standard selective genotyping and different approaches of discordant and concordant sib selection applied to arbitrary or selected families. Strategies were compared as a function of effect and frequency of QTL alleles, heritability, and phenotypic expression of the trait. Large half-sib families were simulated for 100 generations and 2% of the population was genotyped in the final generation. Simple ANOVA was applied and the marker with the greatest F-value was considered the most likely QTL position. For traits with continuous phenotypes, genotyping the most divergent pairs of half-sibs from all families was the best strategy in general, but standard selective genotyping was somewhat more precise when heritability was low. When the phenotype was distributed in ordered categories, discordant sib selection was the optimal approach for positioning QTL for traits with high heritability and concordant sib selection was the best approach when genetic effects were small. Genotyping of a few selected sibs from many families was generally more efficient than genotyping many individuals from a few highly selected sires.     

A unified sampling approach for multipoint analysis of qualitative and quantitative traits in sib pairs

Recent advances in molecular biology have enhanced the opportunity to conduct multipoint mapping for complex diseases. Concurrently, one sees a growing interest in the use of quantitative traits in linkage studies. Here, we present a multipoint sib-pair approach to locate the map position (tau) of a trait locus that controls the observed phenotype (qualitative or quantitative), along with a measure of statistical uncertainty. This method builds on a parametric representation for the expected identical-by-descent statistic at an arbitrary locus, conditional on an event reflecting the sampling scheme, such as affected sib pairs, for qualitative traits, or extreme discordant (ED) sib pairs, for quantitative traits. Our results suggest that the variance about tau&d4;, the estimator of tau, can be reduced by as much as 60%-70% by reducing the length of intervals between markers by one half. For quantitative traits, we examine the precision gain (measured by the variance reduction in tau&d4;) by genotyping extremely concordant (EC) sib pairs and including them along with ED sib pairs in the statistical analysis. The precision gain depends heavily on the residual correlation of the quantitative trait for sib pairs but considerably less on the allele frequency and exact genetic mechanism. Since complex traits involve multiple loci and, hence, the residual correlation cannot be ignored, our finding strongly suggests that one should incorporate EC sib pairs along with ED sib pairs, in both design and analysis. Finally, we empirically establish a simple linear relationship between the magnitude of precision gain and the ratio of the number of ED pairs to the number of EC pairs. This relationship allows investigators to address issues of cost effectiveness that are due to the need for phenotyping and genotyping subjects.     

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.     

The behaviors of some heritability estimators in the complete absence of genetic factors.

Heritability is an important concept in quantitative genetics and is widely used in human genetics. A high or even a moderate value of heritability estimate is usually taken as evidence for a genetic component for a quantitative trait. In this paper, the behaviors of some correlation-based heritability estimators are reexamined under the assumption of complete absence of any genetic factors. It turns out that when monozygotic (MZ) twins (or full sibs) are environmentally more similar than dizygotic twins (or half sibs), or when there is placement bias in MZ twins reared apart, those correlation-based heritability estimates can lead to nonnegligible or even high heritability values, even when genetic factors are completely absent. These alarming results suggest that extreme care should be exercised when using these heritability estimators.     

Whole-genome strategies for marker-assisted plant breeding

Molecular breeding for complex traits in crop plants requires understanding and manipulation of many factors influencing plant growth, development and responses to an array of biotic and abiotic stresses. Molecular marker-assisted breeding procedures can be facilitated and revolutionized through whole-genome strategies, which utilize full genome sequencing and genome-wide molecular markers to effectively address various genomic and environmental factors through a representative or complete set of genetic resources and breeding materials. These strategies are now increasingly based on understanding of specific genomic regions, genes/alleles, haplotypes, linkage disequilibrium (LD) block(s), gene networks and their contribution to specific phenotypes. Large-scale and high-density genotyping and genome-wide selection are two important components of these strategies. As components of whole-genome strategies, molecular breeding platforms and methodologies should be backed up by high throughput and precision phenotyping and e-typing (environmental assay) with strong support systems such as breeding informatics and decision support tools. Some basic strategies are discussed in this article, including (1) seed DNA-based genotyping for simplifying marker-assisted selection (MAS), reducing breeding cost and increasing scale and efficiency, (2) selective genotyping and phenotyping, combined with pooled DNA analysis, for capturing the most important contributing factors, (3) flexible genotyping systems, such as genotyping by sequencing and arraying, refined for different selection methods including MAS, marker-assisted recurrent selection and genomic selection (GS), (4) marker-trait association analysis using joint linkage and LD mapping, and (5) sequence-based strategies for marker development, allele mining, gene discovery and molecular breeding.     

Association Mapping in Outbred Populations: Power and Efficiency When Genotyping Parents and Phenotyping Progeny

We develop expressions for the power to detect associations between parental genotypes and offspring phenotypes for quantitative traits. Three different “indirect” experimental designs are considered: full-sib, half-sib, and full-sib–half-sib families. We compare the power of these designs to detect genotype–phenotype associations relative to the common, “direct,” approach of genotyping and phenotyping the same individuals. When heritability is low, the indirect designs can outperform the direct method. However, the extra power comes at a cost due to an increased phenotyping effort. By developing expressions for optimal experimental designs given the cost of phenotyping relative to genotyping, we show how the extra costs associated with phenotyping a large number of individuals will influence experimental design decisions. Our results suggest that indirect association studies can be a powerful means of detecting allelic associations in outbred populations of species for which genotyping and phenotyping the same individuals is impractical and for life history and behavioral traits that are heavily influenced by environmental variance and therefore best measured on groups of individuals. Indirect association studies are likely to be favored only on purely economical grounds, however, when phenotyping is substantially less expensive than genotyping. A web-based application implementing our expressions has been developed to aid in the design of indirect association studies.     

Selective Genotyping and Phenotyping Strategies in a Complex Trait Context

Selective genotyping and phenotyping strategies are used to lower the cost of quantitative trait locus studies. Their efficiency has been studied primarily in simplified contexts—when a single locus contributes to the phenotype, and when the residual error (phenotype conditional on the genotype) is normally distributed. It is unclear how these strategies will perform in the context of complex traits where multiple loci, possibly linked or epistatic, may contribute to the trait. We also do not know what genotyping strategies should be used for nonnormally distributed phenotypes. For time-to-event phenotypes there is the additional question of choosing follow-up time duration. We use an information perspective to examine these experimental design issues in the broader context of complex traits and make recommendations on their use.     

A Robust Test for Two‐Stage Design in Genome‐Wide Association Studies

Summary A two‐stage design is cost‐effective for genome‐wide association studies (GWAS) testing hundreds of thousands of single nucleotide polymorphisms (SNPs). In this design, each SNP is genotyped in stage 1 using a fraction of case–control samples. Top‐ranked SNPs are selected and genotyped in stage 2 using additional samples. A joint analysis, combining statistics from both stages, is applied in the second stage. Follow‐up studies can be regarded as a two‐stage design. Once some potential SNPs are identified, independent samples are further genotyped and analyzed separately or jointly with previous data to confirm the findings. When the underlying genetic model is known, an asymptotically optimal trend test (TT) can be used at each analysis. In practice, however, genetic models for SNPs with true associations are usually unknown. In this case, the existing methods for analysis of the two‐stage design and follow‐up studies are not robust across different genetic models. We propose a simple robust procedure with genetic model selection to the two‐stage GWAS. Our results show that, if the optimal TT has about 80% power when the genetic model is known, then the existing methods for analysis of the two‐stage design have minimum powers about 20% across the four common genetic models (when the true model is unknown), while our robust procedure has minimum powers about 70% across the same genetic models. The results can be also applied to follow‐up and replication studies with a joint analysis.