Linkage analysis of quantitative trait loci in multiple line crosses

Simple line crosses, for example, backcross and F₂, are commonly used in mapping quantitative trait loci (QTL). However, these simple crosses are rarely used alone in commercial plant breeding; rather, crosses involving multiple inbred lines or several simple crosses but connected by shared inbred lines may be common in plant breeding. Mapping QTL using crosses of multiple lines is more relevant to plant breeding. Unfortunately, current statistical methods and computer programs of QTL mapping are all designed for simple line crosses or multiple line crosses but under a regular mating system. It is not straightforward to extend the existing methods to handle multiple line crosses under irregular and complicated mating designs. The major hurdle comes from irregular inbreeding, multiple generations, and multiple alleles. In this study, we develop a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm for mapping QTL using complicated multiple line crosses. With the MCMC algorithm, we are able to draw a complete path of the gene flow from founder alleles to their descendents via a recursive process. This has greatly simplified the problem caused by irregular mating and inbreeding in the mapping population. Adopting the reversible jump MCMC algorithm, we are able to simultaneously search for multiple QTL along the genome. We can even infer the posterior distribution of the number of QTL, one of the most important parameters in QTL study. Application of the new MCMC based QTL mapping procedure is demonstrated using two different mating designs. Design I involves two inbred lines and their derived F₁, F₂, and BC populations. Design II is a half-diallel cross involving three inbred lines. The two designs appear different, but can be handled with the same robust computer program.     

Linkage disequilibrium mapping of quantitative trait loci under truncation selection

As a dense map of single nucleotide polymorphism (SNP) markers are available, population-based linkage disequilibrium (LD) mapping or association study is becoming one of the major tools for identifying quantitative trait loci (QTL) and for fine gene mapping. However, in many cases, LD between the marker and trait locus is not very strong. Approaches that maximize the potential of detecting LD will be essential for the success of LD mapping of QTL. In this paper, we propose two strategies for increasing the probability of detecting LD: (1) phenotypic selection and (2) haplotype LD mapping. To provide the foundations for LD mapping of QTL under selection, we develop analytic tools for assessing the impact of phenotypic selection on allele and haplotype frequencies, and LD under three trait models: single trait locus, two unlinked trait loci, and two linked trait loci with or without epistasis. In addition to a traditional chi(2) test, which compares the difference in allele or haplotype frequencies in the selected sample and population sample, we present multiple regression methods for LD mapping of QTL, and investigate which methods are effective in employing phenotypic selection for QTL mapping. We also develop a statistical framework for investigating and comparing the power of the single marker and multilocus haplotype test for LD mapping of QTL. Finally, the proposed methods are applied to mapping QTL influencing variation in systolic blood pressure in an isolated Chinese population.     

Linkage between quantitative trait loci and marker loci: resolution power of three statistical approaches in single marker analysis

This paper presents a comparison of three methods of parameter estimation in analysis of linkage between a quantitative trait locus (QTL) and a marker locus: maximum likelihood, mean square for trait cumulative distribution function, and method of moments, employing simulated backcross data. The sensitivity of estimates to violation of assumptions of normality and equal variances were also studied. Some measures of discrepancy between the trait distributions in the QTL groups are considered to evaluate the potential dependence of the resolution capacity of the QTL substitution effect with respect to trait mean value and variance.     

Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.     

Methods for linkage analysis of quantitative trait loci in humans

This paper reviews linkage analysis methods for detecting loci associated with quantitative traits in humans. All such methods are based on the underlying principle that family members who have similar trait values should have higher than expected levels of sharing of genetic material (identity by descent) near the genes that influence those traits. A number of different statistical methods for testing that association between shared trait values and shared identity by descent have been developed over the past 30 or more years. These different types of tests are reviewed here, with emphasis on their theory and derivations. Robustness and power are also discussed.     

Linkage analysis of extremely discordant and concordant sibling pairs identifies quantitative trait loci influencing variation in human menopausal age

Age at natural menopause may be used as parameter for evaluating the rate of ovarian aging. Environmental factors determine only a small part of the large variation in menopausal age. Studies have shown that genetic factors are likely to be involved in variation in menopausal age. To identify quantitative-trait loci for this trait, we performed a genomewide linkage study with age at natural menopause as a continuous quantitative phenotype in Dutch sister pairs, through use of a selective sampling scheme. A total of 165 families were ascertained using extreme selected sampling and were genotyped for 417 markers. Data were analyzed by Haseman-Elston regression and by an adjusted variance-components analysis. Subgroup analyses for early and late menopausal age were conducted by Haseman-Elston regression. In the adjusted variance-components analysis, 12 chromosomes had a LOD score of > or =1.0. Two chromosomal regions showed suggestive linkage: 9q21.3 (LOD score 2.6) and Xp21.3 (LOD score 3.1). Haseman-Elston regression showed rather similar locations of the peaks but yielded lower LOD scores. A permutation test to obtain empirical P values resulted in a significant peak on the X chromosome. To our knowledge, this is the first study to attempt to identify loci responsible for variability in menopausal age and in which several chromosomal regions were identified with suggestive and significant linkage. Although the finding of the region on the X chromosome comes as no surprise, because of its widespread involvement in premature ovarian failure, the definition of which particular gene is involved is of great interest. The region on chromosome 9 deserves further consideration. Both findings require independent confirmation.     

Expression quantitative trait loci analysis of the Rubisco activase gene in maize

Expression quantitative trait loci (eQTL) analyses were applied in order to identify genetic factors that are relevant to the expression of a β-isoform Rubisco activase gene in maize, namely ZmRCAβ, in this study. During two years, a maize recombinant inbred line population was measured for ZmRCAβ expression levels at the grain filling stage. Based on a genetic map containing 916 molecular markers, we detected five eQTLs, namely qRCA2.1 on chromosome 2, and qRCA4.1, qRCA4.2, qRCA4.3, and qRCA4.4 on chromosome 4. These eQTLs explained the phenotypic variation ranging from 6.14% to 7.50% with the logarithm of the odd values ranging from 3.11 to 4.96. Based on the position of the eQTLs and ZmRCAβ on the chromosome, qRCA4.2 was inferred as a cis-eQTL and the remaining as a trans-eQTL, suggesting that a combination of both cis- and trans-acting elements might control ZmRCAβ expression. qRCA4.2, qRCA4.3, and qRCA4.4 were repeatedly detected during two years.     

Linkage analysis of molecular markers and quantitative trait loci in populations of inbred backcross lines of Brassica napus L.

Backcross populations are often used to study quantitative trait loci (QTL) after they are initially discovered in balanced populations, such as F(2), BC(1), or recombinant inbreds. While the latter are more powerful for mapping marker loci, the former have the reduced background genetic variation necessary for more precise estimation of QTL effects. Many populations of inbred backcross lines (IBLs) have been developed in plant and animal systems to permit simultaneous study and dissection of quantitative genetic variation introgressed from one source to another. Such populations have a genetic structure that can be used for linkage estimation and discovery of QTL. In this study, four populations of IBLs of oilseed Brassica napus were developed and analyzed to map genomic regions from the donor parent (a winter-type cultivar) that affect agronomic traits in spring-type inbreds and hybrids. Restriction fragment length polymorphisms (RFLPs) identified among the IBLs were used to calculate two-point recombination fractions and LOD scores through grid searches. This information allowed the enrichment of a composite genetic map of B. napus with 72 new RFLP loci. The selfed and hybrid progenies of the IBLs were evaluated during two growing seasons for several agronomic traits. Both pedigree structure and map information were incorporated into the QTL analysis by using a regression approach. The number of QTL detected for each trait and the number of effective factors calculated by using biometrical methods were of similar magnitude. Populations of IBLs were shown to be valuable for both marker mapping and QTL analysis.     

Lineage-specific mapping of quantitative trait loci

We present an approach for quantitative trait locus (QTL) mapping, termed as ‘lineage-specific QTL mapping'', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed.     

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.     

A quantitative trait loci analysis of zinc hyperaccumulation in Arabidopsis halleri

The mechanisms of metal hyperaccumulation are still not understood, so we conducted a quantitative trait locus (QTL) analysis of zinc (Zn) hyperaccumulation in Arabidopsis halleri, in a cross between this and its sister species, A. petraea, in order to determine the number and approximate location of the genomic regions significantly contributing to this adaptation. An F2 cross between the two species was made, and the leaf Zn concentration of 92 individuals was measured at both low (10 microm) and high (100 microm) Zn concentrations. Twenty-five markers were established that were distributed on all of the eight chromosomes. Mapping of the markers established that they were essentially collinear with previous studies. QTLs exceeding a logarithm to the base 10 of the odds (LOD) value of 3 were found on chromosomes 4 (low Zn), 6 (high Zn) and 7 (both high and low Zn). Evidence for a QTL on chromosome 3 (low Zn) was also found. This analysis validates a previously used method of QTL analysis, based on microarray analysis of segregating families. Genes that have altered during the evolution of this character should also be QTL: this analysis calls into question a number of candidate genes from consideration as such primary genes because they do not appear to be associated with QTLs.     

Linkage disequilibrium analysis of biallelic DNA markers, human quantitative trait loci, and threshold-defined case and control subjects

Linkage disequilibrium (LD) mapping has been applied to many simple, monogenic, overtly Mendelian human traits, with great success. However, extensions and applications of LD mapping approaches to more complex human quantitative traits have not been straightforward. In this article, we consider the analysis of biallelic DNA marker loci and human quantitative trait loci in settings that involve sampling individuals from opposite ends of the trait distribution. The purpose of this sampling strategy is to enrich samples for individuals likely to possess (and not possess) trait-influencing alleles. Simple statistical models for detecting LD between a trait-influencing allele and neighboring marker alleles are derived that make use of this sampling scheme. The power of the proposed method is investigated analytically for some hypothetical gene-effect scenarios. Our studies indicate that LD mapping of loci influencing human quantitative trait variation should be possible in certain settings. Finally, we consider possible extensions of the proposed methods, as well as areas for further consideration and improvement.     

Linkage mapping of quantitative trait loci controlling seed weight in pea (Pisum sativum L.)

Quantitative trait loci (QTLs) affecting seed weight in pea (Pisum sativum L.) were mapped using two populations, a field-grown F₂ progeny of a cross between two cultivated types (Primo and OSU442-15) and glasshouse-grown single-seed-descent recombinant inbred lines (RILs) from a wide cross between a P. sativum ssp. sativum line (Slow) and a P. sativum ssp. humile accession (JI1794). Linkage maps for these crosses consisted of 199 and 235 markers, respectively. QTLs for seed weight in the Primo x OSU442-15 cross were identified by interval mapping, bulked segregant analysis, and selective genotyping. Four QTLs were identified in this cross, demonstrating linkage to four intervals on three linkage groups. QTLs for seed weight in the JI1794 x Slow cross were identified by single-marker analyses. Linkage were demonstrated to four intervals on three linkage groups plus three unlinked loci. In the two crosses, only one common genomic region was identified as containing seed-weight QTLs. Seed-weight QTLs mapped to the same region of linkage group III in both crosses. Conserved linkage relationships were demonstrated for pea, mungbean (Vigna radiata L.), and cowpea (V. unguiculata L.) genomic regions containing seed-weight QTLs by mapping RFLP loci from the Vigna maps in the Primo x OSU442-15 and JI1794 x Slow crosses.     

Linkage analysis and identification of quantitative trait loci associated with freeze tolerance and turf quality traits in St. Augustinegrass

St. Augustinegrass [Stenotaphrum secundatum (Walt.) Kuntze] is a warm-season turfgrass commonly grown in the southern USA. In this study, the first linkage map for all nine haploid chromosomes of the species was constructed for cultivar ‘Raleigh’ and cultivar ‘Seville’ using a pseudo-F₂ mapping strategy. A total of 160 simple sequence repeat markers were mapped to nine linkage groups (LGs) covering a total distance of 1176.24 cM. To demonstrate the usefulness of the map, quantitative trait loci (QTL) were mapped controlling field winter survival, laboratory-based freeze tolerance, and turf quality traits. Multiple genomic regions associated with these traits were identified. Moreover, overlapping QTL were found for winterkill and spring green up on LG 3 (99.21 cM); turf quality, turf density, and leaf texture on LG 3 (68.57–69.50 cM); and surviving green tissue and regrowth on LGs 1 (38.31 cM), 3 (77.70 cM), 6 (49.51 cM), and 9 (34.20 cM). Additional regions, where QTL identified in both field and laboratory-based/controlled environment freeze testing co-located, provided strong support that these regions are good candidates for true gene locations. These results present the first complete linkage map produced for St. Augustinegrass, providing a template for further genetic mapping. Additionally, markers linked to the QTL identified may be useful to breeders for transferring these traits into new breeding lines and cultivars.     

Mapping quantitative trait loci in oligogenic models

We discuss strategies for mapping quantitative trait loci with emphasis on certain issues of study design that have recently received attention: e.g. genotyping only selected pedigrees and the comparative value of large pedigrees versus sib pairs. We use a standard variance components model and a parametrization of the genetic effects in which the 'segregation' parameters are locally orthogonal to the 'linkage' parameters. This permits simple explicit expressions for the expectation of the score statistic, which we use to compare the power of different strategies. We also discuss robustness of the score statistic.     

Mapping quantitative trait loci in tetraploid populations

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound 'gametic effect', which consists of the composite 'genic effect' of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.     

Speed-mapping quantitative trait loci using microarrays

We developed a rapid, economical method for high-resolution quantitative trait locus (QTL) mapping using microarrays for selective genotyping of pooled DNA samples. We generated 21,207 F2 flies from two inbred Drosophila melanogaster strains with known QTLs affecting lifespan, and hybridized DNA pools of young and old flies to microarrays. We used changes of gene frequency of 2,326 single-feature polymorphisms (SFPs) to map previously identified and additional QTLs affecting lifespan.     

Bayesian model selection for genome-wide epistatic quantitative trait loci analysis

The problem of identifying complex epistatic quantitative trait loci (QTL) across the entire genome continues to be a formidable challenge for geneticists. The complexity of genome-wide epistatic analysis results mainly from the number of QTL being unknown and the number of possible epistatic effects being huge. In this article, we use a composite model space approach to develop a Bayesian model selection framework for identifying epistatic QTL for complex traits in experimental crosses from two inbred lines. By placing a liberal constraint on the upper bound of the number of detectable QTL we restrict attention to models of fixed dimension, greatly simplifying calculations. Indicators specify which main and epistatic effects of putative QTL are included. We detail how to use prior knowledge to bound the number of detectable QTL and to specify prior distributions for indicators of genetic effects. We develop a computationally efficient Markov chain Monte Carlo (MCMC) algorithm using the Gibbs sampler and Metropolis-Hastings algorithm to explore the posterior distribution. We illustrate the proposed method by detecting new epistatic QTL for obesity in a backcross of CAST/Ei mice onto M16i.