An empirical Bayes method for updating inferences in analysis of quantitative trait loci using information from related genome scans

Individual genome scans for quantitative trait loci (QTL) mapping often suffer from low statistical power and imprecise estimates of QTL location and effect. This lack of precision yields large confidence intervals for QTL location, which are problematic for subsequent fine mapping and positional cloning. In prioritizing areas for follow-up after an initial genome scan and in evaluating the credibility of apparent linkage signals, investigators typically examine the results of other genome scans of the same phenotype and informally update their beliefs about which linkage signals in their scan most merit confidence and follow-up via a subjective-intuitive integration approach. A method that acknowledges the wisdom of this general paradigm but formally borrows information from other scans to increase confidence in objectivity would be a benefit. We developed an empirical Bayes analytic method to integrate information from multiple genome scans. The linkage statistic obtained from a single genome scan study is updated by incorporating statistics from other genome scans as prior information. This technique does not require that all studies have an identical marker map or a common estimated QTL effect. The updated linkage statistic can then be used for the estimation of QTL location and effect. We evaluate the performance of our method by using extensive simulations based on actual marker spacing and allele frequencies from available data. Results indicate that the empirical Bayes method can account for between-study heterogeneity, estimate the QTL location and effect more precisely, and provide narrower confidence intervals than results from any single individual study. We also compared the empirical Bayes method with a method originally developed for meta-analysis (a closely related but distinct purpose). In the face of marked heterogeneity among studies, the empirical Bayes method outperforms the comparator.     

A general statistical framework for mapping quantitative trait loci in nonmodel systems: issue for characterizing linkage phases

Because of uncertainty about linkage phases of founders, linkage mapping in nonmodel, outcrossing systems using molecular markers presents one of the major statistical challenges in genetic research. In this article, we devise a statistical method for mapping QTL affecting a complex trait by incorporating all possible QTL-marker linkage phases within a mapping framework. The advantage of this model is the simultaneous estimation of linkage phases and QTL location and effect parameters. These estimates are obtained through maximum-likelihood methods implemented with the EM algorithm. Extensive simulation studies are performed to investigate the statistical properties of our model. In a case study from a forest tree, this model has successfully identified a significant QTL affecting wood density. Also, the probability of the linkage phase between this QTL and its flanking markers is estimated. The implications of our model and its extension to more general circumstances are discussed.     

Detecting Marker-Qtl Linkage and Estimating Qtl Gene Effect and Map Location Using a Saturated Genetic Map

A simulation study was carried out on a backcross population in order to determine the effect of marker spacing, gene effect and population size on the power of marker-quantitative trait loci (QTL) linkage experiments and on the standard error of maximum likelihood estimates (MLE) of QTL gene effect and map location. Power of detecting a QTL was virtually the same for a marker spacing of 10 cM as for an infinite number of markers and was only slightly decreased for marker spacing of 20 or even 50 cM. The advantage of using interval mapping as compared to single-marker analysis was slight. ``Resolving power' of a marker-QTL linkage experiment was defined as the 95% confidence interval for the QTL map location that would be obtained when scoring an infinite number of markers. It was found that reducing marker spacing below the resolving power did not add appreciably to narrowing the confidence interval. Thus, the 95% confidence interval with infinite markers sets the useful marker spacing for estimating QTL map location for a given population size and estimated gene effect.     

Interval mapping of quantitative trait loci with selective DNA pooling data

Selective DNA pooling is an efficient method to identify chromosomal regions that harbor quantitative trait loci (QTL) by comparing marker allele frequencies in pooled DNA from phenotypically extreme individuals. Currently used single marker analysis methods can detect linkage of markers to a QTL but do not provide separate estimates of QTL position and effect, nor do they utilize the joint information from multiple markers. In this study, two interval mapping methods for analysis of selective DNA pooling data were developed and evaluated. One was based on least squares regression (LS-pool) and the other on approximate maximum likelihood (ML-pool). Both methods simultaneously utilize information from multiple markers and multiple families and can be applied to different family structures (half-sib, F2 cross and backcross). The results from these two interval mapping methods were compared with results from single marker analysis by simulation. The results indicate that both LS-pool and ML-pool provided greater power to detect the QTL than single marker analysis. They also provide separate estimates of QTL location and effect. With large family sizes, both LS-pool and ML-pool provided similar power and estimates of QTL location and effect as selective genotyping. With small family sizes, however, the LS-pool method resulted in severely biased estimates of QTL location for distal QTL but this bias was reduced with the ML-pool.     

Modeling segregation distortion for viability selection I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F₂ population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.     

Natural variation in MAM within and between populations of Arabidopsis lyrata determines glucosinolate phenotype

The genetic variation that underlies the glucosinolate phenotype of Arabidopsis lyrata ssp. petraea was investigated between and within populations. A candidate glucosinolate biosynthetic locus (MAM, containing methylthioalkylmalate synthase genes) was mapped in A. lyrata to a location on linkage group 6 corresponding to the homologous location for MAM in A. thaliana. In A. thaliana MAM is responsible for side chain elongation in aliphatic glucosinolates, and the MAM phenotype can be characterized by the ratios of long- to short-chain glucosinolates. A quantitative trait loci (QTL) analysis of glucosinolate ratios in an A. lyrata interpopulation cross found one QTL at MAM. Additional QTL were identified for total indolic glucosinolates and for the ratio of aliphatic to indolic glucosinolates. MAM was then used as the candidate gene for a within-population cosegregation analysis in a natural A. lyrata population from Germany. Extensive variation in microsatellite markers at MAM was found and this variation cosegregated with the same glucosinolate ratios as in the QTL study. The combined results indicate that both between- and within-population genetic variation in the MAM region determines phenotypic variation in glucosinolate side chains in A. lyrata.     

Evidence for linkage and association with reading disability on 6p21.3-22

Reading disability (RD), or dyslexia, is a common heterogeneous syndrome with a large genetic component. Several studies have consistently found evidence for a quantitative-trait locus (QTL) within the 17 Mb (14.9 cM) that span D6S109 and D6S291 on chromosome 6p21.3-22. To characterize further linkage to the QTL, to define more accurately the location and the effect size, and to identify a peak of association, we performed Haseman-Elston and DeFries-Fulker linkage analyses, as well as transmission/disequilibrium, total-association, and variance-components analyses, on 11 quantitative reading and language phenotypes. One hundred four families with RD were genotyped with a new panel of 29 markers that spans 9 Mb of this region. Linkage results varied widely in degree of statistical significance for the different linkage tests, but multipoint analysis suggested a peak near D6S461. The average 6p QTL heritability for the 11 reading and language phenotypes was 0.27, with a maximum of 0.66 for orthographic choice. Consistent with the region of linkage described by these studies and others, there was a peak of transmission disequilibrium with a QTL centered at JA04 (chi2=9.48; empirical P=.0033; orthographic choice), and there was strong evidence for total association at this same marker (chi2=11.49; P=.0007; orthographic choice). Although the boundaries of the peak could not be precisely defined, the most likely location of the QTL is within a 4-Mb region surrounding JA04.     

Genetic mapping in hybrid zones

Recent advances in genetic mapping methodologies make it feasible to localize quantitative trait loci (QTL) that contribute to adaptation and speciation. However, it has not been possible to employ these methods in many wild species because of difficulties associated with creating and propagating recombinant populations of sufficient size for QTL mapping. Natural hybrid zones contain recombinant individuals resulting from many generations of hybridization and thus offer a potential solution to these problems. For studies of speciation, hybrid zones offer the possibility of mapping QTL simultaneously with assessments of their effects on assortative mating, hybrid fitness, and interspecific gene flow. Here, we explore the problems and prospects associated with genetic map building and QTL analyses in natural hybrid zones by analyzing correlations among markers of known genomic location in four hybrid zones between the wild sunflower species Helianthus annuus and Helianthus petiolaris. Results indicate that mapping in hybrid zones presents many challenges. These include overlap in the strength of marker correlations between linked and unlinked markers, unevenness in marker frequencies along linkages, and heterogeneity in the relationship between marker distances and correlations. All make it difficult to accurately group and order markers or to estimate the distances between them. These problems can be ameliorated by sampling strategies that maximize the difference in linkage disequilibria between linked and unlinked markers and that minimize differences in frequencies among markers or QTL. In addition, studies that employ a previously determined molecular marker map for gene localization have a greater likelihood of success than those that rely on the hybrid zone data for both map construction and QTL analyses.     

Empirical bayes method for incorporating data from multiple genome scans

Individual genome scans tend to have low power and can produce markedly biased estimates of QTL effects. Further, the confidence interval for their location is often prohibitively large for subsequent fine mapping and positional cloning. Given that a large number of genome scans have been conducted, not to mention the large number of variables and subsets tested, it is difficult to confidently rule out type 1 error as an explanation for significant effects even when there is apparent replication in a separate data set. We adapted Empirical Bayes (EB) methods [1] to analyze data from multiple genome scans simultaneously and alleviate each of these problems while still allowing for different QTL population effects across studies. We investigated the effects of using the EB method to include data from background studies to update the results of a single study of interest via simulation and demonstrated that it has a stable confidence level over a wide range of parameters defining the background studies and increased the power to detect linkage, even when some of the background studies were null or had QTL effect at other markers. This EB method for incorporating data from multiple studies into genome scan analyses seems promising.     

Linkage analysis of quantitative trait loci in the presence of heterogeneity

Variance component modeling for linkage analysis of quantitative traits is a powerful tool for detecting and locating genes affecting a trait of interest, but the presence of genetic heterogeneity will decrease the power of a linkage study and may even give biased estimates of the location of the quantitative trait loci. Many complex diseases are believed to be influenced by multiple genes and therefore genetic heterogeneity is likely to be present for many real applications of linkage analysis. We consider a mixture of multivariate normals to model locus heterogeneity by allowing only a proportion of the sampled pedigrees to segregate trait-influencing allele(s) at a specific locus. However, for mixtures of normals the classical asymptotic distribution theory of the maximum likelihood estimates does not hold, so tests of linkage and/or heterogeneity are evaluated using resampling methods. It is shown that allowing for genetic heterogeneity leads to an increase in power to detect linkage. This increase is more prominent when the genetic effect of the locus is small or when the percentage of pedigrees not segregating trait-influencing allele(s) at the locus is high.     

Identification of quantitative trait loci for wood quality and growth across eight full-sib coastal Douglas-fir families

Typical linkage and quantitative trait locus (QTL) analyses in forest trees have been conducted in single pedigrees with sex-averaged linkage maps. The results of a QTL analysis for wood quality and growth traits of coastal Douglas-fir using eight full-sib families, each consisting of 40 progeny, replicated on four sites are presented. The resulting map of segregating genetic markers consisted of 120 amplified fragment length polymorphism (AFLP) loci distributed across 19 linkage groups. The wood quality traits represent the widest suite of traits yet examined for QTL analysis in a tree species in a single study. Wood fiber traits showed the lowest number of QTLs (3) with relatively small effect (ca. 4%); wood density traits also showed just three QTLs but with slightly larger effect; wood chemistry traits showed more QTLs (7), while ring density traits showed many QTLs with large numbers of QTLs (78) and interesting patterns of temporal variation. Growth traits gave just five QTLs but of major effect (10–16%). Trees, with their long generation times, provide a rich resource for studies of temporal variation of QTL expression.     

Composite interval mapping reveals a major locus influencing embryonic development rate in rainbow trout (Oncorhynchus mykiss)

Little is known about the genetics controlling the rate of embryonic development in salmonids, despite the fact that this trait plays an important role in the life history of wild and cultured stocks. We investigated the genetics of embryonic development rate by performing an analysis of quantitative trait loci (QTL) on two families of androgenetically derived doubled haploid rainbow trout produced from a hybrid of two clonal lines with divergent embryonic development rates. A total of 170 doubled haploid individuals were genotyped at 222 marker loci [219 amplified fragment length polymorphism (AFLP) markers, 2 microsatellites, and p53]. A genetic linkage analysis resulted in a map consisting of 27 linkage groups with 21 of the markers remaining unlinked at a minimum LOD of 3.0 and maximum theta of 0.40. Eight of these linkage groups were matched to published rainbow trout linkage groups. Composite interval mapping (CIM) revealed evidence for two QTL influencing time to hatch, and suggestive evidence for a third. These QTL accounted for a total of 24.6% of the variation in time to hatch. One of these QTL had a large effect on development rate, especially in one family of doubled haploids, in which it explained 25.6% of the variance in time to hatch. QTL influencing embryonic length and weight at the commencement of exogenous feeding were also identified. The QTL with the strongest effect on embryonic length (lenR13) mapped to the same position as the QTL with the strongest effect on time to hatch (tthR13), suggesting a single QTL may have a pleiotropic effect on both these traits. These results suggest that the use of clonal lines with a doubled haploid crossing design is an effective way of analyzing the genetic basis of complex traits in salmonids.     

Joint-multiple family linkage analysis predicts within-family variation better than single-family analysis of the maize nested association mapping population

Quantitative trait locus (QTL) mapping has been used to dissect the genetic architecture of complex traits and predict phenotypes for marker-assisted selection. Many QTL mapping studies in plants have been limited to one biparental family population. Joint analysis of multiple biparental families offers an alternative approach to QTL mapping with a wider scope of inference. Joint-multiple population analysis should have higher power to detect QTL shared among multiple families, but may have lower power to detect rare QTL. We compared prediction ability of single-family and joint-family QTL analysis methods with fivefold cross-validation for 6 diverse traits using the maize nested association mapping population, which comprises 25 biparental recombinant inbred families. Joint-family QTL analysis had higher mean prediction abilities than single-family QTL analysis for all traits at most significance thresholds, and was always better at more stringent significance thresholds. Most robust QTL (detected in >50% of data samples) were restricted to one family and were often not detected at high frequency by joint-family analysis, implying substantial genetic heterogeneity among families for complex traits in maize. The superior predictive ability of joint-family QTL models despite important genetic differences among families suggests that joint-family models capture sufficient smaller effect QTL that are shared across families to compensate for missing some rare large-effect QTL.     

Considerations on study designs using the extreme sibpairs methods under multilocus oligogenic models

Several issues pertinent to study designs employing extreme sibpairs (ESP) methods to detect complex oligogenic quantitative trait loci (QTL) are investigated in the setting of genome-wide multipoint scans. We demonstrate that when stringent alpha-levels are imposed (e.g., alpha = 0.00022 as recommended by Landers and Kruglyak), the power to detect a susceptibility locus could drop from 83.6% under a one-locus model down to a hopeless 22.8% under a two-locus model of the same heritability h(2) = 0.5 and gene frequency (p = 0.1). We introduce the notion of joint power that is the power to detect linkage to at least one location over a given panel of markers across a genomic region and describe the effect of several design factors on such joint power in a multipoint scan. Moreover, power of analysis conditional on the IBD sharings of ESPs at a known/detected locus is examined and shown to increase substantively (to 93.3% under the previous two-locus model) in detecting novel trait loci. We conclude that with such remedies, the ESP design continues to be a relatively powerful design for mapping oligogenic QTL. However, when the effect of individual contributing loci becomes less tractable, especially when their contributions are "asymmetric," deliberation on balancing two types of statistical errors and a careful examination of possible contributions from multiple genetic factors and/or interaction effects are a must in designing an efficient study.     

A mixed model QTL analysis for sugarcane multiple-harvest-location trial data

Sugarcane-breeding programs take at least 12 years to develop new commercial cultivars. Molecular markers offer a possibility to study the genetic architecture of quantitative traits in sugarcane, and they may be used in marker-assisted selection to speed up artificial selection. Although the performance of sugarcane progenies in breeding programs are commonly evaluated across a range of locations and harvest years, many of the QTL detection methods ignore two- and three-way interactions between QTL, harvest, and location. In this work, a strategy for QTL detection in multi-harvest-location trial data, based on interval mapping and mixed models, is proposed and applied to map QTL effects on a segregating progeny from a biparental cross of pre-commercial Brazilian cultivars, evaluated at two locations and three consecutive harvest years for cane yield (tonnes per hectare), sugar yield (tonnes per hectare), fiber percent, and sucrose content. In the mixed model, we have included appropriate (co)variance structures for modeling heterogeneity and correlation of genetic effects and non-genetic residual effects. Forty-six QTLs were found: 13 QTLs for cane yield, 14 for sugar yield, 11 for fiber percent, and 8 for sucrose content. In addition, QTL by harvest, QTL by location, and QTL by harvest by location interaction effects were significant for all evaluated traits (30 QTLs showed some interaction, and 16 none). Our results contribute to a better understanding of the genetic architecture of complex traits related to biomass production and sucrose content in sugarcane.     

Introgression of a quantitative trait locus for yield from <Emphasis Type="Italic">Glycine soja</Emphasis> into commercial soybean cultivars

The value of exotic germplasm in broadening the genetic base of most crops has been demonstrated many times. However, the difficulties involved in working with exotic germplasm have limited their utility in plant breeding. Unwanted linkages often thwart the successful incorporation of beneficial exotic genes into commercial lines. Thus, the use of exotics in traditional breeding makes the process of crop improvement a tedious, time-consuming and expensive endeavor. The availability of molecular markers makes it possible to isolate specific genomic regions and transfer them into commercial varieties with minimal linkage drag. We found a yield-enhancing quantitative trait locus (QTL) from Glycine soja (Siebold and Zucc.) by evaluating a population of 265 BC(2) individuals from a cross between HS-1 and PI 407305. The yield QTL was located on linkage group B2(U26) of the soybean [Glycine max (L.) Merrill] genetic linkage map. In a 2-year, multi-location study, individuals carrying the PI 407305 haplotype at the QTL locus demonstrated a 9.4% yield advantage over individuals that did not contain the exotic haplotype. When tested in a more uniform "HS-1-like" background in two locations, we observed an 8% yield advantage for lines that carry the PI 407305 haplotype. We further assessed the QTL effect in various elite soybean genetic backgrounds. The yield effect was consistently observed in only two of six genetic backgrounds. Individuals carrying the PI 407305 haplotype at the QTL locus had a 9% yield advantage in yield trials across locations. Despite the limited adaptability of this yield-QTL across genetic backgrounds, this study demonstrates the potential of exotic germplasm for yield enhancement in soybean.     

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.     

Analysis of an intraspecific RIL population uncovers genomic segments harbouring multiple QTL for seed relevant traits in lentil (<Emphasis Type="Italic">Lens culinaris</Emphasis> L.)

Improving seed related traits remains key objective in lentil breeding. In recent years, genomic resources have shown great promise to accelerate crop improvement. However, limited genomic resources in lentil greatly restrict the use of genomics assisted breeding. The present investigation aims to build an intraspecific genetic linkage map and identify the QTL associated with important seed relevant traits using 94 recombinant inbreds (WA 8649090 × Precoz). A total of 288 polymorphic DNA markers including simple sequence repeat (SSR), inter simple sequence repeat (ISSR) and random amplified polymorphic DNA (RAPD) were assayed on mapping population. The resultant genetic linkage map comprised 220 loci spanning 604.2 cM of the lentil genome, with average inter-marker distance of 2.74 cM. QTL mapping in this RIL population uncovered a total of 18 QTL encompassing nine major and nine minor QTL. All major QTL were detected for seed related traits viz., seed diameter (SD), seed thickness (ST), seed weight (SW) and seed plumpness (SP) across two locations. A considerable proportion of the phenotypic variation (PV) was accounted to these QTL. For instance, one major QTL on LG5 controlling SW (QTL 15) explained 50% PV in one location, while the same QTL accounted for 34.18% PV in other location. Importantly, the genomic region containing multiple QTL for different seed traits was mapped to a 17-cM region on LG5. The genomic region harbouring QTL for multiple traits opens up exciting opportunities for genomics assisted improvement of lentil.     

Genome-wide scan for bovine twinning rate QTL using linkage disequilibrium

Twinning is a complex trait with negative impacts on health and reproduction, which cause economic loss in dairy production. Several twinning rate quantitative trait loci (QTL) have been detected in previous studies, but confidence intervals for QTL location are broad and many QTL are unreplicated. To identify genomic regions or genes associated with twinning rate, QTL analysis based on linkage combined with linkage disequilibrium (LLD) and individual marker associations was conducted across the genome using high-throughput single nucleotide polymorphism (SNP) genotypes. A total of 9919 SNP markers were genotyped with 200 sires and sons in 19 half-sib North American Holstein dairy cattle families. After SNPs were genotyped, informative markers were selected for genome-wide association tests and QTL searches. Evidence for twinning rate QTL was found throughout the genome. Thirteen markers significantly associated with twinning rate were detected on chromosomes 2, 5 and 14 ( P  < 2.3 × 10⁻⁵). Twenty-six regions on fourteen chromosomes were identified by LLD analysis at P  < 0.0007. Seven previously reported ovulation or twinning rate QTL were supported by results of single marker association or LLD analyses. Single marker association analysis and LLD mapping were complementary tools for the identification of putative QTL in this genome scan.     

Analysis of the prostate cancer-susceptibility locus HPC20 in 172 families affected by prostate cancer

A recent study of hereditary prostate cancer has provided evidence for a prostate cancer-susceptibility locus, HPC20, which maps to 20q13. To assess further the potential contribution of this locus to prostate cancer susceptibility, we studied 172 unrelated families affected by prostate cancer, using 17 polymorphic markers across a 98.5-cM segment of chromosome 20 that contains the candidate region. Parametric analysis, allowing for heterogeneity, resulted in an overall HLOD score of 0.09 (P=.39) at D20S171, under the assumption of linkage in 6% of families. Mode-of-inheritance-free analysis of the entire data set resulted in a maximal Zlr score of 0.76 (LOD 0.13; P=.22) at the same location. The strongest evidence for linkage was seen in the subset of 16 black families (LOD 0.86; Zlr=1.99; P=.023) between markers D20S893 and D20S120, near the putative location of HPC20. Although some positive results were observed, our linkage study does not provide statistically significant support for the existence of a prostate cancer-susceptibility locus HPC20 at 20q13.