Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations

A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the 'Fernando and Grossman' multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the 'Fernando and Grossman' model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.     

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

Background

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics.

Results

Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes.

Conclusions

Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.     

Detection of a quantitative trait locus associated with resistance to Ascaris suum infection in pigs

Helminths almost invariably have an over-dispersed distribution in the host population. Human and animal studies have provided evidence suggesting that a large part of this variation is due to host genetic factors. Recently, the heritability for roundworm (Ascaris suum) infection levels in pigs was estimated to be 0.45. We used single nucleotide polymorphism markers to perform a whole-genome scan on 195 pigs experimentally infected with A. suum. A putative quantitative trait locus for worm burden on chromosome 4 covering 2.5 Mbp was identified by measured genotype analysis, although none of the SNPs reached genome-wide significance. To validate the putative quantitative trait locus, we genotyped two of the SNPs within the region in unrelated, informative animals exposed to experimental or natural infections and from which we had worm counts and/or faecal egg counts; the validation studies showed that one of the SNPs (TXNIP) was associated with total worm burden (P < 0.001) and adult worm burden(P < 0.0001), whereas the other SNP (ARNT) was associated with adult worm burden (P < 0.025) in these populations. We were thus able to confirm the existence of the quantitative trait locus on chromosome 4.This is to our knowledge the first report of a quantitative trait locus associated with helminth burden in pigs.     

Mapping a blood pressure quantitative trait locus to a 5.7-cM region in Dahl salt-sensitive rats

A region on rat Chromosome (Chr) 2 of the Dahl salt-sensitive rat (S) was shown previously to contain a quantitative trait locus (QTL) for blood pressure (BP). This was achieved first by linkage, followed by the use of congenic strains. A congenic strain, designated S.MNS-D2Mit6/Adh, contained a segment of Chr 2 from the Milan Normotensive (MNS) rat in the S genetic background. Since the region containing the QTL was roughly 80 cM in size, a further reduction was needed towards the positional or candidate gene cloning. Currently, two congenic substrains were made from the original strain S.MNS-D2Mit6/Adh. One of these two substrains showed a BP-lowering effect, whereas the other substrain did not. Deducing the segment not shared in the two substrains, the BP QTL has to be present in a chromosome region of roughly 5.7 cM between the marker D2Rat303 and the locus for the neutroendopeptidase gene (Nep). Nep is not included within the segment. This region does not seem to contain any candidate genes well known for the BP control. Thus, the final identification of the QTL will most likely lead to the discovery of a brand new gene for the BP regulation. Received: 14 December 2000 / Accepted: 18 January 2001     

Selective sweep at a quantitative trait locus in the presence of background genetic variation

We model selection at a locus affecting a quantitative trait (QTL) in the presence of genetic variance due to other loci. The dynamics at the QTL are related to the initial genotypic value and to the background genetic variance of the trait, assuming that background genetic values are normally distributed, under three different forms of selection on the trait. Approximate dynamics are derived under the assumption of small mutation effect. For similar strengths of selection on the trait (i.e, gradient of directional selection beta) the way background variation affects the dynamics at the QTL critically depends on the shape of the fitness function. It generally causes the strength of selection on the QTL to decrease with time. The resulting neutral heterozygosity pattern resembles that of a selective sweep with a constant selection coefficient corresponding to the early conditions. The signature of selection may also be blurred by mutation and recombination in the later part of the sweep. We also study the race between the QTL and its genetic background toward a new optimum and find the conditions for a complete sweep. Overall, our results suggest that phenotypic traits exhibiting clear-cut molecular signatures of selection may represent a biased subset of all adaptive traits.     

On estimating the proportion of variance in a phenotypic trait attributable to a measured locus

The measured genotype approach can be used to estimate the variance contributions of specific candidate loci to quantitative traits of interest. We show here that both the naive estimate of measured-locus heritability, obtained by invoking infinite-sample theory, and an estimate obtained from a bias-corrected variance estimate based on finite-sample theory, produce biased estimates of heritability. We identify the sources of bias, and quantify their effects. The two sources of bias are: (1) the estimation of heritability from population samples as the ratio of two variances, and (2) the existence of sampling error. We show that neither heritability estimator is less biased (in absolute value) than the other in all situations, and the choice of an ideal estimator is therefore a function of the sample size and magnitude of the locus-specific contribution to the overall phenotypic variance. In most cases the bias is small, so that the practical implications of using either estimator are expected to be minimal.     

Identification of a major quantitative trait locus for resistance to fire blight in the wild apple species Malus fusca

Fire blight, caused by the Gram-negative bacterium Erwinia amylovora, is the most important bacterial disease affecting apple (Malus × domestica) and pear (Pyrus communis) production. The use of antibiotic treatment, though effective to some degree, is forbidden or strictly regulated in many European countries, and hence an alternative means of control is essential. The planting of fire blight-resistant cultivars seems to be a highly feasible strategy. In this study, we explored a segregating population derived from a cross between the wild apple species Malus fusca and the M. × domestica cultivar Idared. F1 progenies used for mapping were artificially inoculated with Erwinia amylovora strain Ea222_JKI at a concentration of 10⁹ cfu/ml in three different years. The averages of percentage lesion length of all replicates of each genotype were used as numerical traits for statistical analysis. A Kruskal–Wallis analysis was used to determine marker–phenotype association and revealed a linkage group with Diversity Arrays Technology (DArT) markers significantly linked with fire blight. After locating the positions of the DArT markers on the Golden Delicious genome, simple sequence repeat (SSR) markers were developed from chromosome 10 to replace the DArT markers and to determine the quantitative trait locus (QTL) region. Multiple QTL mapping (MQM) revealed a strong QTL (Mfu10) on linkage group 10 of M. fusca explaining about 65.6 % of the phenotypic variation. This is the first report on a fire blight resistance QTL of M. fusca.     

A quantitative trait locus for recognition of foreign eggs in the host of a brood parasite

Avian brood parasites reduce the reproductive output of their hosts and thereby select for defence mechanisms such as ejection of parasitic eggs. Such defence mechanisms simultaneously select for counter-defences in brood parasites, causing a coevolutionary arms race. Although coevolutionary models assume that defences and counter-defences are genetically influenced, this has never been demonstrated for brood parasites. Here, we give strong evidence for genetic differences between ejector and nonejectors, which could allow the study of such host defence at the genetic level, as well as studies of maintenance of genetic variation in defences. Briefly, we found that magpies, that are the main host of the great spotted cuckoo in Europe, have alleles of one microsatellite locus (Ase64) that segregate between accepters and rejecters of experimental parasitic eggs. Furthermore, differences in ejection rate among host populations exploited by the brood parasite covaried significantly with the genetic distance for this locus.     

Fine mapping of a grain-weight quantitative trait locus in the pericentromeric region of rice chromosome 3

As the basis for fine mapping of a grain-weight QTL, gw3.1, a set of near isogenic lines (NILs), was developed from an Oryza sativa, cv. Jefferson x O. rufipogon (IRGC105491) population based on five generations of backcrossing and seven generations of selfing. Despite the use of an interspecific cross for mapping and the pericentromeric location of the QTL, we observed no suppression of recombination and have been able to narrow down the location of the gene underlying this QTL to a 93.8-kb region. The locus was associated with transgressive variation for grain size and grain weight in this population and features prominently in many other inter- and intraspecific crosses of rice. The phenotype was difficult to evaluate due to the large amount of variance in size and weight among grains on a panicle and between grains on primary and secondary panicles, underscoring the value of using multiple approaches to phenotyping, including extreme sampling and NIL group-mean comparisons. The fact that a QTL for kernel size has also been identified in a homeologous region of maize chromosome 1 suggests that this locus, in which the dominant O. rufipogon allele confers small seed size, may be associated with domestication in cereals.     

A quantitative trait locus influencing activin-to-estrogen ratio in pedigreed baboons maps to a region homologous to human chromosome 19.

Activin is a multifunctional hormone playing a major role in the regulation of reproduction and growth and development. We performed a genomewide scan using multipoint linkage analysis implemented in a general pedigree-based variance component approach to identify genes with measurable effects on variation in the activin-to-estrogen ratio in baboons. A microsatellite polymorphism, D19S714, which maps to human chromosome 19p13.2, showed marginal evidence of linkage with a lod (log10 of the odds in favor of genetic linkage) score of 1.95 (0.014). This region contains several potential candidate genes including PKA (protein kinase, cAMP-dependent, catalytic alpha) and the gene pair JUN-B and JUN-D. This is the first evidence of a quantitative trait locus with a significant effect on the activin-to-estrogen ratio.     

The candidate gene, Clock, localizes to a strong spawning time quantitative trait locus region in rainbow trout

We applied a candidate gene mapping approach to an existing quantitative trait loci (QTL) data set for spawning date in rainbow trout (Oncorynchus mykiss) to ascertain whether these genes could potentially account for any observed QTL effects. Several genes were chosen for their known or suspected roles in reproduction, circadian, or circannual timing, including salmon-type gonadotropin-releasing hormone 3A and 3B (GnRH3A and GnRH3B), Clock, Period1, and arylalkylamine N-acetlytransferase-1 and -2 (AANAT-1 and AANAT-2). Genes were sequenced, and polymorphisms were identified in parents of two rainbow trout mapping families, one of which was used previously to detect spawn timing QTL. Interval mapping was used to identify associations between genetic markers and spawning date effects. Using a genetic map that was updated with 574 genetic markers (775 total), we found evidence for 11 significant or suggestive QTL regions. Most QTL were only localized within one of the parents; however, a strong QTL region was identified in both female and male parents on linkage group RT-8 that explained 20% and 50% of trait variance, respectively. The Clock gene mapped to this region. Period1 mapped to a region in the female parent associated with a marginal effect (P = .056) on spawn timing. Other candidate genes were not associated with significant QTL effects.     

Detection of a quantitative trait locus controlling carbon isotope discrimination and its contribution to stomatal conductance in japonica rice

Increasing leaf photosynthesis offers a possible way to improve yield potential in rice (Oryza sativa L.). Carbon isotope discrimination (Δ¹³C) has potential as an indirect selection criterion. In this study, we searched for quantitative trait loci (QTLs) controlling Δ¹³C, and assessed their association with leaf photosynthesis. Substitution mapping by using chromosome segment substitution lines (CSSLs), that carry segments from the indica cultivar Kasalath in the genetic background of the japonica cultivar Koshihikari, identified genomic regions affecting Δ¹³C on chromosomes (Chr.) 2, 3, 6, 7, and 12. One of the CSSLs, SL208, in which most regions on Chr. 3 were substituted with Kasalath segments, showed higher leaf stomatal conductance for CO₂ (g _s) and Δ¹³C than Koshihikari during the vegetative stage although leaf photosynthetic rate did not differ between them. These results suggest an association between Δ¹³C and g _s. To test this association, we performed a QTL analysis for Δ¹³C at vegetative and heading stages in an F₂ population derived from a cross between SL208 and Koshihikari. The results confirmed a QTL controlling Δ¹³C on the long arm of Chr. 3. By using a near-isogenic line specific to Hd6, we ruled out the possibility that variation in Δ¹³C was generated through the pleiotropic effect of heading date.     

Multiple quantitative trait locus analysis of bovine chromosome 6 in the Israeli Holstein population by a daughter design

Nine Israeli Holstein sire families with 2978 daughters were analyzed for quantitative trait loci effects on chromosome 6 for five milk production traits by a daughter design. All animals were genotyped for 2 markers. The three families with significant effects were genotyped for up to 10 additional markers spanning positions 0-122 cM of BTA6. Two sires were segregating for a locus affecting protein and fat percentage near position 55 cM with an estimated substitution effect of 0.18% protein, which is equivalent to one phenotypic standard deviation. This locus was localized to a confidence interval of 4 cM. One of these sires was also heterozygous for a locus affecting milk, fat, and protein production near the centromere. The hypothesis of two segregating loci was verified by multiple regression analysis. A third sire was heterozygous for a locus affecting milk and protein percentage near the telomeric end of the chromosome. Possible candidates for the major quantitative gene near position 55 cM were determined by comparative mapping. IBSP and SSP1 were used as anchors for the orthologous region on human chromosome 4. Twelve genes were detected within a 2-Mbp sequence. None of these genes have been previously associated with lactogenesis.     

Relationships between grain protein content and grain yield components through quantitative trait locus analyses in a recombinant inbred line population derived from two elite durum wheat cultivars

Grain protein content (GPC) in durum wheat (Triticum turgidum var. durum) is negatively correlated with grain yield. To evaluate possible genetic interrelationships between GPC and grain yield per spike, thousand-kernel weight and kernel number per spike, quantitative trait loci (QTL) for GPC were mapped using GPC-adjusted data in a covariance analysis on yield components. Phenotypic data were evaluated in a segregating population of 120 recombinant inbred lines derived from crossing the elite cultivars Svevo and Ciccio. The material was tested at five environments in southern Italy. QTL were determined by composite interval mapping based on the Svevo?×?Ciccio linkage map described in Gadaleta et al. (2009) and integrated with DArT markers. The close relationship between GPC and yield components was reflected in the negative correlation between the traits and in the reduction of variance when GPC values were adjusted to yield components. Ten independent genomic regions involved in the expression of GPC were detected, six of which were associated with QTL for one or more grain yield components. QTL alleles with increased GPC effects were associated with QTL alleles with decreased effects on one or more yield component traits, or vice versa (i.e. the allelic effects were in opposite direction). Four QTL for GPC showed always significant effects, and these QTL should represent genes that influence GPC independently from variation in the yield components. Such genes are of special interest in wheat breeding since they would allow an increase in GPC without a concomitant decrease in grain yield.     

Mapping of a milk production quantitative trait locus to a 1.056 Mb region on bovine chromosome 5 in the Fleckvieh dual purpose cattle breed

Background

In a previous study in the Fleckvieh dual purpose cattle breed, we mapped a quantitative trait locus (QTL) affecting milk yield (MY1), milk protein yield (PY1) and milk fat yield (FY1) during first lactation to the distal part of bovine chromosome 5 (BTA5), but the confidence interval was too large for positional cloning of the causal gene. Our objective here was to refine the position of this QTL and to define the candidate region for high-throughput sequencing.

Methods

In addition to those previously studied, new Fleckvieh families were genotyped, in order to increase the number of recombination events. Twelve new microsatellites and 240 SNP markers covering the most likely QTL region on BTA5 were analysed. Based on haplotype analysis performed in this complex pedigree, families segregating for the low frequency allele of this QTL (minor allele) were selected. Single- and multiple-QTL analyses using combined linkage and linkage disequilibrium methods were performed.

Results

Single nucleotide polymorphism haplotype analyses on representative family sires and their ancestors revealed that the haplotype carrying the minor QTL allele is rare and most probably originates from a unique ancestor in the mapping population. Analyses of different subsets of families, created according to the results of haplotype analysis and availability of SNP and microsatellite data, refined the previously detected QTL affecting MY1 and PY1 to a region ranging from 117.962 Mb to 119.018 Mb (1.056 Mb) on BTA5. However, the possibility of a second QTL affecting only PY1 at 122.115 Mb was not ruled out.

Conclusion

This study demonstrates that targeting families segregating for a less frequent QTL allele is a useful method. It improves the mapping resolution of the QTL, which is due to the division of the mapping population based on the results of the haplotype analysis and to the increased frequency of the minor allele in the families. Consequently, we succeeded in refining the region containing the previously detected QTL to 1 Mb on BTA5. This candidate region contains 27 genes with unknown or partially known function(s) and is small enough for high-throughput sequencing, which will allow future detailed analyses of candidate genes.