Bayesian joint mapping of quantitative trait loci for Gaussian and categorical characters in line crosses

Methodology for joint mapping of quantitative trait loci (QTL) affecting continuous and binary characters in experimental crosses is presented. The procedure consists of a Bayesian Gaussian-threshold model implemented via Markov chain Monte Carlo, which bypasses bottlenecks due to high-dimensional integrals required in maximum likelihood approaches. The method handles multiple binary traits and multiple QTL. Modeling of ordered categorical traits is discussed as well. Features of the method are illustrated using simulated datasets representing a backcross design, and the data are analyzed using mixed-trait and single-trait models. The mixed-trait analysis provides greater detection power of a QTL than a single-trait analysis when the QTL affects two or more traits. The number of QTL inferred in the mixed-trait analysis does not pertain to a specific trait, but the roles of each QTL on specific traits can be assessed from estimates of its effects. The impacts of varying incidence level and sample size on the mixed-trait QTL mapping analysis are investigated as well.     

Bayesian point estimation of quantitative trait loci

In this article, we consider the problem of the estimation of quantitative trait loci (QTL), those chromosomal regions at which genetic information affecting some quantitative trait is encoded. Generally the number of such encoding sites is unknown, and associations between neutral molecular marker genotypes and observed trait phenotypes are sought to locate them. We consider a Bayesian model for simple experimental designs, and discuss the existing approaches to inference for this problem. In particular, we focus on locating positions of the best candidate markers segregating for the trait, a situation which is of primary interest in comparative mapping. We introduce a loss function for estimating both the number of QTL and their location, and we illustrate its application via simulated and real data.     

Mapping quantitative trait loci using the MCMC procedure in SAS

The MCMC procedure in SAS (called PROC MCMC) is particularly designed for Bayesian analysis using the Markov chain Monte Carlo (MCMC) algorithm. The program is sufficiently general to handle very complicated statistical models and arbitrary prior distributions. This study introduces the SAS/MCMC procedure and demonstrates the application of the program to quantitative trait locus (QTL) mapping. A real life QTL mapping experiment in wheat female fertility trait was used as an example for the demonstration. The fertility trait phenotypes were described under three different models: (1) the Poisson model, (2) the Bernoulli model and (3) the zero-truncated Poisson model. One QTL was identified on the second chromosome. This QTL appears to control the switch of seed-producing ability of female plants but does not affect the number of seeds produced once the switch is turned on.     

Joint tests for quantitative trait loci in experimental crosses

Selective genotyping is common because it can increase the expected correlation between QTL genotype and phenotype and thus increase the statistical power of linkage tests (i.e., regression-based tests). Linkage can also be tested by assessing whether the marginal genotypic distribution conforms to its expectation, a marginal-based test. We developed a class of joint tests that, by constraining intercepts in regression-based analyses, capitalize on the information available in both regression-based and marginal-based tests. We simulated data corresponding to the null hypothesis of no QTL effect and the alternative of some QTL effect at the locus for a backcross and an F2 intercross between inbred strains. Regression-based and marginal-based tests were compared to corresponding joint tests. We studied the effects of random sampling, selective sampling from a single tail of the phenotypic distribution, and selective sampling from both tails of the phenotypic distribution. Joint tests were nearly as powerful as all competing alternatives for random sampling and two-tailed selection under both backcross and F2 intercross situations. Joint tests were generally more powerful for one-tailed selection under both backcross and F2 intercross situations. However, joint tests cannot be recommended for one-tailed selective genotyping if segregation distortion is suspected.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameter estimators were marginal posterior means computed using a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage, and the parameters (allele frequency, QTL substitution effect, recombination rate, polygenic and residual variances). Several MCMC algorithms were derived for computing Bayesian tests of linkage, which consisted of the marginal posterior probability of linkage and the marginal likelihood of the QTL variance associated with the marker.     

Healing quantitative trait loci in a combined cross analysis using related mouse strain crosses

Inbred mouse strains MRL and LG share the ability to fully heal ear hole punches with the full range of appropriate tissues without scarring. They also share a common ancestry, MRL being formed from a multi-strain cross with two final backcrosses to LG before being inbred by brother-sister mating. Many gene-mapping studies for healing ability have been performed using these two strains, resulting in the location of about 20 quantitative trait loci (QTLs). Here, we combine two of these crosses (N = 638), MRL/lpr × C57BL/6NTac and LG/J × SM/J, in a single combined cross analysis to increase the mapping power, decrease QTL support intervals, separate multiple QTLs and establish allelic states at individual QTL. The combined cross analysis located 11 QTLs, 6 affecting only one cross (5 LG × SM and 1 MRL × B6) and 5 affecting both crosses, approximately the number of common QTLs expected given strain SNP similarity. Amongst the five QTLs mapped in both crosses, three had significantly different genetic effects, additive in one cross and over or underdominant in the other. It is possible that allelic states at these three loci are different in SM and B6 because they lead to differences in dominance interactions with the LG and MRL alleles. QTL support intervals are 40% smaller in the combined cross analysis than in either of the single crosses. Combined cross analysis was successful in enhancing the interpretation of earlier QTL results for these strains.     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. II. A simulation study

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameters were estimated by marginal posterior means computed with a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), the event of linkage or nonlinkage, and the parameters (allele frequencies, QTL substitution effect, recombination rate, polygenic and residual variances). The analysis was evaluated empirically via application to simulated granddaughter designs consisting of 2000 sons, 20 related sires and their ancestors. Results obtained in this study and preliminary work on multiple linked markers and multiple QTLs support the usefulness of the Bayesian method for the statistical mapping of QTLs.     

A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods

Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets.     

Detection and parameter estimation for quantitative trait loci using regression models and multiple markers

A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.     

Morphological traits defining species differences in wild relatives of maize are controlled by multiple quantitative trait loci

We analyzed the genetic basis of morphological differences between two wild species of teosinte (Zea diploperennis and Z. mays ssp. parviglumis), which are relatives of maize. These two species differ in a number of taxonomically important traits including the structure of the tassel (male inflorescence), which is the focus of this report. To investigate the genetic inheritance of six tassel traits, quantitative trait locus (QTL) mapping with 95 RFLP markers was employed on a population of 425 F2 plants. Each trait was analyzed by interval mapping (IM) and composite interval mapping (CIM) to identify and characterize the QTL controlling the differences in tassel morphology. We detected two to eight QTL for each trait. In total, 30 QTL with IM and 33 QTL with CIM were found for tassel morphology. QTL for several of the traits mapped near each other, suggesting pleiotropy and/or linkage of QTL. The QTL showed small to moderate magnitudes of effect. No QTL of exceptionally large effect were found as seen under domestication and in the case of some other natural species. Thus, the model involving major QTL of large effect seems not to apply to the traits and species analyzed. A mixture of QTL with positive and negative allelic effects was found for most tassel traits and may suggest a history of periodic changes in the direction of selection during the divergence of Z. diploperennis and Z. mays ssp. parviglumis or fixation of QTL alleles by random genetic drift rather than selection.     

Confirmation of quantitative trait loci affecting fatness in chickens

In this report we describe the analysis of an advanced intercross line (AIL) to confirm the quantitative trait locus (QTL) regions found for fatness traits in a previous study. QTL analysis was performed on chromosomes 1, 3, 4, 15, 18, and 27. The AIL was created by random intercrossing in each generation from generation 2 (G₂) onwards until generation 9 (G₉) was reached. QTL for abdominal fat weight (AFW) and/or percentage abdominal fat (AF%) on chromosomes 1, 3 and 27 were confirmed in the G₉ population. In addition, evidence for QTL for body weight at the age of 5 (BW5) and 7 (BW7) weeks and for the percentage of intramuscular fat (IF%) were found on chromosomes 1, 3, 15, and 27. Significant evidence for QTL was detected on chromosome 1 for BW5 and BW7. Suggestive evidence was found on chromosome 1 for AFW, AF% and IF%, on chromosome 15 for BW5, and on chromosome 27 for AF% and IF%. Furthermore, evidence on the chromosome-wise level was found on chromosome 3 for AFW, AF%, and BW7 and on chromosome 27 for BW5. For chromosomes 4 and 18, test statistics did not exceed the significance threshold.     

Quantitative trait loci segregating in crosses between New Hampshire and White Leghorn chicken lines: I. egg production traits

A genome scan was performed to detect chromosomal regions that affect egg production traits in reciprocal crosses between two genetically and phenotypically extreme chicken lines: the partially inbred line New Hampshire (NHI) and the inbred line White Leghorn (WL77). The NHI line had been selected for high growth and WL77 for low egg weight before inbreeding. The result showed a highly significant region on chromosome 4 with multiple QTL for egg production traits between 19.2 and 82.1 Mb. This QTL region explained 4.3 and 16.1% of the phenotypic variance for number of eggs and egg weight in the F₂ population, respectively. The egg weight QTL effects are dependent on the direction of the cross. In addition, genome‐wide suggestive QTL for egg weight were found on chromosomes 1, 5, and 9, and for number of eggs on chromosomes 5 and 7. A genome‐wide significant QTL affecting age at first egg was mapped on chromosome 1. The difference between the parental lines and the highly significant QTL effects on chromosome 4 will further support fine mapping and candidate gene identification for egg production traits in chicken.     

The efficiency of mapping of quantitative trait loci using cofactor analysis in half-sib design

This simulation study was designed to study the power and type I error rate in QTL mapping using cofactor analysis in half-sib designs. A number of scenarios were simulated with different power to identify QTL by varying family size, heritability, QTL effect and map density, and three threshold levels for cofactor were considered. Generally cofactor analysis did not increase the power of QTL mapping in a half-sib design, but increased the type I error rate. The exception was with small family size where the number of correctly identified QTL increased by 13% when heritability was high and 21% when heritability was low. However, in the same scenarios the number of false positives increased by 49% and 45% respectively. With a liberal threshold level of 10% for cofactor combined with a low heritability, the number of correctly identified QTL increased by 14% but there was a 41% increase in the number of false positives. Also, the power of QTL mapping did not increase with cofactor analysis in scenarios with unequal QTL effect, sparse marker density and large QTL effect (25% of the genetic variance), but the type I error rate tended to increase. A priori, cofactor analysis was expected to have higher power than individual chromosome analysis especially in experiments with lower power to detect QTL. Our study shows that cofactor analysis increased the number of false positives in all scenarios with low heritability and the increase was up to 50% in low power experiments and with lower thresholds for cofactors.     

A sampling algorithm for segregation analysis

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated.     

Meta-analysis of results from quantitative trait loci mapping studies on pig chromosome 4

Meta-analysis of results from multiple studies could lead to more precise quantitative trait loci (QTL) position estimates compared to the individual experiments. As the raw data from many different studies are not readily available, the use of results from published articles may be helpful. In this study, we performed a meta-analysis of QTL on chromosome 4 in pig, using data from 25 separate experiments. First, a meta-analysis was performed for individual traits: average daily gain and backfat thickness. Second, a meta-analysis was performed for the QTL of three traits affecting loin yield: loin eye area, carcass length and loin meat weight. Third, 78 QTL were selected from 20 traits that could be assigned to one of three broad categories: carcass, fatness or growth traits. For each analysis, the number of identified meta-QTL was smaller than the number of initial QTL. The reduction in the number of QTL ranged from 71% to 86% compared to the total number before the meta-analysis. In addition, the meta-analysis reduced the QTL confidence intervals by as much as 85% compared to individual QTL estimates. The reduction in the confidence interval was greater when a large number of independent QTL was included in the meta-analysis. Meta-QTL related to growth and fatness were found in the same region as the FAT1 region. Results indicate that the meta-analysis is an efficient strategy to estimate the number and refine the positions of QTL when QTL estimates are available from multiple populations and experiments. This strategy can be used to better target further studies such as the selection of candidate genes related to trait variation.     

Genetic mapping of quantitative trait loci for aseasonal reproduction in sheep

The productivity and economic prosperity of sheep farming could benefit greatly from more effective methods of selection for year-round lambing. Identification of QTL for aseasonal reproduction in sheep could lead to more accurate selection and faster genetic improvement. One hundred and twenty microsatellite markers were genotyped on 159 backcross ewes from a Dorset × East Friesian crossbred pedigree. Interval mapping was undertaken to map the QTL underlying several traits describing aseasonal reproduction including the number of oestrous cycles, maximum level of progesterone prior to breeding, pregnancy status determined by progesterone level, pregnancy status determined by ultrasound, lambing status and number of lambs born. Seven chromosomes (1, 3, 12, 17, 19, 20 and 24) were identified to harbour putative QTL for one or more component traits used to describe aseasonal reproduction. Ovine chromosomes 12, 17, 19 and 24 harbour QTL significant at the 5% chromosome-wide level, chromosomes 3 and 20 harbour QTL that exceeded the threshold at the 1% chromosome-wide level, while the QTL identified on chromosome 1 exceeded the 1% experiment-wide significance level. These results are a first step towards understanding the genetic mechanism of this complex trait and show that variation in aseasonal reproduction is associated with multiple chromosomal regions.     

DNA fingerprint bands applied to linkage analysis with quantitative trait loci in chickens

Summary
An efficient approach to detect association between quantitative traits and bands of DNA fingerprint patterns uses intra-family tail analysis, which compares fingerprints of DNA mixes from individuals at the two tails of a phenotypic distribution. In analysis of 67 paternal half-sibs of a meat-type chicken family, of 57 sire bands generated by two probes, one sire-specific band (S6–6) was associated with abdominal fat deposition. The band effect was estimated by a linear model analysis to be 0–88 standard deviations, or about 30% of the family mean. The association between band S6–6 and abdominal fat was further examined by testing progeny of paternal half-sibs of the chickens which were used in the tail analysis, establishing genetic linkage between the DNA marker and a genetic locus affecting abdominal fat deposition.     

Mapping of quantitative trait loci affecting behaviour in swine

Behavioural indices in vertebrates are under genetic control at least to some extent. In spite of significant behavioural problems in farm animals, information on the genetic background of behaviour is sparse. The aim of this study was to map QTL for behavioural indices in swine under healthy conditions and after infection with Sarcocystis miescheriana , as behaviour can be significantly influenced by disease . This well-described parasite model subsequently leads to acute (day 14 p.i.), subclinical (day 28 p.i.) and chronic disease (day 42 p.i.), allowing the study and comparison of the behaviour of pigs under four different states of health or disease. The study was based on a well-described Pietrain/Meishan F₂ family that has recently allowed the detection of QTL for disease resistance. We have mapped six genome-wide significant and 24 chromosome-wide significant QTL for six behavioural indices in swine. Six of these QTL (i.e. 20% of total QTL) showed effects on behavioural traits of the healthy pigs (day 0). Some of them (QTL on SSC11 and 18) lost influence on behavioural activities during disease, while the effects of others (QTL on SSC5, SSC8) partly remained during the whole experiment, although with different effects on the distinct behavioural indices. The disease model has been of high relevance to detect effects of gene loci on behavioural indices. Considering the importance of segregating alleles and environmental conditions that allow the identification of the phenotype, we conclude that there are indeed QTL with interesting effects on behavioural indices in swine.