QTL detection and allelic effects for growth and fat traits in outbred pig populations

Quantitative trait loci (QTL) for growth and fatness traits have previously been identified on chromosomes 4 and 7 in several experimental pig populations. The segregation of these QTL in commercial pigs was studied in a sample of 2713 animals from five different populations. Variance component analysis (VCA) using a marker-based identity by descent (IBD) matrix was applied. The IBD coefficient was estimated with simple deterministic (SMD) and Markov chain Monte Carlo (MCMC) methods. Data for two growth traits, average daily gain on test and whole life daily gain, and back fat thickness were analysed. With both methods, seven out of 26 combinations of population, chromosome and trait, were significant. Additionally, QTL genotypic and allelic effects were estimated when the QTL effect was significant. The range of QTL genotypic effects in a population varied from 4.8% to 10.9% of the phenotypic mean for growth traits and 7.9% to 19.5% for back fat trait. Heritabilities of the QTL genotypic values ranged from 8.6% to 18.2% for growth traits, and 14.5% to 19.2% for back fat. Very similar results were obtained with both SMD and MCMC. However, the MCMC method required a large number of iterations, and hence computation time, especially when the QTL test position was close to the marker.     

Simple deterministic identity-by-descent coefficients and estimation of QTL allelic effects in full and half sibs

Accurate and rapid methods for the detection of quantitative trait loci (QTLs) and evaluation of consequent allelic effects are required to implement marker-assisted selection in outbred populations. In this study, we present a simple deterministic method for estimating identity-by-descent (IBD) coefficients in full- and half-sib families that can be used for the detection of QTLs via a variance-component approach. In a simulated dataset, IBD coefficients among sibs estimated by the simple deterministic and Markov chain Monte Carlo (MCMC) methods with three or four alleles at each marker locus exhibited a correlation of greater than 0.99. This high correlation was also found in QTL analyses of data from an outbred pig population. Variance component analysis used both the simple deterministic and MCMC methods to estimate IBD coefficients. Both procedures detected a QTL at the same position and gave similar test statistics and heritabilities. The MCMC method, however, required much longer computation than the simple method. The conversion of estimated QTL genotypic effects into allelic effects for use in marker-assisted selection is also demonstrated.     

Multitrait fine mapping of quantitative trait loci using combined linkage disequilibria and linkage analysis

A novel multitrait fine-mapping method is presented. The method is implemented by a model that treats QTL effects as random variables. The covariance matrix of allelic effects is proportional to the IBD matrix, where each element is the probability that a pair of alleles is identical by descent, given marker information and QTL position. These probabilities are calculated on the basis of similarities of marker haplotypes of individuals of the first generation of genotyped individuals, using "gene dropping" (linkage disequilibrium) and transmission of markers from genotyped parents to genotyped offspring (linkage). A small simulation study based on a granddaughter design was carried out to illustrate that the method provides accurate estimates of QTL position. Results from the simulation also indicate that it is possible to distinguish between a model postulating one pleiotropic QTL affecting two traits vs. one postulating two closely linked loci, each affecting one of the traits.     

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

Background

Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞ genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞ model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).

Results

In this paper, we further explore the differences and links between the F_∞ and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞ models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞ model. A new way of linking the Cockerham and F_∞ model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞ models are applied.

Conclusion

The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞ regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞ model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞ model can then be calculated by translating formulas derived for the Cockerham models.

     

A Random Model Approach to Interval Mapping of Quantitative Trait Loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.     

QTL analysis in arbitrary pedigrees with incomplete marker information

Mapping quantitative trait loci (QTL) in arbitrary outbred pedigrees is complicated by the combinatorial possibilities of allele flow relationships and of the founder allelic configurations. Exact methods are only available for rather short and simple pedigrees. Stochastic simulation using Markov chain Monte Carlo (MCMC) integration offers more flexibility. MCMC methods are less natural in a frequentist than in a Bayesian context, which we therefore adopt. Among the MCMC algorithms for updating marker locus genotypes, we implement the descent-graph algorithm. It can be used to update marker locus allele flow relationships and can handle arbitrarily complex pedigrees and missing marker information. Compared with updating marker genotypic information, updating QTL parameters, such as position, effects, and the allele flow relationships is relatively easy with MCMC. We treat the effect of each diploid combination of founder alleles as a random variable and only estimate the variance of these effects, ie, we model diploid genotypic effects instead of the usual partition in additive and dominance effects. This is a variant of the random model approach. The number of QTL alleles is generally unknown. In the Bayesian context, the number of QTL present on a linkage group can be treated as variable. Computer simulations suggest that the algorithm can indeed handle complex pedigrees and detect two QTL on a linkage group, but that the number of individuals in a single extended family is limited to about 50 to 100 individuals.     

Testing for homogeneity of gametic disequilibrium across strata

Background

Variance component (VC) models are commonly used for Quantitative Trait Loci (QTL) mapping in outbred populations. Here, the QTL effect is given as a random effect and a critical part of the model is the relationship between the phenotypic values and the random effect. In the traditional VC model, each individual has a unique QTL effect and the relationship between these random effects is given as a covariance structure (known as the identity-by-descent (IBD) matrix).

Results

We present an alternative notation of the variance component model, where the elements of the random effect are independent base generation allele effects and sampling term effects. The relationship between the phenotypic vales and the random effect is given by an incidence matrix, which results in a novel, but statistically equivalent, version of the traditional VC model. A general algorithm to estimate this incidence matrix is presented. Since the model is given in terms of base generation allele effects and sampling term effects, these effects can be estimated separately using best linear unbiased prediction (BLUP). From simulated data, we showed that biallelic QTL effects could be accurately clustered using the BLUP obtained from our model notation when markers are fully informative, and that the accuracy increased with the size of the QTL effect. We also developed a measure indicating whether a base generation marker homozygote is a QTL heterozygote or not, by comparing the variances of the sampling term BLUP and the base generation allele BLUP. A ratio greater than one gives strong support for a QTL heterozygote.

Conclusion

We developed a simple presentation of the VC QTL model for identification of base generation allele effects in QTL linkage analysis. The base generation allele effects and sampling term effects were separated in our model notation. This clarifies the assumptions of the model and should also enhance the development of genome scan methods.     

Computation of the Full Likelihood Function for Estimating Variance at a Quantitative Trait Locus

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n X n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.     

Using dominance relationship coefficients based on linkage disequilibrium and linkage with a general complex pedigree to increase mapping resolution

Dominance (intralocus allelic interactions) plays often an important role in quantitative trait variation. However, few studies about dominance in QTL mapping have been reported in outbred animal or human populations. This is because common dominance effects can be predicted mainly for many full sibs, which do not often occur in outbred or natural populations with a general pedigree. Moreover, incomplete genotypes for such a pedigree make it infeasible to estimate dominance relationship coefficients between individuals. In this study, identity-by-descent (IBD) coefficients are estimated on the basis of population-wide linkage disequilibrium (LD), which makes it possible to track dominance relationships between unrelated founders. Therefore, it is possible to use dominance effects in QTL mapping without full sibs. Incomplete genotypes with a complex pedigree and many markers can be efficiently dealt with by a Markov chain Monte Carlo method for estimating IBD and dominance relationship matrices (D(RM)). It is shown by simulation that the use of D(RM) increases the likelihood ratio at the true QTL position and the mapping accuracy and power with complete dominance, overdominance, and recessive inheritance modes when using 200 genotyped and phenotyped individuals.     

Anthropogenic effects on population genetics of phytophagous insects associated with domesticated plants

The hypothesis of isolation by distance (IBD) predicts that genetic differentiation between populations increases with geographic distance. However, gene flow is governed by numerous factors and the correlation between genetic differentiation and geographic distance is never simply linear. In this study, we analyze the interaction between the effects of geographic distance and of wild or domesticated status of the host plant on genetic differentiation in the bean beetle Acanthoscelides obvelatus. Geographic distance explained most of the among-population genetic differentiation. However, IBD varied depending on the kind of population pairs for which the correlation between genetic differentiation and geographic distance was examined. Whereas pairs of beetle populations associated with wild beans showed significant IBD (P < 10(-4)), no IBD was found when pairs of beetle populations on domesticated beans were examined (P= 0.2992). This latter result can be explained by long-distance migrations of beetles on domesticated plants resulting from human exchanges of bean seeds. Beetle populations associated with wild beans were also significantly more likely than those on domesticated plants to contain rare alleles. However, at the population level, beetles on cultivated beans were similar in allelic richness to those on wild beans. This similarity in allelic richness combined with differences in other aspects of the genetic diversity (i.e., IBD, allelic diversity) is compatible with strongly contrasting effects of migration and drift. This novel indirect effect of human actions on gene flow of a serious pest of a domesticated plant has important implications for the spread of new adaptations such as resistance to pesticides.     

Incorporation of genotype effects into animal model evaluations when only a small fraction of the population has been genotyped

The method of Israel and Weller (Estimation of candidate gene effects in dairy cattle populations. Journal of Dairy Science 1998, 81, 1653-1662) to estimate quantitative trait locus (QTL) effects when only a small fraction of the population was genotyped was investigated by simulation. The QTL effect was underestimated in all cases, but bias was greater for extreme allelic frequencies, and increased with the number of generations included in the simulations. Apparently, as the fraction of animals with inferred genotypes increases, the genotype probabilities tend to 'mimic' the effect of relationships. Unbiased estimates of QTL effects were derived by a modified 'cow model' without the inclusion of the relationship matrix on simulated data, even though only a small fraction of the population was genotyped. This method yielded empirically unbiased estimates for the effects of the genes DGAT1 and ABCG2 on milk production traits in the Israeli Holstein population. Based on these results, an efficient algorithm for marker-assisted selection in dairy cattle was proposed. Quantitative trait loci effects are estimated and subtracted from the cows' records. Genetic evaluations are then computed for the adjusted records. Animals are then selected based on the sum of their polygenic genetic evaluations and QTL effects. This scheme differs from a traditional dairy cattle breeding scheme in that all bull calves were considered candidates for selection. At year 10, total genetic gain was 20% greater by the proposed algorithm as compared to the selection based on a standard animal model for a locus with a substitution effect of 0.5 phenotypic standard deviations. The proposed method is easy to apply, and all required software are 'on the shelf.' It is only necessary to genotype breeding males, which are a very small fraction of the entire population. The method is flexible with respect to the model used for routine genetic evaluation. Any number of genetic markers can be easily incorporated into the algorithm, and the reduction in genetic gain due to incorrect QTL determination is minimal.     

Optimal haplotype structure for linkage disequilibrium-based fine mapping of quantitative trait loci using identity by descent

A linkage disequilibrium-based method for fine mapping quantitative trait loci (QTL) has been described that uses similarity between individuals' marker haplotypes to determine if QTL alleles are identical by descent (IBD) to model covariances among individuals' QTL alleles for a mixed linear model. Mapping accuracy with this method was found to be sensitive to the number of linked markers that was included in the haplotype when fitting the model at a putative position of the QTL. The objective of this study was to determine the optimal haplotype structure for this IBD-based method for fine mapping a QTL in a previously identified QTL region. Haplotypes consisting of 1, 2, 4, 6, or all 10 available markers were fit as a "sliding window" across the QTL region under ideal and nonideal simulated population conditions. It was found that using haplotypes of 4 or 6 markers as a sliding "window" resulted in the greatest mapping accuracy under nearly all conditions, although the true IBD state at a putative QTL position was most accurately predicted by IBD probabilities obtained using all markers. Using 4 or 6 markers resulted in greater discrimination of IBD probabilities between positions while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Fitting IBD probabilities on the basis of a single marker resulted in the worst mapping accuracy under all conditions because it resulted in poor accuracy of IBD probabilities. In conclusion, for fine mapping using IBD methods, marker information must be used in a manner that results in sensitivity of IBD probabilities to the putative position of the QTL while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Contrary to expectation, use of haplotypes of 4-6 markers to derive IBD probabilities, rather than all available markers, best fits these criteria. Thus for populations similar to those simulated here, optimal mapping accuracy for this IBD-based fine-mapping method is obtained with a haplotype structure including a subset of all available markers.     

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

The estimation of gametic effects via marker-assisted BLUP requires the inverse of the conditional gametic relationship matrix G. Both gametes of each animal can either be identified (distinguished) by markers or by parental origin. By example, it was shown that the conditional gametic relationship matrix is not unique but depends on the mode of gamete identification. The sum of both gametic effects of each animal – and therefore its estimated breeding value – remains however unaffected. A previously known algorithm for setting up the inverse of G was generalized in order to eliminate the dependencies between columns and rows of G. In the presence of dependencies the rank of G also depends on the mode of gamete identification. A unique transformation of estimates of QTL genotypic effects into QTL gametic effects was proven to be impossible. The properties of both modes of gamete identification in the fields of application are discussed.     

Detection of multiple quantitative trait loci and their pleiotropic effects in outbred pig populations

Background

Simultaneous detection of multiple QTLs (quantitative trait loci) may allow more accurate estimation of genetic effects. We have analyzed outbred commercial pig populations with different single and multiple models to clarify their genetic properties and in addition, we have investigated pleiotropy among growth and obesity traits based on allelic correlation within a gamete.

Methods

Three closed populations, (A) 427 individuals from a Yorkshire and Large White synthetic breed, (B) 547 Large White individuals and (C) 531 Large White individuals, were analyzed using a variance component method with one-QTL and two-QTL models. Six markers on chromosome 4 and five to seven markers on chromosome 7 were used.

Results

Population A displayed a high test statistic for the fat trait when applying the two-QTL model with two positions on two chromosomes. The estimated heritabilities for polygenic effects and for the first and second QTL were 19%, 17% and 21%, respectively. The high correlation of the estimated allelic effect on the same gamete and QTL test statistics suggested that the two separate QTL which were detected on different chromosomes both have pleiotropic effects on the two fat traits. Analysis of population B using the one-QTL model for three fat traits found a similar peak position on chromosome 7. Allelic effects of three fat traits from the same gamete were highly correlated suggesting the presence of a pleiotropic QTL. In population C, three growth traits also displayed similar peak positions on chromosome 7 and allelic effects from the same gamete were correlated.

Conclusion

Detection of the second QTL in a model reduced the polygenic heritability and should improve accuracy of estimated heritabilities for both QTLs.     

Pleiotropic effects of the Arabidopsis cryptochrome 2 allelic variation underlie fruit trait-related QTL

The previous molecular identification of a flowering time QTL segregating in the Arabidopsis L er x Cvi cross, demonstrated that natural allelic variation at the blue light photoreceptor CRY2 gene affects flowering time (El-Assal et al., 2001). In addition, previous works on the same cross have mapped several QTL affecting other unrelated life history traits in the CRY2 genomic region. In the present report, we have used a set of Arabidopsis L er transgenic plants carrying four different functional CRY2 transgenes for phenotypic analyses, with the aim of exploring the extent of pleiotropy of CRY2 allelic variation. It is concluded that previously identified QTL affecting fruit length, ovule number per fruit, and percentage of unfertilized ovules are caused by this same Ler/Cvi CRY2 allelic variation. In addition, dose effects of the CRY2-L er allele are detected for fruit length. A seed weight QTL at the map position of CRY2 could not be confirmed and also no effect on seed dormancy was observed. Thus, it is shown that transgenic plants carrying different alleles can be a useful tool to attribute QTL for different complex traits to a specific locus, even when the relationship among the traits has not been previously suggested.     

Estimating genetic variance contributed by a quantitative trait locus: A random model approach

Detecting quantitative trait loci (QTL) and estimating QTL variances (represented by the squared QTL effects) are two main goals of QTL mapping and genome-wide association studies (GWAS). However, there are issues associated with estimated QTL variances and such issues have not attracted much attention from the QTL mapping community. Estimated QTL variances are usually biased upwards due to estimation being associated with significance tests. The phenomenon is called the Beavis effect. However, estimated variances of QTL without significance tests can also be biased upwards, which cannot be explained by the Beavis effect; rather, this bias is due to the fact that QTL variances are often estimated as the squares of the estimated QTL effects. The parameters are the QTL effects and the estimated QTL variances are obtained by squaring the estimated QTL effects. This square transformation failed to incorporate the errors of estimated QTL effects into the transformation. The consequence is biases in estimated QTL variances. To correct the biases, we can either reformulate the QTL model by treating the QTL effect as random and directly estimate the QTL variance (as a variance component) or adjust the bias by taking into account the error of the estimated QTL effect. A moment method of estimation has been proposed to correct the bias. The method has been validated via Monte Carlo simulation studies. The method has been applied to QTL mapping for the 10-week-body-weight trait from an F₂ mouse population.     

Detection and modelling of time-dependent QTL in animal populations

A longitudinal approach is proposed to map QTL affecting function-valued traits and to estimate their effect over time. The method is based on fitting mixed random regression models. The QTL allelic effects are modelled with random coefficient parametric curves and using a gametic relationship matrix. A simulation study was conducted in order to assess the ability of the approach to fit different patterns of QTL over time. It was found that this longitudinal approach was able to adequately fit the simulated variance functions and considerably improved the power of detection of time-varying QTL effects compared to the traditional univariate model. This was confirmed by an analysis of protein yield data in dairy cattle, where the model was able to detect QTL with high effect either at the beginning or the end of the lactation, that were not detected with a simple 305 day model.     

Quantitative trait locus mapping based on resampling in a vast maize testcross experiment and its relevance to quantitative genetics for complex traits

From simulation studies it is known that the allocation of experimental resources has a crucial effect on power of QTL detection as well as on accuracy and precision of QTL estimates. In this study, we used a very large experimental data set composed of 976 F(5) maize testcross progenies evaluated in 19 environments and cross-validation to assess the effect of sample size (N), number of test environments (E), and significance threshold on the number of detected QTL, the proportion of the genotypic variance explained by them, and the corresponding bias of estimates for grain yield, grain moisture, and plant height. In addition, we used computer simulations to compare the usefulness of two cross-validation schemes for obtaining unbiased estimates of QTL effects. The maximum, validated genotypic variance explained by QTL in this study was 52.3% for grain moisture despite the large number of detected QTL, thus confirming the infinitesimal model of quantitative genetics. In both simulated and experimental data, the effect of sample size on power of QTL detection as well as on accuracy and precision of QTL estimates was large. The number of detected QTL and the proportion of genotypic variance explained by QTL generally increased more with increasing N than with increasing E. The average bias of QTL estimates and its range were reduced by increasing N and E. Cross-validation performed well with respect to yielding asymptotically unbiased estimates of the genotypic variance explained by QTL. On the basis of our findings, recommendations for planning of QTL mapping experiments and allocation of experimental resources are given.     

Analysing the genetic control of peach fruit quality through an ecophysiological model combined with a QTL approach

Ecophysiological models are increasingly expected to include genetic information via genotype-dependent parameters. These parameters could be considered as quantitative traits and submitted to analysis. A pre-existing ecophysiological model of fruit quality was used and the distribution of the genotypic parameters in a second backcross population derived from a clone of a wild peach (Prunus davidiana) and commercial nectarine varieties (P. persica (L.) Batsch) was analysed. The correlations between the two years of experimentation were higher for the genotypic parameters than for the quality traits commonly studied by breeders. The correlations between the genotypic parameters and the quality traits were low. Quantitative trait loci (QTLs) for the genotypic key parameters of the ecophysiological model were detected by linear regression. Co-locations of QTLs for parameters were observed as well as co-locations of QTLs for parameters and quality traits. The ecophysiological model and the results of the QTL analysis were combined by substituting each parameter in the model by the sum of QTL effects. This combined model can simulate the behaviour of genotypes carrying diverse combinations of alleles. The quality of this combined model was moderately suitable, but had some shortcomings. Improvements are suggested and further use of this combined model as a tool for breeders is discussed.     

MCQTL: multi-allelic QTL mapping in multi-cross design

The aim of the MCQTL software package is to perform QTL mapping in multi-cross designs. It allows the analysis of the usual populations derived from inbred lines and can link the families by assuming that the QTL locations are the same in all of them. Moreover, a diallel modelling of the QTL genotypic effects is allowed in multiple related families. The implemented model is a linear regression model. A composite interval mapping and an iterative QTL mapping are implemented to deal with multiple QTL models. Marker cofactor selections by forward or backward stepwise methods are implemented as well as computation of threshold test value by permutation. AVAILABILITY: The program is available on request after signing a licence agreement; free of charge for academic and non-profit organizations at http://www.genoplante.org (Bioinformatics products).