Bayesian multi-QTL mapping for growth curve parameters

Background Identification of QTL affecting a phenotype which is measured multiple times on the same experimental unit is not a trivial task because the repeated measures are not independent and in most cases show a trend in time. A complicating factor is that in most cases the mean increases non-linear with time as well as the variance. A two- step approach was used to analyze a simulated data set containing 1000 individuals with 5 measurements each. First the measurements were summarized in latent variables and subsequently a genome wide analysis was performed of these latent variables to identify segregating QTL using a Bayesian algorithm. Results For each individual a logistic growth curve was fitted and three latent variables: asymptote (ASYM), inflection point (XMID) and scaling factor (SCAL) were estimated per individual. Applying an 'animal' model showed heritabilities of approximately 48% for ASYM and SCAL while the heritability for XMID was approximately 24%. The genome wide scan revealed four QTLs affecting ASYM, one QTL affecting XMID and four QTLs affecting SCAL. The size of the QTL differed. QTL with a larger effect could be more precisely located compared to QTL with small effect. The locations of the QTLs for separate parameters were very close in some cases and probably caused the genetic correlation observed between ASYM and XMID and SCAL respectively. None of the QTL appeared on chromosome five. Conclusions Repeated observations on individuals were affected by at least nine QTLs. For most QTL a precise location could be determined. The QTL for the inflection point (XMID) was difficult to pinpoint and might actually exist of two closely linked QTL on chromosome one

Statistical identification of major genes in pigs

Litter size is an important characteristic in pig breeding. Apart from selection within available lines, also the development of a synthetic line with the Chinese Meishan breed could be an interesting approach to obtain a line with an increased level of litter size. To investigate genetic aspects of traits of interest in such a synthetic line, Dutch pig breeding companies have produced F 1 and F 2 Meishan x Western crossbreds. This thesis focusses on one important genetic aspect, the presence of major genes. In Chapters 2 to 4, statistical methodology to model a major gene inheritance is investigated and developed Chapters 5 and 6 consider analysis of data collected on the produced Meishan crossbreds for presence of major genes. To develop a synthetic line with Meishan, presence of major genes affecting litter size, growth and fatness is of interest. Additionally, the presence of major genes is investigated for meat quality traits.Statistical methodologyIn Chapter 2, the possibility to detect major genes by use of F 1 and F 2 is investigated. Here, special attention is paid to the situation where alleles at the major locus are fixed in the founder populations. Using 1000 F 2 observations, the power to detect major genes reaches more than 95% for additive and completely dominant effects (difference between homozygotes) of 4 and 2 residual standard deviations, respectively. When F, data is included, any increase in variance from F 1 to F 2 biases parameter estimates and leads to putative detection of a major gene. Also when in reality alleles at the major locus segregate in the founder populations, parameter estimates become biased, unless the average allele frequency in the founder populations is exactly 0.5. Use of data and use of a model in which alleles segregate in parents, e.g. F 3 data, is concluded to give better robustness and larger power. The latter is confirmed in a separate study, as referenced in Chapter 7, which shows that effects up to 4 times as small can be detected when alleles at the major locus segregate in the founder lines. Based on the findings in Chapter 2, Chapters 3 and 4 focus on the development of general models for a mixed inheritance. Use of such models is referred to as 'segregation analysis'.In Chapter 3, an advancement is made for use of analytical approaches to segregation analysis. It is noted that animal breeding pedigrees, as opposed to human pedigrees, generally contain many loops, such that exact computation of likelihoods isinfeasible. Loops in animal breeding pedigrees arise due to multiple matings, i.e. sires are generally mated to several dams, and due to inbreeding. Multiple matings generally already create many loops when considering 3-generation pedigrees. In Chapter 3, 'iterative peeling' is introduced, a method equivalent to the traditional recursive peeling method to compute exact likelihoods in non-looped pedigrees, but which also can be used to obtain approximate likelihoods in looped pedigrees. In simulations, hypothesis testing and parameter estimation are compared based on approximated likelihoods in looped pedigrees and exact likelihoods in non-looped pedigrees. This shows that no biases are introduced by the approximation in looped pedigrees. Iterative peeling is developed and investigated using a monogenic model, but could be extended to compute likelihoods for a mixed inheritance model. Such extension, however, was not made because an alternative non-analytical approach became available and was developed in Chapter 4. 0In Chapter 4, the application of Gibbs sampling is considered for inference in a mixed inheritance model. Gibbs sampling is a Markov chain Monte Carlo procedure which does not require analytical approximation. The approximation in such an approach is of a different nature: a marginal posterior distribution, or a feature thereof, is estimated based on a finite sample from the true posterior distribution. To generate such a sample, a Markov chain is constructed with an equilibrium distribution equal to the posterior distribution to be approximated. For application of Gibbs sampling to a mixed inheritance model, an implementation on scalar components, as used for human populations, appears not efficient because mixing of parameters in the Markov chain is slow. Therefore, an approach with blockwise sampling of genotypes is proposed for use in animal populations. The blockwise sampling, by which genotypes of a sire and its final progeny were sampled jointly, is effective to improve mixing. In Chapter 4 it is concluded that further measures to improve mixing could be looked for. In later Chapters such a further improvement is found in the additional use of a relaxation technique. In Chapter 4, inferences are made from a single Gibbs chain. In later Chapters, this approach is improved by use of multiple chains from which convergence of the Gibbs sampler is assessed by comparison of between- and within chain variances in an analysis- of-variance. The use of Bayesian estimators, which is feasible when using Gibbs sampling, is found preferable over the use of classical maximum likelihood estimators. In Chapter 7, it is discussed that the use of Bayeslian procedures fits in a general trend to better account for uncertainty in statistical estimation procedures.Analysis of dataIn Chapters 5 and 6, analysis of data obtained on the Meishan crossbreds is presented. In Chapter 5, presence of major genes affecting meat quality traits is investigated using data from F 2 individuals. Cooking loss, drip loss, two pH measurements, intramuscular fat, shearforce and back-fat thickness (by HGP measurement) are found to be likely influenced by a major gene. In all cases, a recessive allele is found, which originates from one of the founder lines, likely the Meishan breed. By studying associations between genotypes for major genes affecting the various traits, it is concluded that cooking loss, two pH measurements and possibly backfat thickness are influenced by one gene, and that a second gene influences intramuscular fat and possibly shearforce and drip loss. The statistical findings are supported by demonstrating marked differences in vanances of families of fathers inferred as carriers and families of fathers inferred as non-carriers.In Chapter 6, presence of major genes is investigated for two growth traits, backfat thickness (by" ultrasonic measurement) and litter size at first and second parity, using data from F 1 and F 2 crossbreds. Here, two analyses are performed for each trait. In a first analysis, joint analysis of F, and F 2 crossbred data is performed, in which different error variances are fitted for F 1 and F 2 observations. In this first analysis, significant contributions of major-gene variance are found for the two growth traits, for backfat, and for litter size at first parity. In a second analysis, analysis of F 2 data only is performed to check whether no biases are introduced in the joint analysis of F 1 and F 2 data. In the second analysis, no major genes are found for growth traits. Major genes affecting backfat and litter size at first parity are confirmed. Effects of the gene affecting backfat are similar to the effects of the gene affecting backfat identified in Chapter 5, and this likely is the same gene. The major genes affecting backfat and litter size are dominant genes, of which the recessive alleles can be considered unfavourable.. the recessive alleles of these genes cause an increase of backfat and a decrease of litter size.General results from the statistical analyses indicate that further molecular genetic research effort to map these genes will have a high probability of success. III Chapter 7 benefits are discussed from selection against the recessive alleles of the genes influencing backfat and litter size, as well as use of the gene affecting intramuscular fat to produce extra-tasty quality meat.ConclusionsIn this thesis, segregation analysis (SA) is made applicable for use in animal populations. SA will be a valuable addition to linkage analysis, where SA will be more typically applied to large amounts of data which are routinely collected. In the search for genes affecting quantitative traits, SA can directly identify functional genes, and can estimate genotypes of animals for such a functional gene. In combination with linkage analyses, this could supply important aids for molecular geneticists to locate functional genes. In this thesis, a number of major genes was identified to affect traits in the Meishan crosses. Further genetic analyses could generate more knowledge on the regulation of the quantitative traits involved and will aid in assessing the value of these genes for practical breeding. Chapter 8 additionally describes expected variance changes in a synthetic line, which could aid to optimise selection in such a line

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

Using SNP Markers to Estimate Additive, Dominance and Imprinting Genetic Variance

The contributions of additive, dominance and imprinting effects to the variance of number of teats (NT) were evaluated in two purebred pig populations using SNP markers. Three different random regression models were evaluated, accounting for the mean and: 1) additive effects (MA), 2) additive and dominance effects (MAD) and 3) additive, dominance and imprinting effects (MADI). Additive heritability estimates were 0.30, 0.28 and 0.27-0.28 in both lines using MA, MAD and MADI, respectively. Dominance heritability ranged from 0.06 to 0.08 using MAD and MADI. Imprinting heritability ranged from 0.01 to 0.02. Dominance effects make an important contribution to the genetic variation of NT in the two lines evaluated. Imprinting effects appeared less important for NT than additive and dominance effects. The SNP random regression model presented and evaluated in this study is a feasible approach to estimate additive, dominance and imprinting variance