Estimation of effects of quantitative trait loci in large complex pedigrees

A simple strategy for managing many recessive disorders in a dairy cattle breeding program

Background

High-density single nucleotide polymorphism genotypes have recently been used to identify a number of novel recessive mutations that adversely affect fertility in dairy cattle, as well as to track other conditions such as red coat color and polled. Most current methods for mate allocation fail to consider this information, and it will become increasingly difficult to manage matings as the number of recessive mutations to be accounted for increases.

Methods

A modified version of a mating strategy that constrains inbreeding based on genomics (the Pryce method) was developed that also accounts for the economic effects of Mendelian disorders on overall economic merit (modified Pryce method) and compared with random mating, truncation selection, and the Pryce scheme. Several scenarios were considered, including scenarios with six hypothetical recessive alleles and 12 recessive alleles that are currently segregating in the US Holstein population.

Results

The Pryce method and the modified Pryce method showed similar ability to reduce frequencies of recessive alleles, particularly for loci with frequencies greater than 0.30. The modified Pryce method outperformed the Pryce method for low-frequency alleles with small economic value. Cumulative genetic gain for the selection objective was slightly greater when using the Pryce method, but rates of inbreeding were similar across methods.

Conclusions

The proposed method reduces allele frequencies faster than other methods, and also can be used to maintain or increase the frequency of desirable recessives. It can be easily implemented in software for mate allocation, and the code used in this study is freely available as a reference implementation.

Genetic evaluation with major genes and polygenic inheritance when some animals are not genotyped using gene content multiple-trait BLUP

Background

In pedigreed populations with a major gene segregating for a quantitative trait, it is not clear how to use pedigree, genotype and phenotype information when some individuals are not genotyped. We propose to consider gene content at the major gene as a second trait correlated to the quantitative trait, in a gene content multiple-trait best linear unbiased prediction (GCMTBLUP) method.

Results

The genetic covariance between the trait and gene content at the major gene is a function of the substitution effect of the gene. This genetic covariance can be written in a multiple-trait form that accommodates any pattern of missing values for either genotype or phenotype data. Effects of major gene alleles and the genetic covariance between genotype at the major gene and the phenotype can be estimated using standard EM-REML or Gibbs sampling. Prediction of breeding values with genotypes at the major gene can use multiple-trait BLUP software. Major genes with more than two alleles can be considered by including negative covariances between gene contents at each different allele. We simulated two scenarios: a selected and an unselected trait with heritabilities of 0.05 and 0.5, respectively. In both cases, the major gene explained half the genetic variation. Competing methods used imputed gene contents derived by the method of Gengler et al. or by iterative peeling. Imputed gene contents, in contrast to GCMTBLUP, do not consider information on the quantitative trait for genotype prediction. GCMTBLUP gave unbiased estimates of the gene effect, in contrast to the other methods, with less bias and better or equal accuracy of prediction. GCMTBLUP improved estimation of genotypes in non-genotyped individuals, in particular if these individuals had own phenotype records and the trait had a high heritability. Ignoring the major gene in genetic evaluation led to serious biases and decreased prediction accuracy.

Conclusions

CGMTBLUP is the best linear predictor of additive genetic merit including pedigree, phenotype, and genotype information at major genes, since it considers missing genotypes. Simulations confirm that it is a simple, efficient and theoretically sound method for genetic evaluation of traits influenced by polygenic inheritance and one or several major genes.

Mapping QTLs with digenic epistasis under multiple environments and predicting heterosis based on QTL effects

Mixed linear model approach was proposed for mapping QTLs with the digenic epistasis and QTL by environment (QE) interaction as well as additive and dominant effects. Monte Carlo simulations indicated that the proposed method could provide unbiased estimations for both positions and genetic main effects of QTLs, as well as unbiased predictions for QE interaction effects. A method was suggested for predicting heterosis based on individual QTL effects. The immortalized F(2) (IF(2)) population constructed by random mating among RI or DH lines is appropriate for mapping QTLs with epistasis and their QE interaction. Based on the models and methodology proposed, we developed a QTL mapping software, QTLMapper 2.0 on the basis of QTLmapper 1.0, which is suitable for analyzing populations of DH, RIL, F(2) and IF(2). Data of thousand grain weight of IF(2) population with 240 lines derived from elite hybrid rice Shanyou 63 were analyzed as a worked example.

Mixture model equations for marker-assisted genetic evaluation

Marker-assisted genetic evaluation needs to infer genotypes at quantitative trait loci (QTL) based on the information of linked markers. As the inference usually provides the probability distribution of QTL genotypes rather than a specific genotype, marker-assisted genetic evaluation is characterized by the mixture model because of the uncertainty of QTL genotypes. It is, therefore, necessary to develop a statistical procedure useful for mixture model analyses. In this study, a set of mixture model equations was derived based on the normal mixture model and the EM algorithm for evaluating linear models with uncertain independent variables. The derived equations can be seen as an extension of Henderson's mixed model equations to mixture models and provide a general framework to deal with the issues of uncertain incidence matrices in linear models. The mixture model equations were applied to marker-assisted genetic evaluation with different parameterizations of QTL effects. A sire-QTL-effect model and a founder-QTL-effect model were used to illustrate the application of the mixture model equations. The potential advantages of the mixture model equations for marker-assisted genetic evaluation were discussed. The mixed-effect mixture model equations are flexible in modelling QTL effects and show desirable properties in estimating QTL effects, compared with Henderson's mixed model equations.

Polygenic variation and transmission factors involved in the resistance/susceptibility to scrapie in a Romanov flock

Data from 4049 Romanov sheep belonging to a flock affected by natural scrapie were analysed by using survival-analysis techniques. Failure time was defined as the period of time between first exposure to infection and the date that animals left the flock with scrapie signs. Four hundred and forty-seven sheep were identified as ‘scrapie animals’. Several models, including level of exposure as a time-dependent effect, PrP genotype, sex, age at first exposure, litter size and factors related to vertical transmission, were tested. The best model was extended to a sire–dam frailty model, in order to estimate the polygenic variation in addition to that in the Prnp gene. A combined effect of rearing type and the dam's disease status was detected. Thus, only sheep with a low degree of exposure to infection as lambs (lambs reared artificially and born out of a healthy dam) showed less risk than others. Animals first exposed to infection at older ages seemed to be less susceptible to scrapie. In this Romanov population, new genotypes (AHQ/AHQ, AHQ/VRQ, ARR/VRQ and ARR/ARQ) were associated with risk, suggesting the effect of genotypes on the incubation period of animals. Polygenic variance was responsible for 21 % of the total genetic variability that was related to susceptibility to scrapie. Therefore, the genetic susceptibility to scrapie may be explained by the joint effect of point mutations at the Prnp major gene and a number of genes that modulate its effect.

Strategies to utilize marker-quantitative trait loci associations

Marker-assisted selection holds promise because genetic markers provide completely heritable traits than can be measured at any age in either sex and that are potentially correlated with traits of economic value. Theoretical and simulation studies show that the advantage of using marker-assisted selection can be substantial, particularly when marker information is used, because normal selection is less effective, for example, for sex-limited or carcass traits. Assessment of the available information and its most effective use is difficult, but approaches such as crossvalidation may help in this respect. Marker systems are now becoming available that allow the high density of markers required for close associations between marker loci and trait loci. Emerging technologies could allow large numbers of polymorphic sites to be identified, practically guaranteeing that markers will be available that are in complete association with any trait locus. Identifying which polymorphism out of many that is associated with any trait will remain problematic, but multiple-locus disequilibrium measures may allow performance to be associated with unique marker haplotypes. This type of approach, combined with cheap and high density markers, could allow a move from selection based on a combination of "infinitesimal" effects plus individual loci to effective total genomic selection. In such a unified model, each region of the genome would be given its appropriate weight in a breeding program. However, the collection of good quality trait information will remain central to the use of these technologies for the foreseeable future.

Detection and utilization of single genes without DNA assays

Quantitative traits are often assumed to be controlled by a large number of loci that each have a small effect. Under this assumption, the distribution of genotypic and phenotypic values can be adequately modeled by a multivariate normal distribution. Thus, most genetic analyses are based on mixed linear models. Evidence is accumulating, however, for the presence of loci that have large effects on traits of economic importance. If the genotypes for such loci can be observed without error, then--conditional on these observed genotypes--genotypic and phenotypic values follow a multivariate normal distribution, and data from very large pedigrees can be analyzed using a mixed linear model that includes the genotypic effects for these loci as fixed effects. However, when the major genotype is not observed, the genotypic and phenotypic values follow a mixture of multivariate normal distributions, and analyses based on fitting a mixed linear model may not be optimum, especially for populations undergoing selection and nonrandom mating. Several approaches are discussed for the genetic analysis of data when the major genotypes are not known.

Advances in statistical methods to map quantitative trait loci in outbred populations

Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLs on a chromosome as an unknown.